Chapter 22 Electromagnetic Induction

1) Induced emf and induced current Changing B-field induces current

Changing coil area or orientation induces current

Changing the number of lines of force through loop induces current Induced current indicates induced emf and induced electric field Changing magnetic field produces electric field

2) Motional emf a)The principle B-field exerts force on moving charges + v FBFB - v FBFB

==> free charges separate E E separated charges produce electric field and a corresponding potential difference

E E E - field exerts force on charges + FEFE - FEFE

E E Charges stop moving when the forces balance: Induced emf predicted from statics so,

b) Application

c) Induced emf from conservation of energy F A = F B FBFB

FBFB Power to push rod at speed v: Using,

F A = F B FBFB Power to push rod at speed v: Electrical power consumed: So,

3) Magnetic flux,  a)Define Flux: - Proportional to the lines of force through a surface

Flux depends on angle

b) Flux and motional emf t

4) Lenz’s law Direction of induced current produces a magnetic field that opposes the change in flux -flux through loop (in) increases because of v:  t > 0 - induced current produces flux out of diagram (opposite direction) -Define flux from external field as positive. Then

-flux through loop (in) decreases because of v:  t < 0 - induced current produces flux into loop (same direction to oppose the decrease) -Define external flux as positive. Then induced flux is also positive, so again v

5) Faraday’s Law For any changing flux in any loop, the emf induced in the loop is (for N turns) where  is the flux through one turn

a) Conservation of energy Lenz’s law is statement of energy conservation Flux increases Induced field repels magnet; work required to produce current

Flux decreases Induced field attracts magnet; work required to produce current

Example: Find direction of the current in each loop zero ccw cw

b) Induced polarity Inside the loop, current is forced from negative to positive (by work that produces the change in flux) I (like inside a battery) In the external circuit, current flows from positive to negative

c) Eddy currents Power loss hence, laminated cores in transformers

Induction stove

6) Electric Generator

a) The principle

b) Conservation of energy and countertorque If I = 0, coil turns without resistance If I > 0, force on wires resists spinning Larger load requires more fuel

c) Back emf of an electric motor Rotating coil in a motor acts like a generator According to Lenz’s law, the induced emf opposes external current more power required initially to accelerate motor higher speed produces higher back emf, and lower current max speed --> minimum current (minimum power) stopped motor draws maximum current

7) Induction and sound Microphone

Guitar pickup

Magnetic tape