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. 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
This
holds ONLY if B, l, & v are mutually perpendicular.
If they are not, then it is true for
their perpendicular components.

5. 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. Electromagnetic Blood-flow measurement
Example
Electromagnetic Blood-flow measurement
The rate of blood flow in our body’s vessels can be
measured using the apparatus shown, since blood
contains charged ions. Suppose that the blood vessel is
2.0 mm in diameter, the magnetic field is T, & the
measured emf is 0.10 mV.
Calculate the flow
velocity v of the blood.
Solution: v = E/Bl = 0.63 m/s.

7. Example: Force on a rod. Calculate
To make the rod move to the right at speed v, you
need to apply an external force on the rod 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).

8. 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: .

9. Under this force, electrons move to the lower end of the conductor & accumulate there. As a result of this charge separation, an electric field is produced inside the conductor.
The charges accumulate at both ends of the conductor until they are in equilibrium with regard to the electric and magnetic forces. At equilibrium,
qE = qvB or E = vB.

10. As a result of this charge separation, an electric field is produced 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 potential difference is maintained between the ends of the conductor as long as it continues to move through the uniform magnetic field. If the direction of the motion is reversed, the polarity of the potential difference is also reversed.

11. Sliding Conducting Bar
A conducting bar moving through a uniform field and the equivalent circuit diagram. Assume the bar has zero resistance. The stationary part of the circuit has a resistance R.

12. Sliding Conducting Bar
The induced emf is
Since the resistance in the circuit is R, the current is

13. Sliding Conducting Bar
The applied force does work
on the bar. It moves the
charges through a magnetic
field & establishes 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.

14. More on Lenz’s Law 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.
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 to keep the original
magnetic flux through the circuit from changing.

15. Lenz’ Law, Example
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.

16. Electric Generators
A generator is the opposite of a motor. It transforms mechanical energy into electrical energy. The figure shows an ac generator:
The axle is rotated by an external force such as falling water or steam.
The brushes are in constant electrical contact with the slip rings.
Figure An ac generator.

17. If the loop is rotating with constant angular velocity ω, the induced emf is sinusoidal:
For a coil of N Loops:
Figure An ac generator produces an alternating current. The output emf E = E0 sin ωt, where E0 = NABω.

18. Example: AC generator. AC DC
The armature of a 60-Hz ac generator rotates in a 0.15 T magnetic field. The coli area is 2.0  10-2 m2, Calculate the number of loops needed for the peak output to be E = 170 V.
A dc generator is similar to an ac generator, except that it has a split-ring commutator instead of slip rings.
Solution: N = E0/BAω = 150 turns. Remember to convert 60 Hz to angular units. AC DC

19. Automobiles now use alternators rather than dc generators, to reduce wear.
Figure (a) Simplified schematic diagram of an alternator. The input current to the rotor from the battery is connected through continuous slip rings. Sometimes the rotor electromagnet is replaced by a permanent magnet. (b) Actual shape of an alternator. The rotor is made to turn by a belt from the engine. The current in the wire coil of the rotor produces a magnetic field inside it on its axis that points horizontally from left to right, thus making north and south poles of the plates attached at either end. These end plates are made with triangular fingers that are bent over the coil—hence there are alternating N and S poles quite close to one another, with magnetic field lines between them as shown by the blue lines. As the rotor turns, these field lines pass through the fixed stator coils (shown on the right for clarity, but in operation the rotor rotates within the stator), inducing a current in them, which is the output.