1. Back EMF, Counter Torque & Eddy Currents
Example: Back EMF in a Motor.
The armature windings of a dc motor have a resistance of 5.0 Ω. The motor is connected to a 120-V line, & when the motor reaches full speed against its normal load, the back EMF is 108 V.
Calculate
(a) The current into the motor
when it is just starting up
(b) The current when the motor reaches full speed.
Solution: a. At startup, I = V/R = 24 A.
b. The back emf means that the total emf in the circuit is 12 V, so the current is 2.4 A.

2. Conceptual Example: Motor Overload.
When using an appliance such as a blender, electric drill, or sewing machine, if the appliance is overloaded or jammed so that the motor slows appreciably or stops while the power is still connected, the device can burn out and be ruined. Explain why this happens.
A similar effect occurs in a generator – if it is connected to a circuit, current will flow in it, and will produce a counter torque. This means the external applied torque must increase to keep the generator turning.
The motor is designed to operate at a particular speed, which means there will be a particular back emf. If the appliance slows or stops, the back emf becomes much less, the current becomes much more than designed, and the appliance may burn out.

3. These are called eddy currents,
Induced currents can flow in bulk material as well as through wires.
These are called
eddy currents,
& they can dramatically slow a conductor moving into or out of a magnetic field.
Figure Production of eddy currents in a rotating wheel. The grey lines in (b) indicate induced current.

4. Transformers & Transmission of Power
A transformer consists of two coils, either interwoven or linked by an iron core. A changing emf in one induces an emf in the other. The ratio of the emfs equals the ratio of the number of turns in each coil:
The figure is a step-up transformer – the emf in the secondary coil is larger than the emf in the primary. Energy must be conserved; therefore, in the absence of losses, the ratio of the currents must be the inverse of the ratio.

5. Example: Cell phone charger.
The charger for a cell phone contains a transformer that reduces 120-V ac to 5.0-V ac to charge the 3.7-V battery. (It also contains diodes to change the 5.0-V ac to V dc.) If the secondary coil contains 30 turns& the charger supplies 700 mA,
Calculate
(a) The number of turns in the primary coil,
(b) The current in the primary,
(c) The power transformed.
Solution: a. NP = NS VP/VS = 720 turns.
b. IP = IS NS/NP = 29 mA.
c. P = ISVS = 3.5 W.

6. Transformers work only if the current is changing; this is one reason why electricity is transmitted as ac.
Figure The transmission of electric power from power plants to homes makes use of transformers at various stages.

7. Example: Transmission Lines.
An average of 120 kW of electric power is sent to a small town from a power plant 10 km away. The transmission lines have a total resistance of 0.40 Ω. Calculate the power loss if the power is transmitted at
(a) 240 V
(b) 24,000 V.
Solution: a. The total current is 120 kW/240 V = 500 A. Then the power loss is I2R = 100 kW.
b. Same reasoning, different numbers: the current is 5.0 A, and the power loss is 10 W. This is why electricity is transmitted at very high voltages.

8. A Changing Magnetic Flux Induces an Electric Field.
This is a generalization of Faraday’s law.
The electric field will exist regardless of whether there are any conductors around.

9. Example: E Produced by Changing B.
A magnetic field B between the pole faces of an electromagnet is nearly uniform at any instant over a circular area of radius r0. The current in the windings of the electromagnet is increasing in time so that B changes in time at a constant rate dB/dt at each point. Beyond the circular region (r > r0), assume B = 0 at all times.
Calculate the electric field E at any point P a distance r from the center of the circular area due to the changing B.
Figure (a) Side view of nearly constant B. (b) Top view, for determining the electric field E at point P. (c) Lines of E produced by increasing B (pointing outward). (d) Graph of E vs. r.
Example 29–14.
Solution: Because of symmetry, E will be perpendicular to B and constant at radius r. Integrate around a circle of radius r as shown. For r < r0, the enclosed flux is Bπr2, and E = r/2 dB/dt. For r > r0, the enclosed flux is Bπr02, and E = r02/2r dB/dt.

10. Applications of Induction: Sound Systems, Computer Memory, Seismograph
This microphone works by induction; the vibrating membrane induces an emf in the coil.
Figure Diagram of a microphone that works by induction.

11. Differently magnetized areas on an audio tape or disk induce signals in the read/write heads.
Figure (a) Read/Write (playback/recording) head for tape or disk. In writing or recording, the electric input signal to the head, which acts as an electromagnet, magnetizes the passing tape or disk. In reading or playback, the changing magnetic field of the passing tape or disk induces a changing magnetic field in the head, which in turn induces in the coil an emf that is the output signal. (b) Photo of a hard drive showing several platters and read/write heads that can quickly move from the edge of the disk to the center.

12. A seismograph has a fixed coil and a magnet hung on a spring (or vice versa), and records the current induced when the Earth shakes.
Figure One type of seismograph, in which the coil is fixed to the case and moves with the Earth. The magnet, suspended by springs, has inertia and does not move instantaneously with the coil (and case), so there is relative motion between magnet and coil.

13. A ground fault circuit interrupter (GFCI) will interrupt the current to a circuit that has shorted out in a very short time, preventing electrocution. (Circuit breakers are too slow.)
Figure A ground fault circuit interrupter (GFCI).

14. A Changing Magnetic Field Produces an Electric Field.
Summary of Chapter
Magnetic Flux:
Faraday’s Law: A changing magnetic flux
induces an emf.
Lenz’s Law: An induced emf produces
current that opposes original flux change.
General Form of Faraday’s Law:
A Changing Magnetic Field Produces an Electric Field.