1. The document discusses the motor effect, which is the force experienced by a current-carrying conductor in a magnetic field. It describes how the interaction between the magnetic field generated by the current and an external magnetic field produces a force. 2. Key factors that influence the magnitude of the motor effect force are outlined, including the strength of the magnetic field, current magnitude, length of the conductor in the field, and angle between the field and conductor. 3. Rules for determining the direction of the force are provided, such as the left hand motor rule. Parallel conductors experience attractive or repulsive forces depending on whether their currents are parallel or anti-parallel.

1. Topic 9.3
3.1.1 – The Motor Effect

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.

7. Magnetic Fields around Current
Carrying Wires
● Current Into Page ● Current Out Of Page

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.