1. EMF Induced in a Moving Conductor (“Motional EMF”)
Figure 29-12a. A conducting rod is moved to the right on a U-shaped conductor in a uniform magnetic field B that points out of the page. The induced current is clockwise.

2. This figure shows another way the magnetic flux can change.
It can change if a conducting loop is moved in a static magnetic field.
Figure 29-12a. A conducting rod is moved to the right on a U-shaped conductor in a uniform magnetic field B that points out of the page. The induced current is clockwise.

3. It takes an external force to keep it moving.
The induced current in the figure is in a direction
that tends to slow the moving bar. That is,
It takes an external force to keep it moving.
Figure 29-12b. Upward force on an electron in the metal rod (moving to the right) due to B pointing out of the page.

4. holds ONLY if B, l, & v are mutually perpendicular.
The induced emf has magnitude
= B[(A)/(t)] = Bℓ(x)/(t) = Bℓv
This
holds ONLY if B, l, & v are mutually perpendicular.
If they are not, then it is true for
their perpendicular components.

5. Does a moving plane develop a large emf?
Induced emf magnitude:
Example:
Does a moving plane develop a large emf?
A plane travels at speed
v = 1000 km/h in a region
where Earth’s magnetic field B
= 5  10-5 T & is nearly vertical.
Calculate the potential difference induced
between the wing tips that are l = 70 m apart.
Solution:  = B l v  1 V

6. Motional emf Electrons in the conductor experience a
Motional emf is the emf
induced in a conductor
moving through a
constant magnetic field.
Electrons in the conductor experience a
force that is directed along ℓ: .

7. qE = qvB or E = vB. This charge separation produces an
This force causes electrons move to the
lower end of the conductor & accumulate.
This charge separation produces an
electric field inside the conductor.
The charges accumulate at both ends of
the conductor until they are at steady
state. When that happens,
qE = qvB or E = vB.

8. This charge separation produces an electric field inside the conductor.
qE = qvB or E = vB.
This electric field is related to the potential difference
across the ends of the conductor: V = E ℓ =B ℓ v.
This V is maintained between the ends of the
conductor as long as it continues to move through the
uniform B field. If the direction of the motion is
reversed, the polarity of the V is also reversed.

9. Example: Force on a conducting bar.
To make the bar move to the right at speed v, you
need to apply an external force on the bar to the right.
Calculate (a) The magnitude of the required force.
(b) The external power needed to move the rod.
Solution: a. The external force needs to be equal and opposite to the magnetic force (IlB) if the rod is to move at a constant speed. I = Blv/R, so F = B2l2v/R.
b. The external power is Fv = B2l2v2/R, which is equal to the power dissipated in the resistance of the rod (I2R).

10. Sliding Conducting Bar
The induced emf is
The resistance in the circuit is R, so the
current is

11. Sliding Conducting Bar
The applied force does work
on the bar. It moves the charges through a magnetic field
& induces a current. The change in energy of the system
during some time interval must be equal to the transfer of
energy into the system by work.
The power input is equal to the
rate at which energy is delivered
to the resistor.

12. Lenz’s Law: More on Lenz’s Law
Faraday’s Law says that the induced emf & the
change in magnetic flux have opposite algebraic
signs. This has a physical interpretation known as
Lenz’s Law:
The induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop.
The induced current tends be in a direction so to
keep the original magnetic flux through the circuit
from changing.

13. Lenz’ Law, Example The induced current must produce a magnetic
The conducting bar
slides on the two fixed
conducting rails.
The magnetic flux due
to the external magnetic
field through the enclosed
area increases with time.
The induced current must produce a magnetic
field out of the page. So, the induced current must
be counterclockwise If the bar moves in the
opposite direction, the direction of the induced
current will also be reversed.