Chapter 20Induced Voltages and Inductance1. Induce emf and Magnetic flux2. Faraday’s law of induction3. Lenz’s law4. Motional emf5. Generators6. Self-Inductance7. RL circuits8. Energy stored in a magnetic field

Michael Faraday 1791 – 1867 Great experimental

scientist Invented electric

motor, generator and transformers

Discovered electromagnetic induction

Discovered laws of electrolysis

Faraday’s Experiment – Set Up What is induced emf? How is it produced?

Magnetic Flux What is magnetic

flux? How do I calculate

it? What is the SI

units? Why the angle

dependence? Flux and B

Electromagnetic Induction –An Experiment

What is electromagnetic induction?

What is induced current?

Example1. The quarter-circle loop shown in figure has an

area of 15 cm2. A magnetic field, with B=0.16T exists in the +x direction. Find the flux through the loop in each orientation shown.

Example

B

70º

20º

20º

20º

B

b) c)

B

B

B

B

n

normal

plane

planenormal

a)

Faraday’s Law and Electromagnetic Induction What is Faraday’s law? What is the formula? What is the SI units? How to change the flux? What is Lenz’s law?

Example1. As shown a metal rod makes contact with a partial

circuit. The circuit is perpendicular to the magnetic field. Find the induced emf if the rod moves with velocity of v=2m/s. Assume L=0.5m

Lenz’ Law – Example

Example1. See figures

Example1. See figures

Applications of Faraday’s Law – Ground Fault Interrupters

Applications of Faraday’s Law – Apnea Monitor

Application of Faraday’s Law – Motional emf

What is motional emf? How is it produced?

The force on charges The potential difference

Motional emf in a Circuit How do I calculate

motional emf? Motional emf and

Battery What is the

resulting current?

Example1. As shown, a metal rod makes contact with a

partial circuit and completes the circuit. The circuit area is perpendicular to the magnetic field with B=0.15T. If the resistance of the total circuit is 3 ohm, how large a force is needed to move the rod as indicated with a speed of 2 m/s.

Lenz’ Law Revisited – Moving Bar Example

How do I calculate the direction of induced current?

One possibility

Lenz’ Law, Bar Example

Another possibility

Conservation of energy

Lenz’ Law – Moving Magnet Example

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

AC Generators What is a

generator? How does it work? Emf of the loop

DC Generators

Motors What is a Motor? Motors an Back

Joseph Henry 1797 – 1878 First director of the

Smithsonian First president of the

Academy of Natural Science

First to produce an electric current with a magnetic field

Improved the design of the electro-magnetic and constructed a motor

Discovered self-inductance

Self-inductance What is self-inductance? How do I calculate it? What are it SI units? What is inductance? How do I calculate it?

Example1. A coiled telephone cord has 70 turns, a cross-

sectional diameter of 1.3 cm, and an unstrectched length of 60 cm. Determine an approximate value for the self-inductance of the unstretched cord.

Inductor and RL Circuit What is an inductor? How does it work in a

circuit? RL circuit What is the time

constant? How do I find the current

in the circuit? What is the energy

stored in the inductor?

Example1. For the circuit shown, determine

1. Time constant2. Current after one time constant3. Change in potential at t=0 and t=first time constant4. The rate of change of current after first time constant