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QUESTIONS? PLEASE ASK!

From last time… Magnetic Flux

ΦB = BA = B A cos θ

Faraday’s Law: instantaneous emf induced in a circuit = time rate of change of magnetic flux through the circuit

Lenz’s Law:induced emf travels in the direction that creates a magnetic field with flux opposing the change in the original flux through the circuit

Motional emf: ε= B ℓ v

Motional EMF in a Circuit Now place the conductor on

a pair of rails and pull it with an applied force Fapp

assume the moving bar has negligible resistance

The magnetic force Fapp on the charges sets up an induced current

the charges are free to move in the closed path!

Motional emf in a Circuit II

The changing magnetic flux through the loop and the corresponding induced emf in the bar result from the change in area of the loop

The induced ‘motional’ EMF acts like a battery in the circuit

20.4 Lenz’ Law Revisited Current due to the induced EMF travels in

the direction that creates a magnetic field with flux opposing the change in the original flux through the circuit

In the diagram to the right, B is decreasing with time

B is decreasing; current I is induced in counterclockwise direction to increase B

If B were increasing with time, then the induced current would travel in the clockwise direction

When applying Lenz’ Law, there are two magnetic fields to consider

The external changing magnetic field that induces the current in the loop

The magnetic field produced by the current in the loop

Lenz’ Law Revisited, Conservation of Energy

Assume the induced current I is clockwise in the figure

The magnetic force Fm on the bar would be to the right

Fm causes bar to accelerate v would increase Magnetic flux B would

increase Current I would increase in

clockwise direction

A perpetual motion machine?? Sorry…

Violation of conservation of energy is not allowed!!

Thus, current I is counterclockwise

Example Problem 20.32A conducting bar of length L = 35 cm moves to the right on two frictionless rails connected by a resistor R = 9.0 Ω. A uniform magnetic field directed into the page has a magnitude of 0.30 T.

(a) At what speed should bar move to produce an 8.5 mA current in the resistor?(b) At what rate is energy delivered to the resistor?(c) Explain the origin of energy being delivered to the resistor.

20.5 Generators Alternating Current (AC) generator

Converts mechanical energy to electrical energy using induction

The opposite of a motor! Consists of a wire loop rotated by

some external means falling water (hydroelectric), heat

by burning coal to produce steam (coal-fired), nuclear fission reactor, solar heater

Basic AC generator operation Loop rotates from external force, Magnetic flux through the loop

changes with time, inducing an EMF and a current in the external circuit

The ends of the loop are connected to slip rings that rotate with the loop

Connections to the external circuit are made by stationary brushes in contact with the slip rings

AC Generators, mathematics

The emf generated by the rotating loop can be found by:

ε =2 B ℓ v=2 B ℓ v sin θ

If the loop rotates with a constant angular speed, ω, and N turns:

θ = ω t v = r ω = (a/2) ω A = ℓ a

ε = N B A ω sin ω t

a/2

Example Problem 20.37In a model AC generator, a 500 turn rectangular coil 8.0 cm by 20 cm rotates at 120 rev/min in a uniform magnetic field of 0.60 T

(a) What is the maximum EMF induced in the coil?(b) What is the instantaneous value of EMF in the coil at t = (/32) s? Assume the EMF is zero at t = 0(c)What is the smallest value of t for which the EMF will have its maximum value?

Motors and Back EMF Motors convert electrical

energy into mechanical energy A motor is a generator run in

reverse

Back EMF is the self-induced EMF that tends to reduce the applied current

When a motor is turned on, no back EMF initially

The current is very large because it is limited only by the resistance of the coil

x x x x x x x x xx x x x x x B x x xx x x x x x x x xx x x x x x x x x

Motors and Back EMF As the coil begins to

rotate, the induced back emf opposes the applied voltage

The current in the coil is reduced

The power requirements for starting a motor and for running it under heavy loads are greater than those for running the motor under average loads

x x x x x x x x xx x x x x x B x x xx x x x x x x x xx x x x x x x x x

20.6 Self-inductance Self-inductance occurs when

the changing flux through a circuit arises from the circuit itself

The self-induced EMF must be proportional to the time rate of change of the current

L is inductance of the device

The negative sign is important! It indicates that a changing current induces an EMF in opposition to that change

Self-inductance The inductance of a coil depends

on geometric factors The SI unit of self-inductance is the

Henry 1 H = 1 (V · s) / A

The expression for L is

Solution to 20.32

Solution to 20.37