ch. 31 faradays law

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Chapter 31Faraday’s Law

Induced Fields

Introduction

Michael FaradayJoseph Henry.

Dr. Hayel ShehadehSummer 2015

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EMF Produced by a Changing Magnetic Field

Section 31.1Dr. Hayel Shehadeh Summer 2015

Faraday’s Law of Induction – Mathematical Statements

The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit.

Mathematically,

Remember B is the magnetic flux through the circuit and is found by

If the circuit consists of N loops, all of the same area, and if B is the flux through one loop, an emf is induced in every loop and Faraday’s law becomes

tB

ABB

tN B


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Introduction

Magnetic Flux

The unit of magnetic flux is T.m2 = Wb

AdBd B

Dr. Hayel Shehadeh Summer 2015

Section 31.1

cos(


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Faraday’s Law – Example

Section 31.1

cosBAABB

t

BA

tB cos


Ways of Inducing an emf

The magnitude of the magnetic field can change with time.

The area enclosed by the loop can change with time.

The angle between the magnetic field and the normal to the loop can change with time.

Any combination of the above can occur.

Section 31.1

t

BA cos


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Section 31.1

Ex.1: Consider the situation shown. A triangular, aluminum loop is slowly moving to the right. Eventually, it will enter and pass through the uniform magnetic field region represented by the tails of arrows directed away from you. Initially, there is no current in the loop. When the loop is entering the magnetic field, what will be the direction of any induced current present in the loop?

a) clockwise

b) counterclockwise

c) No current is induced.


Section 31.1

Ex.2: Consider the situation shown. A triangular, aluminum loop is slowly moving to the right. Eventually, it will enter and pass through the uniform magnetic field region represented by the tails of arrows directed away from you. Initially, there is no current in the loop. When the loop is exiting the magnetic field, what will be the direction of any induced current present in the loop?

a) clockwise

b) counterclockwise



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Section 31.1

Ex.3: A rigid, circular metal loop begins at rest in a uniform magnetic field directed away from you as shown. The loop is then pulled through the field toward the right, but does not exit the field. What is the direction of any induced current within the loop?

a) clockwise

b) counterclockwise



Ex.4: A balloon has an initial radius of 0.075 m. A circle is painted on the balloon using silver metal paint. When the paint dries, the circle is a very good electrical conductor. With the balloon oriented such that a 1.5-T magnetic field is oriented perpendicular to the plane of the circle, air is blown into the balloon so that it expands uniformly. The silver circle expands to a radius 0.125 m in 1.5 s. Determine the induced emf for this silver circle during this period of expansion.


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Ex.5: Find the change in flux for each of the following loops.


Applications of Faraday’s Law


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Motional emf

Fm=q v B

FE= E q

E =ℰ L

qvBqL

vBL


Section 31.2

R. H. R.

Fm

Fm = I L B sin900


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Section 31.2

Does the rod moves faster in (a) or in (b) ? Why? Consider F.B.D.

What happens to the conservation of energy in part (b)?

Part of G.P.E is converted into K.E. and Heat dissipated in R.

When v is constant, all of the G.P.E. is dissipated as a heat in R.


Motional emf

Section 31.2

Generators


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Sliding Conducting Bar

A conducting bar moving through a uniform field and the equivalent circuit diagram.

Assume the bar has zero resistance.

The stationary part of the circuit has a resistance R.

Section 31.2

Iε B v

R R

Blv

t

xBl

tB


Sliding Conducting Bar, Energy Considerations

The applied force does work on the conducting bar.

Model the circuit as a non-isolated system.

This moves the charges through a magnetic field and establishes a current.

The change in energy of the system during some time interval must be equal to the transfer of energy into the system by work.

The power input is equal to the rate at which energy is delivered to the resistor.

2

app

εP F v B v

R I

Section 31.2

FB


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Lenz’s Law


Induced Current Directions – Conceptual Physics

A magnet is placed near a metal loop.

a)Find the direction of the induced current in the loop when the magnet is pushed toward the loop (a and b).

b)Find the direction of the induced current in the loop when the magnet is pulled away from the loop (c and d).


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Rotating LoopAssume a loop with N turns, all of the same area rotating in a magnetic field.

The flux through the loop at any time tis B = BA cos = BA cos t

This is sinusoidal, with max = NAB

tNABt

N

sin


DC Generators

The DC (direct current) generator has essentially the same components as the AC generator.

The main difference is that the contacts to the rotating loop are made using a split ring called a commutator.


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Section 31.4

Hybrid Drive Systems


Hybrid Drive SystemsIn an automobile with a hybrid drive system, a gasoline engine and an electric motor are combined to increase the fuel economy of the vehicle and reduce its emissions.

Power to the wheels can come from either the gasoline engine or the electric motor.

In normal driving, the electric motor accelerates the vehicle from rest until it is moving at a speed of about 15 mph.

During the acceleration periods, the engine is not running, so gasoline is not used and there is no emission.

At higher speeds, the motor and engine work together so that the engine always operates at or near its most efficient speed.

The result is significantly higher gas mileage than a traditional gasoline-powered automobile.

Section 31.5 Dr. Hayel ShehadehSummer 2015

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ch. 31 faradays law

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