ELECTROMAGNETIC ELECTROMAGNETIC INDUCTIONINDUCTION

Electric fields are produced by electric charges: Electrostatics.

Electric fields can also be produced by

a changing magnetic field:electromagnetic induction

Physics for Scientistsand Engineers

Chapter 28:Magnetic Induction

Copyright © 2004 by W. H. Freeman & Company

Paul A. Tipler • Gene Mosca

Fifth Edition

Learning Aims

•To illustrate that electric fields can be generated not only by charges but also by changing magnetic fields

•To show that these induced electric fields can be used to drive currents in electrical circuits

Learning Outcomes•To understand the concept of electromagnetic induction – producing an induced voltage –

•To understand the physical properties which determine the size of an induced voltage – Faraday’s Law

•To understand that energy conservation allows us to deduce the polarity of an induced voltage – Lenz’s Law

For you:

For me, Business as usual

Lecture observation

1. Pretend as though you are naturally interested in the topic.

2. From time to time, gesturing to your friends that you feel excited about the physics.3. Sleep with your eyes open please. 4. Raise your hands when I ask you a question.

Magnetic Field Lines

•the number of field lines drawn per unit cross sectional area is proportional to the magnitude of B

•the tangent to a field line at a point P gives the direction of B at that point

A

€

φB = B.dAsurface

∫

The magnetic flux B passing through the small area A shown is defined by:

€

φB = Bcosθ × ΔA = B.ΔA

Magnetic Flux

Hans Christian Oersted

(1777-1851)In 1820 Oersted demonstrated that a magnetic field exists near a current-carrying wire - first connection between electric and magnetic phenomena.

So, an electric current can generate a magnetic field.

A great British scientist thought that the reverse might be possible – to generate electricity from magnetism.

Michael Faraday 1791 - 1867Central to our study is the pioneering work of the British scientist Faraday. He discovered that whenever magnetic field lines move or change in anyway, they induce an electric field. This kind of electric field exerts the usual forces on charges – but it does not have its origin in charged particles!

The unit for capacitance was named after Faraday

( )BvEqF ∧+=in direction of E

to v and BUse Lorentz force law

Moving Conductors

The Motion of a Conductor in a B Field

Electrons accumulate until FE = FB

Get an induced voltage across the ends of the conductor

e-

v

FB=evB FE=eE Conducting Rod length l- +

B

e-

v

FB=evB FE=eE

In equilibrium E = vB

Potential difference

induced = El = vBl

Question: If we can generate a potential difference across a rod, is it possible to use

this to light up a bulb?

YES!

v

The ends of the rod are in sliding contact with a pair of wires, a current will flow around the circuit

The moving rod has become a source of electrical energy

I

I

v

l

Force on wire is: F = BIl

B

To maintain motion at constant speed a force of equal magnitude must be applied in the direction of v - Rate of work = Fv = BIlv

F

€

dr F = Id

r l ×

r B

Rate of work done by electrical energy

= I

Conservation of Energy

= Blv= BlvBIlv = I

l

In a time dt the rod travels a distance vdt

lvdt

Area Change

A

B

This can be given an interesting interpretation in terms of the MAGNETIC FLUX

In a time dt the conductor sweeps out an area lvdt. The flux change in time dt is:

€

dΦB = Blvdt

€

dΦB

dt= Blv

€

=dΦB

dtMagnitude of Induced Voltage

dt

d B=

Linking the Induced Voltage with

•Magnitude of induced voltage is equal to the rate of flux change

Faraday’s Law of Electromagnetic Induction

The unit for magnetic flux:1 weber= 1Wb= 1 T m2

Note, that an induced voltage can be a result of a change in area or magnetic field, or both!

l

B

B=B0sint

Area=r2

B= r2 B0sint

€

=dΦB

dt= πr2B0ω cosωt

l

people use “induced electromotive force” (emf). This is a misconception - the quantity involved is not a force. The quantity is a potential difference.

€

=dΦB

dt

Major Application

Conversion of one form of energy (e.g. gravitational, chemical, nuclear) to electric energy

Production of Electricity

Summary of the Laws of Electromagnetic Induction (so far)

What about the direction of the induced voltage?

dt

d B =

The Polarity of an Induced Voltagev

The motion induces a voltage and hence a current in the metal ring. The current produces a magnetic field so that the ring behaves like a bar magnet.

Question:

The B-field from the induced current repels the approaching magnet, Yes or no?

NS

Would the forces differ if the magnet were moving away from the metal ring?

Lenz’s Law:The direction of an induced current (if one were to flow) is such that its effect would oppose the change in magnetic flux which give rise to the current

The Laws of Electromagnetic Induction (continued)

It’s all to do with conservation of energy!

The magnetic field generated can only hinder the motion. Helping the motion would result in the creation of a perpetual motion machine, which violates the conservation of energy.

Mathematically

dt

d B−=

B

dt

dQI =

The electric field associated with an induced voltage. A non-conservative E-

field.

E

0>dt

d B

€

= r

E ∫ • dr l

dtd

ldE B .

Faraday’s Law of Electromagnetic Induction

A time varying magnetic field induces a non-conservative electric field loop.

•An induced electric field is present even if the loop through which a magnetic flux is changing is not a physical conductor but an imaginary line. A changing flux induces a non-conservative E-field at every point of such a loop.

Review and Summary

Relative movement of a wire through a magnetic field (start with the Lorentz Equation)

Changing the magnetic field strength around a wire

dt

d B−=

Induced current if wire forms part of a complete circuit – the faster the changes, the larger the current.

Learning outcome: You should be able to

1. Use Faraday’s Law of electromagnetic induction to calculate the magnitude of an induced voltage

2. Use Lenz’s law to determine the polarity (direction) of an induced voltage and hence the direction of an induced current in a circuit

A4

Student ExerciseA Stealth aircraft is diving vertically downwards at Mach 5 in a region where the speed of sound is 330 m s-1 and the Earth’s horizontal magnetic field is 20.6 micro Tesla. Calculate the magnitude of the voltage induced between the wing tips, 8.0 m apart, if the wings point east-west.Mach 5 means a speed 5 times the (local) speed of sound (Ans. 0.27 V (comment on the size of this!))

Student ExerciseA uniform magnetic field makes an angle of 30O with the axis of a circular coil of 300 turns and a radius of 4 cm. The field changes at a rate of 85 T/s. Find the magnitude of the induced voltage in the coil.

First “picture the problem” – the induced voltage equals N (=300) times the rate of change of flux through each turn. Since B is uniform, the flux through each turn is simply BAcos where A is the area of the coil. (Ans. 111 V)

Components in electric circuits

Resistance R: R= V/I

Capacitance C: C=Q/V

Inductance: L: L=/I

This lecture provides principles that we need to understand electrical energy conversion devices, including motors, generators, and transformers. It also paves the way to the understanding of

electromagnetic radiation.

E-field generated whether or not there is a conducting loop

Suppose we remove the conducting ring, and change the magnetic field.

Will there be an electric field induced?!!

YES!

This raises another very interesting question . . . . .can a changing electric field produce a magnetic field?

YES! James Clerk Maxwell

1831-1879

•A Changing Magnetic Field Creates an Electric Field (Electromagnetic Induction)

•A Changing Electric Field Creates a Magnetic Field

Light is an electromagnetic wave – a wave made up of oscillating electric and magnetic fields – electromagnetic waves are self-propagating!

Thus thanks to electromagnetic induction we can “see” the Universe

Review and Summary•The Laws of Electromagnetic Induction

dt

d B−= = =

Next Topic

Self and Mutual Inductance