2. Magnetic Field Direction
● The direction of a magnetic field is defined to
be the direction that a small North monopole
(assuming one existed) would move if place in
the field.
● Magnetic field lines always point away from North
and towards South and do not cross.
3. Magnetic Field Strength
● The strength of a magnetic field is indicated by
how close together the lines of flux are.
● For this reason, the strength of the magnetic
field B is known as the magnetic flux density.
● B is measured in Teslas (T)
● 1 Tesla is the strength of the magnetic field when a
charge of 1C feels a force of 1N when moving with
a velocity of 1ms-1 perpendicular to the field.
● B measures the strength of the magnetic field
as it is observed externally to the system.
4. Electric Charge and Magnetism
● A moving charge creates a small magnetic field
around it.
● The magnetic field around a wire forms a
circular field around the axis of motion.
● The magnetic flux density gives an indication of
how close together the lines of magnetic force
are and hence the strength of the magnetic
field.
5. Magnetic field around a current
carrying wire
● A current is simply a flow of
charged particles.
● Therefore, the magnetic field
around a long straight current
carrying wire is cylindrical
around the axis of the wire.
● The direction of the field is
given by the right hand
thumb rule.
6. Right hand Thumb Rule
● Grab the wire in your
right hand
● Point your thumb in
the direction of the
current.
● Your fingers curl in
the direction of the
magnetic field.
8. Forces on Wires
● A current passing through a
wire will generate a magnetic
field around it.
● If this wire is placed inside a
magnetic field then the two
magnetic fields will interact.
● This will cause a force.
● This is known as the motor
effect.
● Consider the diagram below.
● A current I flows in the wire
through a region of uniform
magnetic field into the page (B)
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
I
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + B +
9. Forces on Wires
● The current creates a
circular magnetic field
around it (Red)
● According to the right
hand grip rule, the
field is out of the page
above the wire, and
into the page below it.
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
· · · I · · · · · · · ·
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + B +
10. Forces on Wires
● The additional +'s below the line
increase the local field strength in
this region.
● The · and + cancel out above the
wire decreasing the strength of the
local field.
● There is therefore a thrust force
(FT) upwards on the wire as the
field pushes the wire to try to
balance out the local changes.
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + B +
FT
· · · I · · · · · · · ·
+ + + + + + + + + + +
11. Forces on Wires
● Looking at exactly the
same situation but end on
to the wire (from the Left
hand end) gives the
diagram shown.
● Note how the fields above
the wire cancel out and
below reinforce.
● This induces a force
upwards on the wire.
FORCE
S + N
12. The Left Hand Motor Rule.
● The left hand rule is
used to determine the
direction of the motor
effect force for a
conventional current.
● First finger = Field
● seCond finger = Current
● Thumb = Thrust
13. The Right Hand Palm Rule
● The right hand palm
rule is also used to
determine the
direction of the motor
effect force for a
conventional current.
● Fingers = Field
● Thumb = Current
● Palm Slap = Force
14. Forces on Wires
● It is interesting to note that
the force is perpendicular
to both the current and
magnetic field.
● This implies that the
direction of the Force is
given by the cross product
of the current and
magnetic field vectors.
● i.e.
●
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + B +
FT
· · · I · · · · · · · ·
+ + + + + + + + + + +
⃗F ∝⃗I×⃗B
15. Factors affecting the Force
● There are 4 factors that effect the magnitude of
the force on the current carrying wire:
● The strength of the
magnetic field
● The magnitude of the
current
● The length of the
conductor in the field
● The angle between the
field and the conductor
● A stronger field means more
flux lines means more force.
● A larger current means more
flux lines means more force.
● A longer conductor means
more flux lines means more
force.
● The angle controls the magnitude of the
component of the length in the field. A
bigger angle means a smaller component
means less force.
16. Forces on Wires
● For a wire of length L in
a uniform magnetic field
this becomes:
● Where θ is the angle
between the current and
the normal to the plane
of magnetic field.
Note: In the diagram below, the
wire has been turned out of the
page and not turned in the plane
of the page.
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + B +
· ·
T
· · F· · · + +
· · + + · · I + + + + + + + ⃗F=L⃗I×⃗B
⃗F=LIBsinθ
θ
17. Forces on Charged Particles
● A current is simply a flow of charge carriers in a wire.
● Each has a charge of q and an average speed of v covering a distance of L
in 1 second.
● The current due to a simple charge is therefore given by:
⃗I=
q⃗v L
● The force on a moving charge therefore is given by:
⃗F=q⃗v
×⃗B
⃗F=qvBsinθ
● Here θ is the angle between the B field line and the velocity of the charge.
18. Parallel Wires
● It follows that if two
parallel conducting
wires are carrying
currents next to each
other that:
● They will both induce
magnetic fields
● They will both interact
● They will both feel an
equal force.
+
FORCE
+
19. Parallel Wires
● If the two wires are
carrying currents in
the same direction
(parallel) then:
● The fields between
them cancel out
● The fields outside
therefore push them
together equally.
● Parallel current attract
+
FORCE
+
FORCE
20. Parallel Wires
● If the two wires are
carrying currents in the
opposite direction
(anti-parallel) then:
● The fields between
them cancel reinforce
● The fields inside
therefore push them
outwards equally.
● Anti-Parallel currents
Repel
+
FORCE
.
FORCE
21. Parallel wires
● The magnitude of the force per unit length on
parallel conducting wires is given by:
F
l =k
I1 I 2
d
● A positive answer indicates attraction, a
negative answer indicates repulsion.
