# Chapter 20 Induced Voltages and Inductance

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Chapter 20 Induced Voltages and Inductance
Induce emf and Magnetic flux Faraday’s law of induction Lenz’s law Motional emf Generators Self-Inductance RL circuits 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

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?

Example 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 a) n plane normal 20º B 20º 70º B normal 20º plane b) c)

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

Example 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

Example See figures

Example 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?

Example 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?

Example 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?

Example For the circuit shown, determine Time constant
Current after one time constant Change in potential at t=0 and t=first time constant The rate of change of current after first time constant