Chapter 20Chapter 20

Induced Voltages and Inductance

General Physics

Electromagnetic Induction

Sections 1–4

General Physics

Michael Faraday

1791 – 1867 Great experimental

scientist Discovered

electromagnetic induction Invented electric motor,

generator and transformer Discovered laws of

electrolysis

General Physics

Faraday’s Experiment A current can be induced by a changing magnetic field First shown in an experiment by Michael Faraday

– A primary coil is connected to a battery and a secondary coil is connected to an ammeter

– When the switch is closed, the ammeter reads a current and then returns to zero

– When the switch is opened, the ammeter reads a current in the opposite direction and then returns to zero

– When there is a steady current in the primary circuit, the ammeter reads zero

– WHY?

General Physics

Faraday’s Startling Conclusion

An electrical current in the primary coil creates a magnetic field which travels from the primary coil through the iron core to the windings of the secondary coil

When the primary current varies (by closing/opening the switch), the magnetic field through the secondary coil also varies

An electrical current is induced in the secondary coil by this changing magnetic field

The secondary circuit acts as if a source of emf were connected to it for a short time

It is customary to say that an induced emf is produced in the secondary circuit by the changing magnetic field

General Physics

Magnetic Flux

The emf is actually induced by a change in the quantity called the magnetic flux rather than simply by a change in the magnetic field

Magnetic flux is defined in a manner similar to that of electrical flux

Magnetic flux is proportional to both the strength of the magnetic field passing through the plane of a loop of wire and the area of the loop

General Physics

Magnetic Flux, cont

Consider a loop of wire with area A in a uniform magnetic field The magnetic flux through the loop is defined as

where θ is the angle between B and the normal to the plane SI units of flux are T. m² = Wb (Weber)

B

cosBAABB

Active Figure: Magnetic Flux

General Physics

Magnetic Flux, cont The value of the magnetic flux is

proportional to the total number of lines passing through the loop

When the field is perpendicular to the plane of the loop (maximum number of lines pass through the area), θ = 0 and ΦB = ΦB, max = BA

When the field is parallel to the plane of the loop (no lines pass through the area), θ = 90° and ΦB = 0

Note: the flux can be negative, for example if θ = 180°

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Electromagnetic Induction –An Experiment

When a magnet moves toward a loop of wire, the ammeter shows the presence of a current (a)

When the magnet is held stationary, there is no current (b)

When the magnet moves away from the loop, the ammeter shows a current in the opposite direction (c)

If the loop is moved instead of the magnet, a current is also detected in a similar manner

An induced emf is set up in the circuit as long as there is relative motion between the magnet and the loop

Active Figure: Induced Currents

General Physics

Faraday’s Law and Electromagnetic Induction

The instantaneous emf induced in a circuit equals the time rate of change of magnetic flux through the circuit

If a circuit contains N tightly wound loops and the flux changes by ΔΦB during a time interval Δt, the average emf induced is given by Faraday’s Law:

tN B

General Physics

Faraday’s Law and Lenz’ Law

The change in the flux, ΔΦB, can be produced by a

change in B, A or θ– Since ΦB = B A cos θ

The negative sign in Faraday’s Law is included to indicate the polarity of the induced emf, which is found by Lenz’ Law – The current caused by the induced emf travels in the

direction that creates a magnetic field whose flux opposes the change in the original flux through the circuit

General Physics

Lenz’ Law – Example 1

Consider an increasing magnetic field through the loop

The magnetic field becomes larger with time– magnetic flux increases

The induced current I will produce an induced field ind in the opposite direction which opposes the increase in the original magnetic field

B

B

General Physics

Lenz’ Law – Example 2

Consider a decreasing magnetic field through the loop

The magnetic field becomes smaller with time– magnetic flux decreases

The induced current I will produce an induced field ind in the same direction which opposes the decrease in the original magnetic field

B

B

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Applications of Faraday’s Law – Electric Guitar

A vibrating string induces an emf in a pickup coil

A permanent magnet inside the coil magnetizes a portion of the string nearest the coil

As the string vibrates at some frequency, its magnetized segment produces a changing flux through the pickup coil

The changing flux produces an induced emf that is fed to an amplifier

t

BA

t

General Physics

Applications of Faraday’s Law – Transformer

A varying voltage is applied to the primary coil

This causes a varying current in the primary coil which creates a changing magnetic field which travels from the primary coil through the iron core to the windings of the secondary coil

An electrical current is induced in the secondary coil by this changing magnetic field

The secondary circuit acts as if a voltage were connected to it

11

22 V

N

NV

General Physics

A complete electrical circuit is fashioned by a rectangular loop composed of a conductor bar, two conductor rails, and a load resistance R.

As the bar moves to the right with a given velocity, the free charges in the conductor experience a magnetic force along the length of the bar

This force sets up an induced current because the charges are free to move in the closed path of the electrical circuit

Application of Faraday’s Law – Motional emf

General Physics

Motional emf, cont

As the bar moves to the right, the area of the loop increases by a factor of Δx during a time interval Δt

This causes the magnetic flux through the loop to increase with time

An emf is therefore induced in the loop given by

vBt

xB

t

AB

t

General Physics

Motional emf, cont

The changing magnetic flux through the loop and the corresponding induced emf in the bar result from the change in area of the loop

The induced, motional emf, acts like a battery in the circuit

The induced current, by Ohm’s Law, is

Active Figure: Motional emf

General Physics

Lenz’ Law Revisited – Moving Bar Example 1

As the bar moves to the right, the magnetic flux through the circuit increases with time because the area of the loop increases

The induced current must be in a direction such that it opposes the change in the external magnetic flux

The induced current must be counterclockwise to produce its own flux out of the page which opposes the increase in the original magnetic flux

General Physics

The bar is moving toward the left

The magnetic flux through the loop decreases with time because the area of the loop decreases

The induced current must be clockwise to produce its own flux into the page which opposes the decrease in the original magnetic flux

Lenz’ Law Revisited – Moving Bar Example 2

General Physics

Lenz’ Law Revisited – Moving Magnet Example 1

A bar magnet is moved to the right toward a stationary loop of wire– As the magnet moves, the

magnetic flux increases with time The induced current produces a

flux to the left which opposes the increase in the original flux, so the current is in the direction shown

General Physics

Lenz’ Law Revisited – Moving Magnet Example 2

A bar magnet is moved to the left away from a stationary loop of wire– As the magnet moves, the

magnetic flux decreases with time The induced current produces

an flux to the right which opposes the decrease in the original flux, so the current is in the direction shown

General Physics

Lenz’ Law, Final Note

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