REALTION BETWEEN ELECTRICFIED AND POTENID Neeraj sharma (2)

1. Rai Saheb Bhanwar Singh College
Nas.ganj

2. Work
• You do work when you push an object up a hill
• The longer the hill the more work you do: more
distance
• The steeper the hill the more work you do: more
force
The work W done on an object by an agent
exerting a constant force is the product of the
component of the force in the direction of the
displacement and the magnitude of the
displacement
dFW ||=

3. Work done by gravity
θcosFdW =
m
mg
d
θcosF
θ

4. Energy is capacity to do work
note Ep aka UG
• Gravitational Potential Energy
• Kinetic Energy
• Energy can be converted into other forms of
energy
• When we do work on any object we transfer
energy to it
• Energy cannot be created or destroyed
mghUG =
2
2
1
mvK =
GU∆−=∆Κ
GUKW ∆−=∆=

5. • A person lifts a heavy box of mass ‘m’ a
vertical distance ‘h’
• They then move a distance ‘d’, carrying the
box
• How much work is done carrying the box?
Quiz

6. Conversion of Gravitational
Potential Energy to Kinetic
Energy
m
mg
m
v
mghUG −=∆
2
2
1
mvK =∆
ghv
ghv
mghmv
2
2
2
1
2
2
=
=
=
Work done on object
h

7. What’s an electric field?
• A region around a charged
object through which another
charge will experience a force
• Convention: electric field
lines are drawn out of (+) and
into (-); so the lines will show
the movement of a “positive
test charge”
• E = F / q
• units are in N/C
+Q
+Q

8. Electric Potential Energy
charges also have electrical potential energy
E
EF Q=
+Q
+Q
d
FdW =
QEd=
QEdUe −=∆
v

9. Electric Potential Energy
• Work done (by electric field) on
charged particle is QEd
• Particle has gained Kinetic Energy
(QEd)
• Particle must therefore have lost
Potential Energy ∆U=-QEd

10. Electric Potential
The electric potential energy depends on
the charge present
We can define the electric
potential V which does not depend
on charge by using a “test” charge
EdQU 0−=∆
0Q
U
V
∆
=∆
Change in potential is
change in potential energy
for a test charge per unit
charge
Ed
Q
U
V −=
∆
=∆
0
for uniform field

11. Electric Potential
0Q
U
V
∆
=∆
compare with the Electric Field and Coulomb Force
0Q
F
E =
If we know the potential field this allows us to
calculate changes in potential energy for any
charge introduced
VQU ∆=∆ EF Q=

12. Electric Potential
Electric Potential is a scalar field
it is defined everywhere
but it does not have any direction
it doesn’t depend on a charge being there

13. Electric Potential, units
SI Units of Electric Potential
0Q
U
V
∆
=∆
EdV −=∆
Units are J/C
Alternatively called Volts (V)
We have seen
dVE /∆= Thus E also has units of V/m

14. Potential in Uniform field
E
+Q +Q
+Q
A B
C
0|| == dFWBC
|||| QEddFWAB ==
BCABAC WWW +=
||QEd=
||QEdUAC −=∆
d||
||EdVAC −=∆

15. Electric Potential of a single
charge
+
r
E
B
A
Advanced

16. Equi-potential Lines
Like elevation, potential can be displayed as contours
A contour diagram
Like elevation, potential requires a zero
point, potential V=0 at r=∞
Like slope & elevation we
can obtain the Electric Field
from the potential field
r
V
E
∆
∆
=

17. Potential Energy in 3 charges
∑=
r
Q
V
04
1
πεQ2
Q1
Q3
12
1
0
2212
4
1
r
Q
QVQU
πε
==
12
21
0
12
4
1
r
QQ
U
πε
=






++=+=
23
2
13
1
0
3123312
4
1
r
Q
r
Q
QUVQUU
πε
231312 UUUU ++=






++=
23
32
13
31
12
21
04
1
r
QQ
r
QQ
r
QQ
U
πε

18. Capacitors
A system of two conductors, each
carrying equal charge is known as
a capacitor

19. -
Capacitance of charged sphere
+Q
r=∞
V
Q
C
∆
= definition
R
r
Q
V
0 4
1
πε
+ = potential due to
isolated charge

20. Capacitors
-
+ +Q -Q
e.g. 1: two metal spheres
e.g. 2: two parallel sheets
Each conductor is called a plate

21. Capacitance
Capacitance…….. is a measure of the
amount of charge a capacitor can store
(its “capacity”)
Experiments show that the charge
in a capacitor is proportional to the
electric potential difference
(voltage) between the plates.

22. Units
V
Q
C
∆
= Thus SI units of capacitance are:
C/V
This unit is also known as the farad
after Michael Faraday
Remember that V is also
J/C so unit is also C2
J-1
1F=1C/V

24. Capacitance
The constant of proportionality C is
the capacitance which is a property
of the conductor
VQ ∆∝ VCQ ∆=
V
Q
C
∆
=
Experiments show that the charge in a
capacitor is proportional to the electric
potential difference (voltage) between the
plates.

25. Capacitance of parallel plates
+Q -Q
Intutively
The bigger the plates the
more surface area over
which the capacitor can
store charge C ∝ A
E
Moving plates togeth`er
Initially E is constant (no
charges moving) thus
∆V=Ed decreases charges
flows from battery to
increase ∆V⇒ C ∝ 1/dNever Ready
+
∆V

26. Batteries, Conductors & PotentialNeverReady
+
A battery maintains a
fixed potential
difference (voltage)
between its terminals A conductor
has E=0
within and
thus
∆V=Ed=0
∆V
∆V= 0

27. Capacitance of parallel plates
+Q -Q
Physically
E
Never Ready
+
EdV =∆
V
Q
C
∆
=
property of conductor
∆V

29. Rai Saheb Bhanwar Singh College
Nas.ganj