Arizona State University Department of Physics PHY 132 –.docx

Arizona State University
Department of Physics
PHY 132 – University Physics Lab II – Section #: 30531
TA – Alan Moran
Lab 3
Capacitors
Submitted by:
Charles Foxworthy
6 April 2015
Abstract: This lab focuses on experimenting with parallel plate
capacitors. The first part of the
lab uses a test set up that allows the user to vary the surface
area and the separation of plates in
a capacitor. When the plate was its smallest (100mm2) and
furthest apart (10.0mm) it yielded its
lowest capacitance (0.04 pF). The first experiment demonstrated

that insertion of a dielectric
increases capacitance, using a constant sized capacitor of
250mm2, with a constant separation of
7mm a dielectric was inserted and capacitance increase to 5
times its original value to 0.79pF.
Then a new dielectric was inserted and slow removed and the
capacitance decreased as
expected.
Part 2 and 3 of the experiment focused on parallel and series
circuits with only switches and
capacitors. The first experiment was parallel capacitors and it
demonstrated that charge was
conserved and that it was additive when capacitors are parallel.
Part 3 had a capacitor in
parallel with other capacitors in series. It demonstrated that
charge is constant among
capacitors that are in series, and reiterated that charge is
additive when capacitors are parallel.
Both experiments had an initial charge of 0.9 and that charge
stayed constant throughout the
experiments.
When it was all done the theoretical values matched the
experimental values and all the
experiments were successful, and the hypotheses were proven.
Objectives: 2
Procedure:
........................................................................................ .......
....................................... 3
Experimental Data:
...............................................................................................
........................ 15
Results:
...............................................................................................

........................................... 17
Discussion and Analysis:
...............................................................................................
............... 19
Conclusion:
...............................................................................................
.................................... 20

1
Objective:
The purpose of this experiment is to explore capacitors. The
first experiment focuses on air gap
capacitors, and exploring changes based on a bigger gap, and/or
smaller plates. The second part
to that experiment adds a nonconductive material to see the
effect on the capacitance. The third
part of the experiment adds a nonconductive material and
slowly removes it from the capacitor
and shows its effects. The second experiment uses capacitors in
parallel and charges one then
removes the power source and charges the rest of the capacitors
using only the initial charge. The
last experiment is similar to the second experiment but this time
the capacitors being charged are
in parallel, and essentially create a voltage divider.

2
Procedure:
Part 1:
Part 1 of this experiment consists of three subsets, using
similar methods and techniques.
They are all performed using the capacitors lab on PhET

Interactive simulations website. First
check all boxes except electric field detector. Then set the
separation to 7.0mm and the plate area
to 250.2 mm2. The program doesn’t allow the user to select
250.0 mm2 for plate area. This was
the closest achievable value to the desired value. Then place the
red lead on the positive plate
and the black lead on the negative plate and adjust the voltage
to 1.02V again the closest to one
volt that can be achieved. Then take note of the capacitance
“C1,” plate charge “Q1,” and stored
energy “E1.” After this change the separation to minimum and
call the values obtained subscript
2. Then the separation to max and call the values subscript 3.
Then vary plate area to minimum
and call those subscript 4. And finally change the plate area to
max and call those subscript 5.
These will be shown in figures 1 through 5 below. This leads to
the addition of a dielectric
element. Go to the dielectric tab and use a custom dielectric
with a dielectric constant 5 and place
it in the capacitor with a 0.0 mm offset. Next set the separation
to 7.0 mm and the plate area to
248.0 mm2. Closet achievable. Again use the multimeter to
measure the value of the voltage
being applied to the capacitor and set that value to 1.02V. Now
record all the same values and
call them subscript 6, reference figure 6. Now select the
dielectric as paper which has a known
constant of 3.5 and note the same values and call them subscript
7. Then set the offset to 3.5 mm
and note the same values as subscript 8. Set offset to 7.0 mm,
10.0 mm, and 14.0 mm and call
those values subscript 9, 10, and 11 respectively. Reference
figures 7 through 11. All calculated
values will have a subscript c following the number.

��0 = ��0
��
�� = ��0
��
�� ;�� =
��
∆�� ; �� =
1
2��∆��
2
3
Figure 1
Figure 2
4
Figure 3

Figure 4
5
Figure 5
Figure 6
6
Figure 7
Figure 8
7
Figure 9
Figure 10

8
Figure 11
Part 2:
This experiment studies capacitors in parallel. Build a circuit
as in figure 12 using the
PhET application call circuit construction. V0=9 V, C1=0.1 F,
C2=0.1 F, and C3=0.05 F. Ensure
switch 2 and 3 are open and close switch 1. Capacitor 1 should
charge to 9v, then open switch 1
and only close switch 2, and measure the voltage across
capacitor 2. Then open switch 2 and
close switch 3 and measure the voltage across capacitor 3. Then
close switch 2, all voltages
should equalize, and measure any capacitors voltage.
9
Figure 12
Figure 13
10

Figure 14
Figure 15
11
Part 3:
This explores capacitors in series. Create a circuit as shown in
figure 16 and set the
battery voltage to 9V, C1 to 0.1F, C2 to 0.05F, C3 to 0.1F and
C4 to 0.2F. Then ensure switch 2
is open and close switch 1. Then open switch 1 and close switch
2. Lastly measure the voltage
across all capacitors. As in figures 17 to 20.
Figure 16
12
Figure 17
Figure 18

13
Figure 19
Figure 20
14
Experimental Data:
Part 1:
C1 0.32x10-12 F C1c 0.32x10-12 F C5 0.35x10-12 F C5c
0.35x10-12 F C9 0.08x10-11 F C9c 0.08x10-11 F
Q1 0.32x10-12 C Q1c 0.32x10-12 C Q5 0.36x10-12 C Q5c
0.36x10-12 C Q9 0.08x10-11 C Q9c 0.08x10-11 C
E1 0.16x10-12 J E1c 0.16x10-12 J E5 0.18x10-12 J E5c
0.18x10-12 J E9 0.38x10-12 J E9c 0.38x10-12 J
C2 0.44x10-12 F C2c 0.44x10-12 F C6 0.16x10-11 F C6c
0.16x10-11 F C10 0.06x10-11 F C10c 0.06x10-11 F

Q2 0.44x10-12 C Q2c 0.44x10-12 C Q6 0.16x10-11 C Q6c
0.16x10-11 C Q10 0.06x10-11 C Q10c 0.06x10-11 C
E2 0.22x10-12 J E2c 0.22x10-12 J E6 0.79x10-12 J E6c
0.79x10-12 J E10 0.30x10-12 J E10c 0.30x10-12 J
C3 0.22x10-12 F C3c 0.22x10-12 F C7 0.11x10-11 F C7c
0.11x10-11 F C11 0.04x10-11 F C11c 0.04x10-11 F
Q3 0.22x10-12 C Q3c 0.22x10-12 C Q7 0.11x10-11 C Q7c
0.11x10-11 C Q11 0.04x10-11 C Q11c 0.04x10-11 C
E3 0.11x10-12 J E3c 0.11x10-12 J E7 0.55x10-12 J E7c
0.55x10-12 J E11 0.20x10-12 J E11c 0.20x10-12 J
C4 0.09x10-12 F C4c 0.09x10-12 F C8 0.09x10-11 F C8c
0.09x10-11 F d 7.0 mm A 250.2 mm2
Q4 0.09x10-12 C Q4c 0.09x10-12 C Q8 0.09x10-11 C Q8c
0.09x10-11 C dmax 10.0 mm Amax 400.0 mm2
E4 0.04x10-12 J E4c 0.04x10-12 J E8 0.46x10-12 J E8c
0.46x10-12 J dmin 5.0 mm Amin 100.0 mm2
Part 2
SW1 closed; SW2 open, SW3 open; C1=9V, C2=0V, C3=0V
SW1 open; SW2 closed, SW3 open; C1=4.5V, C2=4.5V, C3=0V
SW1 open; SW2 open, SW3 closed; C1=4.5V, C2=3V, C3=3V
15

SW1 open; SW2 closed, SW3 closed; C1=3.6V, C2=3.6V,
C3=3.6V
Part 3:
SW1 closed; SW2 open; C1=9V, C2=0V, C3=0V, C4=0V
SW1 open; SW2 closed; C1=7V, C2=4V, C3=2V, C4=1V

16
Results:
All equations were shown in the procedures section so that the
content would flow more
smoothly into the experimental results section. Also since there
are an enormous amount of
calculations it has been limited to one example per concept, for
part 1.
Part 1:
Applies to subscript 1 to 5 calculations:
��1 = ��0
��0,��,��
��0,��,��

= 8.854 × 10−12
2.504 × 10−4
0.007 = 3.16 × 10
−13 ≈ 0.32 × 10−12��
��1 =
��1
∆�� =
3.16 × 10−13
1.02 = 3.16 × 10
−13 ≈ 0.32 × 10−12��
��1 =
1
2��∆��
2 =
1
2 × 0.32 × 10
−12 × (1.02)2 = 1.58 × 10−13 ≈ 0.16 × 10−12��
Applies to subscript 6 calculations:
��6 = ��0��
��
�� = 8.854 × 10
−12(5)
2.48 × 10−4
0.007 = 1.57 × 10
−12 ≈ 0.16 × 10−11��

��0 =
��0
∆�� =
1.57 × 10−12
1.02 = 1.57 × 10
−12 ≈ 0.16 × 10−11��
��6 =
1
2��∆��
2 =
1
2 × 1.57 × 10
−12 × (1.02)2 = 7.85 × 10−13 ≈ 0.79 × 10−12��
Applies to subscript 7 to 11 calculations:
��8 = ��0(1 − ��)
√��
�� + ��0��
��
��
= 8.854 × 10−12(1 − 3.5)
√2.48 × 10−4
0.007 0.0035 + 8.854
× 10−12(3.5)
2.48 × 10−4

0.007 = 9.23 × 10
.13 ≈ 0.09 × 10−11��
��8 =
��0
∆�� =
9.23 × 10.13
1.02 = 9.23 × 10
.13 ≈ 0.09 × 10−11��
��8 =
1
2��∆��
2 =
1
2 × 0.09 × 10
−11 × (1.02)2 = 4.61 × 10−13 ≈ 0.46 × 10−12��
Part 2:
�� = ��1��1 = 0.1 × 9 = 0.9, ��ℎ��
��ℎ�� ℎ��
�� 1
��,��2,�� =
��
��
=
. 9

. 2 = 4.5��
��1,2 = ��2��,��2,�� = 0.1 ×
4.5 = 0.45 ��ℎ�� ℎ�� ℎ��
�� 1 �� 2
��,��3,�� =
��2
��
=
. 45
. 15 = 3.0��
��3 = ��3��,��3,�� = 0.05 × 3.0
= 0.15 ��ℎ�� ℎ�� ℎ��
��3
17
��2 = ��2��,��3,�� = 0.1 × 3.0
= 0.3 ��ℎ�� ℎ�� ℎ��
��2��
�� = ��1 + ��2 + ��3 = .9 ��ℎ�� ℎ��
��
When both SW2 and SW3 are closed the following applies.
��0 =
��
��

=
. 9
0.1 + 0.1 + 0.05
= 3.6
Part 3:
�� = ��1��1 = 0.1 × 9 = 0.9, ��ℎ��
��ℎ�� ℎ��
�� 1
��0 =
��
��1 + ��
=
. 9
��1 + �
1
��2
+ 1��3
+ 1��4
�
−1 = 7��
��1 = 7, �� ℎ��
�� 1
�� = ��1 → �� = �� = 0.2

��2 =
��2
��2
; ��3 =
��3
��3
; ��4 =
��4
��4
2��2 = ��3 ; 4��2 = ��4 ; ��2 = 2��3 ;��2 = 4��4 ;
��1 = ��2 + ��3 + ��4 = 7��4
��4 = 1 �� → ��3 = 2 �� → ��2 = 4 �� ; ��2 = .2 →
��3 = .2 → ��4 = .2 → ��1 = .7
�� = ��1 + ��2,3,4 = .9, ��ℎ��
��
18

Discussion and Analysis:
Part 1:
This first experiment gave the expected results. There was no
error. This can be seen
viewing the table for part 1 in the experimental data section.
This is probably due to the fact that
the same equations are used to calculate the experimental values
as are used to calculate the
theoretical values. The only time error could be induced is
through rounding, but this was done
as little as possible. The first experiment had a lot of
calculations and to save time they were
mostly done on the calculator using the same equations and
methods as outlined in the results
section. This section was a study on the construction of a
parallel plate capacitor, the user varied
the surface area of the plates and their separation. Then inserted
a dielectric. The capacitor with a
dielectric yielded a higher capacitance then the capacitor with
only an air gap. This experiment
also touched on capacitors with only a partial dielectric which
is also the same as if the plates
were offset slightly. It was also noticed that as the surface area
increased and distance decreased
that capacitance increased. And as the surface area decreased
and distance increased that
capacitance decreased and the same held true with a dielectric
in place.
Part 2:
This experiment was also yielded the expected results and it
can be seen because there

was no error and all the values matched the theoretical values in
the results section. Again this is
due to the fact that the algorithms used to calculate the
experimental values in the program are
the same theoretical formulas used to compute the theoretical
values. This experiment focused on
the conservation of charge among parallel capacitors. It was
shown that charges in parallel across
capacitors are additive. This was shown when the Q-values for
each capacitor was added
together and the sum was Qinitial.
Part 3:
This experiment was also yielded the expected results and it
can be seen because there
was no error and all the values matched the theoretical values in
the results section. Again this is
due to the fact that the algorithms used to calculate the
experimental values in the program are
the same theoretical formulas used to compute the theoretical
values. This experiment focused on
the conservation of charge among series capacitors. It was
shown that charges in series across
capacitors are constant. This was proven at the end when it was
shown that all the series
capacitor’s Q-value was the same and that when it was added to
the charge of Q1 it was equal to
Qinitial.

19
Conclusion:
The stated objectives were met, all values were calculated
within an acceptable amount of error.
Since the deviation from theoretical to practical values didn’t
differ the lab was successful. This
lab teaches an abstract applications of parallel plate capacitance
with and without a dielectric,
since none of these were really performed practically only
computer simulation which uses the
theoretic equations in its algorithm to predict expected values.
The second and third experiments
were so similar it was hardly practical to break them up, they
demonstrated conservation of
charge and that charge is additive in a parallel bank of
capacitors and constant in a series bank of
capacitors.
20
Objective:Procedure:Experimental Data:Results:Discussion and
Analysis:Conclusion:
4/21/16, 3:00 AMTake Test: Prelab: Magnetic Fields
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Take Test: Prelab: Magnetic Fields
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Instructions
Multiple Attempts This test allows 3 attempts. This is attempt
number 1.
Force Completion This test can be saved and resumed later.
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Calculate the force between two wires each 0.96 m long,
carrying 27 A current in
opposite directions and separated by 2.8 mm, ignoring Earth’s
magnetic field. Express
the answer with three decimal places.
QUESTION 1
5 points Save AnswerSave Answer
A solenoid is wound with N=327 turns on a form D=4 cm in
diameter and L=48 cm long.
The windings carry a current in the sense that is shown. The
current produces a
magnetic field, of magnitude 5.5 mT, at the center of the
solenoid. What is the value of
the current in the solenoid windings? Express the answer with
two decimal places. ( µ0 =

1.26×10-6 T·m/A).
QUESTION 2
QUESTION 3
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Answers to save all answers.
An electron enters a magnetic field of 0.42 T with a velocity
perpendicular to the direction
of the field. What is the value f ×10-10, where f is the
frequency (in Hz) at which the
electron traverse a circular path? (The mass of an electron is
9.1×10-31 kg and the
charge of an electron is 1.6×10-19 C). Express the answer with
two decimal places.

QUESTION 3
Lab Experiment (procedure)
Hi. Today we will do lab experiment magnetic field. Or it's
called, as
well, tangent galvanometer. The objectives of the lab are to
verify the
vector nature of magnetic fields, verify that the field at the
center of a
current carrying loop is normal to the loop and directed in
accordance
with the Right Hand Rule, to investigate the relationship
between the
magnetic field and the number of turns in the loop-- in other
words,
investigate B as a function of n. n is the number of the loops in
a
current carrying loop. Investigate the relationship between the
magnetic field and the value of the current inside the current [?
carrying
?] coil. Investigate B versus I. And to determine the strength of
the
horizontal component of Earth's magnetic field.
We will use virtual apparatus from the KET website. Please
visit this
website. You have the link in your lab manual. Login using your
username and password. Click Log In.
And go to Labs tab. And find Tangent Galvanometer It's called
The
Tangent Galvanometer. Here is tangent galvanometer. Run the

experiment. Before starting the experiment, please get practice
with
the virtual equipment. Move your mouse over each part of the
apparatus to get some practice.
The apparatus is viewed from two perspectives, overhead and
oblique.
By clicking on this button, you are changing the perspectives.
Now it's
overhead perspective. And this will be oblique perspective.
In the overhead view, you see two vectors. You see this one is
the Earth
magnet. It shows the Earth magnetic field vector. This colored
magnetic
field vector. And then you turn on the apparatus, there will be
another
vector, shorter, which is the magnetic field of the loop. And that
magnetic field of the loop is produced by the current carrying
wires in
the loop.
Neither vector automatically points in the appropriate direction.
As you
can see, I can rotate freely any of these vectors. Good. Rather,
these
vectors can be rotated as needed by dragging the points of the
arrows.
Just dragging you can any of these arrows in the corresponding
direction.
Then the apparatus can be rotated in overhead view by dragging
the
handle. Clicking on handle and dragging, you can rotate the
entire
apparatus. And there is the power supply. You can turn on and

off the
power supply.
On this part, the current will be fixed for overhead view. The
current is
fixed at 3 amperes, and the number of turns in the coil is n. n
equals 4.
Oblique view does not rotate. In the oblique view frame with a
pair of
vertical supports, you have two vertical supports. They can
support
from 1 to 5 loops of insulated wires. You can add the number of
loops
here. You see add the turn, and remove the turn. The minimum
number
is 1. The maximum number of turns of the loops is 5.
A horizontal platform holds a sheet of paper, polar paper, for
measuring
angles in a horizontal plane. At the center, you see there is a
compass.
Here is the compass. And we have polar graph paper to measure
the
angle in horizontal plane.
The compass at the bottom right provides a close up of the real
compass. Here is another compass from which you will take the
readings for the angle. Remember that end of the compass-- red
end
of the compass-- is its north end, seeking its north pole. Notice
how
the deflection of the compass is affected by the power switch.
When

you turn on the power switch and turn on the current, you see
that the
compass needle is deflected. Turning on and off, you are
deflecting the
compass needle.
And besides that, if you add and remove the-- I am removing
now the
loops. You can see again, how it's affecting on the compass.
When the
power is on, the current flows the loop and magnetic field, due
to the
current, is produced inside the loop. We expect it to be normal
to the
plane of the loop.
If the Earth's magnetic field were non-existent, the compass
needle
would point in the direction of perpendicular to the loop's
plane.
However, under the influence of two magnetic fields, Earth's
magnetic
field and the magnetic field of the loop, the compass takes the
direction of their resultant field B Net.
Part 1, direction of the magnetic field at the center of current
carrying
loop. You will use the overhead view for this part of the
experiment.
Select the overhead view. To verify the magnetic field of the
loop loops,
B loop at the center of loop is normal to the plane of the loop.
The goal
is to verify that the magnetic field will be perpendicular to the
plane of
the loop when you have current through the loop.

In this view, the number of loops, N, is fixed and the current, I,
is fixed
to 3 amperes. You cannot change the current through the loop.
It's
fixed at 3 amperes.
Begin with the power turned off. Now power is off. Drag the
handle to
arrange the frame so that's 0 degrees. 0 degrees. End of the loop
is
pointing north, the direction of the red and of the compass. My
0 must
be in the same direction as the compass red end. Adjust as
accurately
as you can. I am assuming that now it is adjusted well.
Drag the end of the vector B Earth. And compass-- remember,
there is
no current through the loop, and compass is showing the
direction of
Earth's magnetic field. That's why drag this blue vector, Earth's
magnetic field vector, and align with the compass needle. In
this case,
to the left. And that will be the direction of magnetic north
direction.
The Earth's magnetic field shows magnetic north direction.
Now with the current off, the needle points in the same
direction as B
Earth. And as you turn on the power supply, the needle will
deflect
showing the direction of net magnetic field B net, which is the

vector
sum of the fields B Earth vector and B loop vector.
Now if you turn on the power, you will see the needle is
deflecting,
which shows the net magnetic field direction, which must be the
sum of
two vectors, Earth's magnetic field and loop magnetic field
vectors--
vectors of sum.
Now you can guess what will be the direction of the B magnetic
field of
the loop. If we can see there that it is perpendicular to the loop,
it could
be directed upward or downward. You will need to experiment a
bit. It
will involve switching the current on and off and the rotating
the
apparatus.
Rotate the apparatus and find the position where the needle
stays still
when the power is turned on. OK. The goal is find the position
when
you turn the power on the needle will stay still. OK. Let's try
now. Is still
needle is not still. Yes? I will rotate more. Let's try now.
Almost. Slightly.
We need to make some adjustment. I don't know, now, which.
Very
sensitive.
It looks like we are there. As you can see, I am turning on and
off the
power, but the needle is not deflecting. What does that mean?

That
means the magnetic field of the loop is then perpendicular,
which is
perpendicular to the plane of the loop. It must be directed to left
or
directed to right. Why? There is two cases.
Because the Earth's magnetic field is larger than the magnetic
field of
the loop, I am showing both possible cases. This will be the
first case,
for example. Earth's magnetic field is directed to the left as the
red
arrow is showing when the power is off. This is the direction of
Earth's
magnetic field.
When you turn on the power, still it stays in the same position.
That
means the magnetic field vector has the same or opposite
direction to
the Earth's magnetic field. And since the magnetic field of the
loop is
smaller-- you see the vector is shorter. This ground vector is
shorter
than the blue vector. That's why there are two possible ways of
orientation of B loop.
That is first one-- is this one. It's oriented, B loop, oriented to
the right.
And second one is when two vectors, they have the same
direction.
This, they are parallel. Both have the same direction. And the

second
case, when they are anti-parallel. But in these cases, the needle
will
stay still. It will not deflect.
You can see the drawing in your manual. The sum vector, in
both cases,
will have the same direction. The net net vector, B net, will
have the
same direction to the left in this case. But it will be just
smaller. The
vector net vector will be smaller, which will be the sum of these
anti-
parallel vectors. And in this case, the net vector becomes larger,
the
sum of these two vectors. But still it will be directed to the left
in this
configuration.
Hopefully you have noticed how the loop is at the right angle to
the
Earth's magnetic field. The loop Earth's magnetic field is
perpendicular
to the loop. The needle does not move when the current is
turned on
and off. So the loop's field is perpendicular to the plane of the
loop the
two possible directions 180 degrees apart.
But only one of them can match our Right Hand Rule. To find
out the
direction of B loop, now align-- again, the Earth's magnetic
field when
the power is off. Align Earth's magnetic field with the compass.
And
align the plane of the loop in such a way that the compass will

be in the
plane of the loop.
Now my compass is in the plane of the loop. This is the plane of
the
loop. And Earth's magnetic field also is directed in that plane.
In this
case, if we turn on the power on and off, there are two
possibilities.
Magnetic field vector-- first it could be straight down on this
diagram,
you see, or straight up. It depends on which way will deflect the
compass needle.
We will figure out. If the compass needle will deflect and stay
in the
second quadrant, that means my magnetic field is straight up. If
the
compass needle will deflect and stay in the third quadrant, that
means
my magnetic field is straight down. From the experiment, now,
we will
figure out. OK.
I turn on the power. And you see the compass is in the second
quadrant,
about 10, 20, 30-- roughly 35, 40 degrees. And that means
magnetic
field of the loop is straight up. And this vector, you can rotate
it. It is
arbitrary initially. You can rotate and put it straight up. This is
the real
direction of magnetic field of the loop. And when the Earth's

magnetic
field is in this direction and you turn on the power, the compass
will
show the net magnetic field, which is the sum of these two
vectors.
In your lab report, show the vector addition of B Earth with
each of the
two possible B loop. This is the first possible B loop. And this
will be
the second possible B loop. But from the experiment, you
already found
out this is the right one. But in your lab report, you have to
show what
will be the net magnetic field, if the B loop is straight down or
straight
up.
What is the current direction in the loop? Is the current flowing
into the
screen at 180 degrees and out at 0 degrees or into the screen at
0
degrees and out at 180 degrees? You have to show which way is
the
current going into the screen at this point and out of the screen
at this
point. Otherwise, reverse it. Using the Right Hand Rules, you
can easily
figure it out.
Part 2, the magnetic field at the center of current loop. You will
investigate the relationship between the strength of magnetic
field at
the center of loop, how it depends on the number, n, of the
loops and
how it depends on the current through the loop. A question

three from
your writeup shows that magnetic field at the center of the loop
is
directly proportional to the tangent theta. Theta is the angle
between
Earth's magnetic field and the net magnetic field.
Therefore, you should find that plots of tangent theta versus n
or
tangent theta versus current, I, both should yield a straight line
through
the origin as you can see from my question four. You will use
the
oblique view this time. Change to the oblique view. And
investigate this
relationship to test equation number one.
To read the compass as accurately as possible, use zooming
with right-
click. You can zoom in many. To test the effect of the number
of turns
and on the strength of the loops [INAUDIBLE], measure of that
angle of
deflection with respect to north of the compass for 1 to 5 loops
by
keeping the current of the constant value I equals 3 amperes.
Now let's now make the number of loops 1. Remove the loop.
You have
1 loop now. Turn on the power. Adjust the current accurately to
3
amps. You can rotate this knob to adjust the current. You can
click on
it and move forward and make fine adjustments when the clicker
is far
from the knob. OK. I get 3 amps. You have 1 loop and you have

3
amps.
And now you need to read what is the compass reading. Just
zoom in.
This will be about-- this is north, 0 position. 10, 20, maybe 21,
22
degrees. For 1 loop you have 22 degrees.
Now add the number of loops, 2 loops, and read again what will
be the
reading. 1, 2, 3, 37-- about 37 degrees. 10, 20, 30, 37, 38
degrees.
Add turn. You'll see now it is about 40 and so on. Read all this
from the
compass when you have 1, 2, 3, 4, 5, turns and make a graph in
Logger
Pro.
In Logger Pro, just make a graph of tangent theta versus n first.
First
graph, make theta versus n. And on the same graph, put a graph
tangent theta versus n on the same graph using right y-axis
feature.
And on the toolbar, select Options. Graph Options. Axis
Options. Mark
Right Y-axis. And now, you will have on the left and-- OK.
You have to enter data. And make graphs. On the left axis, will
show you
theta versus n. And on right access, will be tangent theta versus
n.
Are both graphs linear? Describe the graph tangent theta versus

n. Apply
linear field to the graph tangent theta versus n to find the slope
with
uncertainty. And assuming that the radius of the circular loop--
radius
equals 20 centimeters-- calculate the value of the B Earth. I call
B Earth,
N. When N, that means that was calculated from changing the
number
of loops. Calculate the field, B Earth, with the arrow.
To test the effect of a current through the loop on the strength
of the
loop's magnetic field, measure the angle deflection for currents
of 0 to
3.5 amperes in 0.5 amp increments keeping the number of the
loop
fixed at n equals 5. Show everything. Now, the second part, we
will
keep the number of the loop, n equals 5. The maximum of the
loop, n
equals 5. Turn off the power first. OK.
Now you have to make investigation. When your current will be
changed
from 0 to 3.5 amperes when the power is on you can adjust--
and with
the increment 0.5 amps. This will be my first [INAUDIBLE]
position, 0.5
ampere. I have a number of loop as n is 5. And just from the
compass,
you need to read the position of the needle. It's about 10, 17 or
18
degrees. And so on.
Now you can-- this was for the current 0.5 ampere. And then

you adjust
another value. For example, for two amps, you change the
current and
put 2 amps. And then read from the compass that angle 10,20,
30, 40,
53 maybe. 53 degrees. You can zoom in one more time to read
more
accurately if you want. OK.
Now again, get this data in Logger Pro. Plot both theta versus
current
and tangent theta versus current on the same graph using the
right y-
axis feature from graph options described above. Are both
graphs
linear? Describe the graph tangent theta versus current. Apply
linear
field to the graph tangent theta versus current and to find the
slope
with uncertainty and calculate the value of the B Earth from this
part, B
Earth I.
Read the arrow. Assuming again that's the radius of-- this is
diameter,
remember. That is diameter from here to here. That is diameter.
Radius
of the circular part from the center to the outer point is 20
centimeters.
Capture the average value B Earth equals from finding from 2
part of
this experiment. From B Earth N and plus B Earth I over 2.
Average

value from the two experiments. OK.
Part 3, strength of the horizontal component over Earth's
magnetic field.
According to the equation number 1, the field at the center of
the loop
is directly proportional to the product n multiply I, where n is
the
number of loops and I is current through the loop. Now you will
test
the complete equation by using E to calculate the horizontal
component of Earth's magnetic field, B Earth, and compare it
with the
value from part two.
You will do that as follows. Using the convenient point on the
line of
best fit from near the middle of your graph tangent theta versus
I, find
the value of the current. And by equation 1, calculate B loop.
For that
value of the current, you may use the value of the current when
tangent
theta equals 1. That will be more easy to make the calculation.
Assume the radius, r equals 20 centimeters for the circular loop.
And
calculate B loop. And you can use the value of the tangent and
calculate
B Earth, finally. Compute the horizontal components of B Earth,
magnetic field B Earth, using equation 2 from given value of
value
tangent theta and calculate value of B loop.
You can notice that when theta equals 45 degrees, tangent will
be equal

to 1. That means that 45 degrees B Earth equals to B loop.
That's why
it's easy to calculate-- find that current when tangent equals 1
and
plug that value of the current in the equation to calculate B loop
and
indirectly calculate the B Earth.
Compare your calculated value of Earth's magnetic field, B
Earth, with
the average value from part 2. You have to compare this new
calculated
value with the average value with the part 2. You have to show
in your
lab report how your experimental findings are supporting the
question
number 1 from your manual. How does the magnet field of coil
depend
on the current in the coil? Thank you.
Page 1 of 5
Magnetic Fields – Tangent Galvanometer
Introduction and Theory:
Just like an electric field exists around electric charges, there
is a magnetic field surrounding a

permanent magnet and around moving electric charges. Since
electric current is a flow of charge, there
is a magnetic field around any current carrying wire. This
magnetic field can be detected by observing
the behavior of a compass needle in the presence of current
carrying elements. Like an electric field,
the magnetic field also is a vector quantity and has both a
magnitude and a direction. The direction of a
magnetic field at any point in space is the direction indicated by
the north pole of a small compass
needle placed at that point.
The magnetic field of the earth is thought to be caused by
convection currents in the outer core of
the earth working in concert with the rotation of the earth. The
field has a shape very similar to the field
produced by a bar magnet. Incidentally, the north magnetic pole
of the earth does not coincide with the
north geographic pole. In fact, the north magnetic pole is
located close to the Earth's South Pole (in
Antarctica), while the south magnetic pole is located close to
the Earth's North Pole (in Canada).
For a loop of wire consisting of N turns wound close together
to form a flat coil with a single
radius R, the magnetic field resembles the pattern of a short bar

magnet, and its magnitude at the center
of the coil according the Biot-Savart law is
� = � ��
(1)
where �� is the permeability of free space (4π × 10-7 T·m/A)
and I is the current in the coil. If the
current is expressed in amperes (A), and the radius in meters
(m), the unit of magnetic field strength is
Tesla (T). Note that this field vector is parallel to the axis of
the coil. In many situations the magnetic
field has a value considerably less than one Tesla. For example,
the strength of the magnetic field near
the earth’s surface is approximately 10
-4
T. The more convenient unit of magnetic field strength is a
gauss (1 G = 10
-4
T).
The instrument used in this experiment is a tangent
galvanometer that consists of 1-5 turns of wire
oriented in a vertical plane that produce a horizontal magnetic
field. The direction of the magnetic field
at the center of the wire loop can be determined with the help of
the right-hand-rule. If the curled

fingers of the right hand are pointed in the direction of the
current the thumb, placed at the center of the
loop, indicates the direction of the magnetic field. The magnetic
field of the coil is parallel to the coil
axis.
Figure 1 shows the vector sum Bnet of the Earth's magnetic
field (BEarth) and the magnetic field due
to the current (BLoop) for the case when the coils of the
galvanometer are oriented so that the Earth's
magnetic field (BEarth) is parallel to the plane of the coils. The
magnetic field due to the current (BLoop)
being perpendicular to the coils plane will then be perpendicular
to the Earth's field. Therefore the
relationship between the horizontal component of the earth's
magnetic field BEarth and the magnetic
field of the coil BLoop can be expressed as
tanθ = BLoop / BEarth (2)
where θ is the angle between BEarth and Bnet. From equations
(1) and (2) we get
�� = � ��
/�� (3)
This can be rewritten as

of 5
tanθ = M·N·I (4)
where � = ��
/�� = constant.
The horizontal component of the earth's field can now be found
by measuring the field due to the
coils and the direction of the net magnetic field relative
to the direction of the earth's field. The angle θ can be
found by using a compass. If the compass is first (with
no current: I = 0)
aligned with the magnetic field BEarth
and then current is supplied to the coils, the compass
needle will undergo an angular deflection θ. Because of
the relationship given by equation (4) this equipment is
called a tangent galvanometer. Note that for θ = 45
o
,
tanθ = 1 and BLoop = BEarth.
Objectives:

To verify:
• the vector nature of magnetic fields;
• that the field at the center of a current loop is normal to the
loop and directed in accordance with
right hand rule;
To investigate the relationship between the magnetic field and:
• the number of turns - B(N);
• the value of the current - B(I) inside a current carrying coil.
To determine the strength of the horizontal component of the
Earth’s magnetic field.
Equipment:
Virtual Tangent Galvanometer with two views: Overhead and
Oblique. Virtual DC power supply,
ammeter and compass mounted in the center from the Tangent
Galvanometer Apparatus lab (Magnetic
Fields - The Tangent Galvanometer on the web site
http://virtuallabs.ket.org/physics/); Logger Pro
(LP) software. LP is available at MyASU > My Apps.
Procedure:

Before starting the experiment please get practice with the
virtual equipment!
Log in to Virtual Physics Labs using your KET ID and
password. Load the virtual “Tangent
Galvanometer Apparatus Lab” and familiarize yourself with the
setup.
The apparatus is viewed from two perspectives: Overhead
(Figure 2a), and Oblique (Figure 2b).
You will switch between views using the buttons at the top left
edge of the screens. Take some time to
become familiar with each view.
In the Overhead view shown in Figure 2a, you see two vector
arrows. One represents the
horizontal component of the Earth’s magnetic field. The other
represents the magnetic field produced
by the current-carrying wire loops. Neither vector automatically
points in the appropriate direction.
Rather these vectors can be rotated as needed by dragging the
points of the arrows. The entire apparatus
can be rotated in the overhead view by dragging the Handle.
θ
BEarth Bnet
Figure 1. Vector sum of the magnetic fields.

BLoop
Page 3 of 5
The coil unit has a compass mounted in the middle. With no
current applied to the coil, the
compass responds only to the horizontal component of the
earth’s magnetic field.
Figure 2a. View 1: Overhead Figure 2b. View 2: Oblique
The Oblique view shown in Figure 2b does not rotate. Explore
the following in the Oblique view. A
frame with a pair of vertical supports provides two nails which
hold 1 to 5 circular loops of insulated
wire.
A horizontal platform holds a sheet of polar graph paper for
measuring angles in the horizontal
plane. The compass at the bottom right provides a close - up of
the real compass. You will take
compass reading there. Remember that the red end of the
compass is its north end (seeking Earth's

North Pole). Notice how the deflection of the compass is
affected by the power switch, the voltage
adjust knob, and the number of loops of wire.
When the power is on and current flows through the loop, a
magnetic field due to the current is
produced inside the loop. We expect it to be normal to the plane
of the loop. If the Earth’s magnetic
field were nonexistent the compass needle would point in the
direction perpendicular to the loop’s
plane. However, under the influence of the two magnetic fields,
the compass takes the direction of their
resultant field Bnet.
The two views are completely independent. You will only work
with one view while performing a
given part of the lab. You will use the overhead view for part 1
and the oblique view in part 2 and part
3 of the lab.
Part 1. The direction of the magnetic field at the center of a
current loop
You will use the overhead view for this part of experiment to
verify that the magnetic field of the
current loop’s BLoop at the center of a loop is normal to the

plane of the loop. In this view the number of
loops N is fixed at 4 and the current I is fixed at 3.0 A when the
power is turned on. Begin with the
power turned off. Drag the handle to orient the frame so that the
0° end of the loop is pointing north -
the direction of the red end of the compass. Drag the end of the
vector BEarth to point in the magnetic
north direction as shown in Figure 3a.
direction as the BEarth and as you turn on
the power supply the needle will deflect showing the direction
of the net magnetic field Bnet which is
vector sum of the fields BEarth and BLoop.
You might want to arrange the BLoop vector to point in the
direction you think is correct.
Page 4 of 5
You will need to experiment a bit. It will involve switching the
current on and off and rotating the
apparatus. Rotate the apparatus and find the position(s) where
the needle stays still when the power is
turned on and off.

You should have noticed that there are two different
orientations of the loop that result in no
change in the needle’s direction when the current is turned on
and off (this is because the magnitude of
the BEarth is greater than BLoop as you can see from Overhead
view). At these two orientations of the
loop the direction of the total magnetic field Bnet (and therefore
the direction of the needle) is
unchanged (only the magnitude is changed) when the current is
turned on and off. In other words in
these orientations of the loop the magnetic field vectors BEarth
and BLoop are parallel or antiparallel (see
Figure 4a and Figure 4b).
Bnet
BLoop BEarth
BEarth
BLoop Bnet
Figure 4a. Figure 4b.

Hopefully, you have noticed that as the loop is at right angles
to the Earth’s field the needle does
not move when the current is turned on and off. So the loop’s
field is perpendicular to the plane of the
loop with two possible directions - 180° apart. But only one of
them can match our right hand rule.
Align again the direction of the vector BEarth with compass
needle (to North) as in Figure 3a. You have
confirmed that the loop’s field BLoop is perpendicular to the
loop - up (East) or down (West). You also
observed that with the current on, the compass always points in
the direction of Bnet - about 37° north of
east. Because Bnet is in the second quadrant so it must have a
north and an east component. BEarth
supplies the northward component, so BLoop must be to the east
as in Figure 3b.
In your lab report show the vector addition of BEarth with each
of the two possible BLoop. What is
the current direction? Is the current flowing into the screen at
180° (and out at 0°) or into the screen at
0° (and out at 180°)? Apply the right hand rule to figure out the
current direction.
Part 2. The magnetic field at the center of a current loop

You will investigate the relationship between the strength of
the magnetic field at the center of
loop and: a) the number N of loops; b) the current I through
the loop.
Equation (3) shows that the field BLoop at the center of the
loop is directly proportional to the
tangent of θ (the Earth’s field remaining constant). Therefore,
you should find that the plots of tanθ vs.
Figure 3a.
Figure 3b.
E
N
Page 5 of 5
N or tanθ vs. I both should yield a straight line through the
origin (equation (4)). You will use the
oblique view this time and investigate these relationships to test
equation (1). To read the compass as
accurately as possible use zooming with right-click on the

apparatus and select “Zoom In” from the
menu. You can then drag the apparatus around as needed.
To test the effect of the number of turns N on the strength of
the loop’s field BLoop, measure the
angle of deflection (with respect to north) of the compass for 1
to 5 loops by keeping the current at
constant value I = 3 A. Enter your data in Logger Pro and plot
both θ vs. N and tanθ vs. N on the same
graph using “Right Y-Axis” feature: on toolbar select Options >
Graph Options > Axes Options > mark
Right Y-Axis (be sure the preferences in LP for angles are set in
degrees: select File > Settings for
startup > Degrees). Are both graphs linear? Describe the graph
tanθ vs.N. Apply linear fit to the graph
tanθ vs. N to find the slope with uncertainty and assuming that
the radius of the circular loop R=20 cm,
calculate the value of BEarth,N with the error.
To test the effect of the current through the loop on the
strength of the loop’s magnetic field,
measure the angle of deflection for currents of 0 to 3.5 A in 0.5
A increments keeping the number of the
loops fixed at N = 5. In Logger Pro plot both θ vs. I and tanθ vs.
I on the same graph using “Right Y-

Axis” feature from Graph Options described above. Are both
graphs linear? Describe the graph tanθ
vs. I. Apply linear fit to the graph tanθ vs. I to find the slope
with uncertainty and calculate the value of
BEarth, I with the error assuming R=20 cm.
Compute the average value BEarth = (BEarth,N + BEarth, I)/2
with the error.
Part 3. The strength of the horizontal component of the Earth’s
magnetic field
According to equation (1) the field at the center of the loop is
directly proportional to the product
N·I. Now you will test the complete equation by using it to
calculate the horizontal component of the
Earth’s magnetic field BEarth and compare it with the value
from part 2.
You will do that as follows.
Using a convenient point on the line of best fit from near the
middle of your graph tanθ vs. I find
the value of the current and by equation (1) calculate BLoop for
that value of the current (hint: do your
calculation for the current when tanθ = 1). Assume that the
radius R=20 cm for circular loop.

Compute the horizontal component of Earth’s magnetic field
BEarth using equation (2) for given
value of tanθ and calculated value of BLoop (notice if tanθ = 1,
then BEarth = BLoop). Compare your
calculated value of the earth’s magnetic field Bearth with the
average value from part 2.
Final conclusion:
Do your experimental findings support equation (1)? How does
the magnetic field of a coil depend
on the current in the coil?
* Include answers to all questions in lab report
Tangent Galvanometer - Lab Report Check List
current loop
· Show the vector addition of BEarth with each of the two
possible BLoop.
· Answer on the questions.
· Measure the angle of deflection (with respect to north) of the

compass for 1 to 5 loops by keeping the current at constant
value I = 3 A.
· Plot two graphs: θ vs. N and tanθ vs. N on the same graph.
· Describe the graphs.
· Using the slope of the graph tanθ vs. N calculate BEarth,N
with the error.
· Measure the angle of deflection for currents of 0 to 3.5 A in
0.5 A increments keeping the number of the loops fixed at N =
5.
· Pro plot both θ vs. I and tanθ vs. I on the same graph.
· Describe the graphs.
· Using the slope of the graph tanθ vs. I calculate BEarth,I with
the error.
· Compute the average value BEarth = (BEarth,N + BEarth, I)/2
with the error.
magnetic field
· For given value of tanθ =1 calculated value of BLoop, and
then compute the horizontal component of Earth’s magnetic
field BEarth using equation (2).
Magnetic Fields – Tangent Galvanometer
Introduction and Theory:
Just like an electric field exists around electric charges,
there is a magnetic field surrounding a permanent magnet and
around moving electric charges. Since electric current is a flow
of charge, there is a magnetic field around any current carrying
wire. This magnetic field can be detected by observing the
behavior of a compass needle in the presence of current
carrying elements. Like an electric field, the magnetic field also
is a vector quantity and has both a magnitude and a direction.

The direction of a magnetic field at any point in space is the
direction indicated by the north pole of a small compass needle
placed at that point.
The magnetic field of the earth is thought to be caused by
convection currents in the outer core of the earth working in
concert with the rotation of the earth. The field has a shape very
similar to the field produced by a bar magnet. Incidentally, the
north magnetic pole of the earth does not coincide with the
north geographic pole. In fact, the north magnetic pole is
located close to the Earth's South Pole (in Antarctica), while the
south magnetic pole is located close to the Earth's North Pole
(in Canada).
For a loop of wire consisting of N turns wound close
together to form a flat coil with a single radius R, the magnetic
field resembles the pattern of a short bar magnet, and its
magnitude at the center of the coil according the Biot-Savart
law is
(1)
where is the permeability of free space (4π × 10-7 T·m/A) and I
is the current in the coil. If the current is expressed in amperes
(A), and the radius in meters (m), the unit of magnetic field
strength is Tesla (T). Note that this field vector is parallel to the
axis of the coil. In many situations the magnetic field has a
value considerably less than one Tesla. For example, the
strength of the magnetic field near the earth’s surface is
approximately 10-4 T. The more convenient unit of magnetic
field strength is a gauss (1 G = 10-4 T).
The instrument used in this experiment is a tangent
galvanometer that consists of 1-5 turns of wire oriented in a
vertical plane that produce a horizontal magnetic field. The
direction of the magnetic field at the center of the wire loop can
be determined with the help of the right-hand-rule. If the curled
fingers of the right hand are pointed in the direction of the
current the thumb, placed at the center of the loop, indicates the
direction of the magnetic field. The magnetic field of the coil is
parallel to the coil axis.

Figure 1 shows the vector sum Bnet of the Earth's
magnetic field (BEarth) and the magnetic field due to the
current (BLoop) for the case when the coils of the galvanometer
are oriented so that the Earth's magnetic field (BEarth) is
parallel to the plane of the coils. The magnetic field due to the
current (BLoop) being perpendicular to the coils plane will then
be perpendicular to the Earth's field. Therefore the relationship
between the horizontal component of the earth's magnetic field
BEarth and the magnetic field of the coil BLoop can be
expressed as
tanθ = BLoop / BEarth (2)
where θ is the angle between BEarth and Bnet. From equations
(1) and (2) we get
(3)
This can be rewritten as
tan = M·N·I (4)
where = constant.
The horizontal component of the earth's field can now be
found by measuring the field due to the coils and the direction
of the net magnetic field relative to the direction of the earth's
field. The angle θ can be found by using a compass. If the
compass is first (with no current: I = 0)aligned with the
magnetic field BEarth and then current is supplied to the coils,
the compass needle will undergo an angular deflection θ.
Because of the relationship given by equation (4) this
equipment is called a tangent galvanometer. Note that for θ =
45o, tanθ = 1 and BLoop = BEarth.
θ
BEarth
Bnet
Figure 1. Vector sum of the magnetic fields.
BLoop

Objectives:
To verify:
· the vector nature of magnetic fields;
· that the field at the center of a current loop is normal to the
loop and directed in accordance with right hand rule;
To investigate the relationship between the magnetic field and:
· the number of turns - B(N);
· the value of the current - B(I) inside a current carrying coil.
To determine the strength of the horizontal component of the
Earth’s magnetic field.
Equipment:
Virtual Tangent Galvanometer with two views: Overhead
and Oblique. Virtual DC power supply, ammeter and compass
mounted in the center from the Tangent Galvanometer
Apparatus lab (Magnetic Fields - The Tangent Galvanometer on
the web site http://virtuallabs.ket.org/physics/); Logger Pro
(LP) software. LP is available at MyASU > My Apps.
Procedure:
Before starting the experiment please get practice with the
virtual equipment!
Log in to Virtual Physics Labs using your KET ID and
password. Load the virtual “Tangent Galvanometer Apparatus
Lab” and familiarize yourself with the setup.
The apparatus is viewed from two perspectives: Overhead
(Figure 2a), and Oblique (Figure 2b).
You will switch between views using the buttons at the top left
edge of the screens. Take some time to become familiar with
each view.
In the Overhead view shown in Figure 2a, you see two
vector arrows. One represents the horizontal component of the
Earth’s magnetic field. The other represents the magnetic field

produced by the current-carrying wire loops. Neither vector
automatically points in the appropriate direction. Rather these
vectors can be rotated as needed by dragging the points of the
arrows. The entire apparatus can be rotated in the overhead
view by dragging the Handle.
The coil unit has a compass mounted in the middle. With
no current applied to the coil, the compass responds only to the
horizontal component of the earth’s magnetic field.
Figure 2a. View 1: Overhead
Figure 2b. View 2: Oblique
The Oblique view shown in Figure 2b does not rotate.
Explore the following in the Oblique view. A frame with a pair
of vertical supports provides two nails which hold 1 to 5
circular loops of insulated wire.
A horizontal platform holds a sheet of polar graph paper
for measuring angles in the horizontal plane. The compass at the
bottom right provides a close - up of the real compass. You will
take compass reading there. Remember that the red end of the
compass is its north end (seeking Earth's North Pole). Notice
how the deflection of the compass is affected by the power
switch, the voltage adjust knob, and the number of loops of
wire.
When the power is on and current flows through the loop,
a magnetic field due to the current is produced inside the loop.
We expect it to be normal to the plane of the loop. If the Earth’s
magnetic field were nonexistent the compass needle would point
in the direction perpendicular to the loop’s plane. However,
under the influence of the two magnetic fields, the compass
takes the direction of their resultant field Bnet.
The two views are completely independent. You will only
work with one view while performing a given part of the lab.
You will use the overhead view for part 1 and the oblique view

in part 2 and part 3 of the lab.
current loop
You will use the overhead view for this part of experiment
to verify that the magnetic field of the current loop’s BLoop at
the center of a loop is normal to the plane of the loop. In this
view the number of loops N is fixed at 4 and the current I is
fixed at 3.0 A when the power is turned on. Begin with the
power turned off. Drag the handle to orient the frame so that the
0° end of the loop is pointing north - the direction of the red
end of the compass. Drag the end of the vector BEarth to point
in the magnetic north direction as shown in Figure 3a.
direction as the BEarth and as you turn on the power supply the
needle will deflect showing the direction of the net magnetic
field Bnet which is vector sum of the fields BEarth and BLoop.
You might want to arrange the BLoop vector to point in
the direction you think is correct.
You will need to experiment a bit. It will involve
switching the current on and off and rotating the apparatus.
Rotate the apparatus and find the position(s) where the needle
stays still when the power is turned on and off.
E
N
Figure 3a.
Figure 3b.

You should have noticed that there are two different
orientations of the loop that result in no change in the needle’s
direction when the current is turned on and off (this is because
the magnitude of the BEarth is greater than BLoop as you can
see from Overhead view). At these two orientations of the loop
the direction of the total magnetic field Bnet (and therefore the
direction of the needle) is unchanged (only the magnitude is
changed) when the current is turned on and off. In other words
in these orientations of the loop the magnetic field vectors
BEarth and BLoop are parallel or antiparallel (see Figure 4a and
Figure 4b).
Bnet
BLoop BEarth
BEarth
BLoop Bnet
Figure 4a. Figure 4b.
Hopefully, you have noticed that as the loop is at right
angles to the Earth’s field the needle does not move when the
current is turned on and off. So the loop’s field is perpendicular
to the plane of the loop with two possible directions - 180°
apart. But only one of them can match our right hand rule.
Align again the directionof the vector BEarth with compass
needle (to North) as in Figure 3a. You have confirmed that the
loop’s field BLoop is perpendicular to the loop - up (East) or
down (West). You also observed that with the current on, the
compass always points in the direction of Bnet - about 37° north
of east. Because Bnet is in the second quadrant so it must have
a north and an east component. BEarth supplies the northward
component, so BLoop must be to the east as in Figure 3b.
In your lab report show the vector addition of BEarth with
each of the two possible BLoop. What is the current direction?
Is the current flowing into the screen at 180° (and out at 0°) or

into the screen at 0° (and out at 180°)? Apply the right hand
rule to figure out the current direction.
You will investigate the relationship between the strength
of the magnetic field at the center of loop and: a) the number N
of loops; b) the current I through the loop.
Equation (3) shows that the field BLoop at the center of
the loop is directly proportional to the tangent of θ (the Earth’s
field remaining constant). Therefore, you should find that the
plots of tanθ vs. N or tanθ vs. I both should yield a straight line
through the origin (equation (4)). You will use the oblique view
this time and investigate these relationships to test equation (1).
To read the compass as accurately as possible use zooming with
right-click on the apparatus and select “Zoom In” from the
menu. You can then drag the apparatus around as needed.
To test the effect of the number of turns N on the strength
of the loop’s field BLoop, measure the angle of deflection (with
respect to north) of the compass for 1 to 5 loops by keeping the
current at constant value I = 3 A. Enter your data in Logger Pro
and plot both θ vs. N and tanθ vs. N on the same graph using
“Right Y-Axis” feature: on toolbar select Options > Graph
Options > Axes Options > mark Right Y-Axis (be sure the
preferences in LP for angles are set in degrees: select File >
Settings for startup > Degrees). Are both graphs linear?
Describe the graph tanθ vs.N. Apply linear fit to the graph tanθ
vs. N to find the slope with uncertainty and assuming that the
radius of the circular loop R=20 cm, calculate the value of
BEarth,N with the error.
To test the effect of the current through the loop on the
strength of the loop’s magnetic field, measure the angle of
deflection for currents of 0 to 3.5 A in 0.5 A increments
keeping the number of the loops fixed at N = 5. In Logger Pro
plot both θ vs. I and tanθ vs. I on the same graph using “Right
Y-Axis” feature from Graph Options described above. Are both

graphs linear? Describe the graph tanθ vs. I. Apply linear fit to
the graph tanθ vs. I to find the slope with uncertainty and
calculate the value of BEarth, I with the error assuming R=20
cm.
Compute the average value BEarth = (BEarth,N + BEarth,
I)/2 with the error.
magnetic field
According to equation (1) the field at the center of the
loop is directly proportional to the product N·I. Now you will
test the complete equation by using it to calculate the horizontal
component of the Earth’s magnetic field BEarth and compare it
with the value from part 2.
You will do that as follows.
Using a convenient point on the line of best fit from near
the middle of your graph tanθ vs. I find the value of the current
andbyequation (1) calculate BLoop for that value of the current
(hint: do your calculation for the current when tanθ = 1).
Assume that the radius R=20 cm for circular loop.
Compute the horizontal component of Earth’s magnetic
field BEarth using equation (2) for given value of tanθ and
calculated value of BLoop (notice if tanθ = 1, then BEarth=
BLoop). Compare your calculated value of the earth’s magnetic
field Bearth with the average value from part 2.
Final conclusion:
Do your experimental findings support equation (1)? How
does the magnetic field of a coil depend on the current in the
coil?
* Include answers to all questions in lab report

of 5
q
Magnetism
Magnetic fields affect moving charges.
Moving charges produce magnetic fields.
Changing magnetic fields can create electric fields.
Introduction
www.
www.ahmedmater.com
1
Magnets
Two poles, called north and south
Like poles, repel each other and unlike poles, attract each other.
Magnetic poles cannot be isolated.
Section 19.1
http://www.ece.neu.edu/faculty/nian/mom/work.html
Magnetic Fields
Sources
The region of space surrounding a moving charge includes a
magnetic field.
The charge will also be surrounded by an electric field.
A magnetic field surrounds a properly magnetized magnetic
material.
Section 19.1

Magnetic Fields
A vector quantity symbolized by
North pole of a compass needle points in the direction of
magnetic field vector at that location.
Section 19.1
Magnetic Field Lines, Sketch
A compass can be used to show the direction of the magnetic
field lines (a).
A sketch of the magnetic field lines (b)
www.ahmedmater.com
Earth’s Magnetic Field
Section 19.2
Magnetic Fields
The magnitude of the magnetic force is
F = q v B sin θ
This force is zero when the charge moves along the field lines
(θ= 0) and is maximum when the charge moves perpendicularly
to the magnetic field lines (θ = 90).
Section 19.3
Units of Magnetic Field
The SI unit of magnetic field is the Tesla (T)

- Wb is a Weber
The cgs unit is a Gauss (G)
- 1 T = 104 G
Section 19.3
Finding the Direction of Magnetic Force
The direction of the magnetic force is always perpendicular to
both and
Fmax occurs when ┴
F = 0 when II
Section 19.3
Right Hand Rule #1
Point your fingers in the direction of the velocity.
Curl the fingers in the direction of the magnetic field,
Your thumb points in the direction of the force on a positive
charge.
If the charge is negative, the force is directed opposite that
obtained from the right-hand rule.
Section 19.3

Force on a Wire
The magnetic field is directed into the page.
- The x represents the tail of the arrow.
Green dots would be used to represent the field directed out of
the page.
- The • represents the head of the arrow.
I =0 therefore F = 0.
Section 19.4
Force on a Wire
B is into the page.
The force is to the left (b).
The force is to the right (c).
Section 19.4
Force on a Wire, Equation
F = B I ℓ sin θ
θ is the angle between and the direction of I
The direction is found by the right hand rule, placing your
fingers in the direction of I instead of
Section 19.4
Particle Moving in an External Magnetic Field
Section 19.6

Magnetic Fields –
Long Straight Wire
The compass needle deflects in directions tangent to the circle
and points in direction of the magnetic field.
Section 19.7
Direction of the Field
of a Long Straight Wire
Right Hand Rule #2
Grasp the wire in your right hand.
Point your thumb in the direction of the current.
Your fingers will curl in the direction of the field.
Section 19.7
Magnitude of the Field
of a Long Straight Wire
µo = 4 π x 10-7 T.m / A
µo is called the permeability of free space
Section 19.7
Magnetic Force
Between Two Parallel Conductors
The force per unit length is:
Section 19.8

Magnetic Field
of a Current Loop
All the segments, Δx, contribute to the field, increasing its
strength.
Section 19.9
Magnetic Field
of a Current Loop
The magnetic field lines for a current loop resemble those of a
bar magnet.
Magnetic Field
of a Current Loop – Equation
The magnitude of the magnetic field at the center of a circular
loop
With N loops in the coil, this becomes
Section 19.9
Magnetic Field
of a Solenoid
B = µo n I
n is the number of turns per unit length

Arizona State University Department of Physics PHY 132 –.docx

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