Chapter 22

Electromagnetic Induction

21.7 Magnetic Fields Produced by Currents

The direction of the magnetic field due to a current-carrying wire can be determined by the RHR-2.

21.7 Magnetic Fields Produced by Currents

A loop of wire also generates a magnetic field. Once again the direction can be determined with the RHR-2.

21.7 Magnetic Fields Produced by Currents

Comparison of the magnetic field of a current-carrying loop with that of a bar magnet

21.7 Magnetic Fields Produced by Currents

A solenoid consists of multiple loops of wire. It’s magnetic field is shown below

Induced Current

• A current creates a magnetic field

• Is the opposite true?• Can a magnetic field

create, or induce a current?

• In 1831, Michael Faraday made an exciting discovery

Faraday’s Discovery

• Faraday was hoping that the magnetic field generated by the current on the left circuit would induce a current in the wire on the right.

• But no luck, as the meter shows.

Faraday’s Discovery

• Disappointed, he shut down for lunch.

• But when he opened the switch to cut off the current in the left circuit, the meter suddenly moved, showing a momentary current in the wire on the right.

• It quickly went back to zero.

Faraday’s Discovery

• Baffled, he closed the switch again.

• And noticed that the meter jumped again momentarily, and this time the meter needle went the other way.

• I bet he actually did it a bunch of times before he noticed that it went the other way..

Faraday’s Law• Faraday found that he could induce a

current in a closed wire, but only if the magnetic field through the coil is changing.

• This is an informal statement of Faraday’s Law.

22.1 Induced Emf and Induced Current

There are a number of ways a magnetic field can be used to generate an electric current.

It is the changing magnetic field that produces the current.

Magnetic Flux due to an external magnetic field

Φm = AB cos θ

A = cross-sectional area of the loop (m2 )

B = strength of magnetic field (Tesla)

θ = angle between B, and normal to AUnits: 1 weber = 1Wb = 1Tm2

Rank the magnitude of magnetic flux that passes through the coil, shown below (edge view) in three different orientations relative to an external magnetic field. Rank from greatest flux to least.

a. 1,2,3 b. 3,2,1 c. (1,3), 2 d.(3,1), 2

Rank the magnitude of magnetic flux that passes through the coil, shown below (edge view) in three different orientations relative to an external magnetic field. Rank from greatest flux to least.

a. 1,2,3 b. 3,2,1 c. (1,3), 2 d.(3,1), 2

Numerical Problem

• A magnetic field has a a magnitude of 0.078 T and is uniform over a circular surface of radius 0.10 m. the field is oriented at an angle of 25˚ with respect to the normal of the surface. What is the magnetic flux through the surface?

Numerical Problem

• A magnetic field has a a magnitude of 0.078 T and is uniform over a circular surface of radius 0.10 m. the field is oriented at an angle of 25˚ with respect to the normal of the surface. What is the magnetic flux through the surface?

• Answer: 2.2 x 10-3 Wb

22.3 Magnetic Flux

GRAPHICAL INTERPRETATION OF MAGNETIC FLUX

The magnetic flux is proportionalto the number of field lines that passthrough a surface.

Lenz’s Law

• There is an induced current in a closed conducting loop only if the magnetic flux is changing (either B, A or θ). The direction of the induced current is such that the induced magnetic field opposes the change.

22.5 Lenz’s Law

LENZ’S LAW

The induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change.

Using Lenz Law1. Determine the direction of the external magnetic

field. 2. Determine how the flux is changing. Is it increasing,

decreasing, or staying the same?3. Determine the direction of an induced magnetic field

that will oppose the change in the flux.– Increasing: induced magnetic field points opposite

the external magnetic field.– Decreasing: induced magnetic field points in the

same direction as the external magnetic field.– Constant: no induced magnetic field.

4. Determine the direction of the induced current. Use the right-hand rule.

Lenz’s Law

An induced current in a coil or loop can be created 2 ways:– Change the size or

orientation of the coil in a stationary magnetic field.

– Change the strength of the magnetic field through a stationary circuit.

Both of these create a changing magnetic flux.

The current exists because the changing magnetic flux has induced an emf. In a closed circuit with a resistance, R:

I = ε/R

The current is a consequence of the induced emf.

The emf is a consequence of changing flux (Φm )

Lenz’s LawAn external magnetic

field, B is directed into the page. A sliding rail completes the circuit. The rail is pushed to the right, increasing the area of the circuit.

Lenz’s LawIn which direction is

the induced magnetic field?

a. into the page

b.out of the page

c. zero, since field is stationary

d. in the direction of the moving rail

Lenz’s LawIn which direction is

the induced magnetic field?

a. into the page

b.out of the page

c. zero, since field is stationary

d. in the direction of the moving rail

Area of loop (A) is getting bigger so magnetic flux Abcos ɸ increases.

Lenz’s Law

Lenz’s Law

22.4 Faraday’s Law of Electromagnetic Induction

FARADAY’S LAW OF ELECTROMAGNETIC INDUCTION

The average emf induced in a coil of N loops is

tN

ttN

o

o

E

SI Unit of Induced Emf: volt (V)

If the coil makes a closed circuit, a current will flow as a result of the induced emf (potential difference).

The negative sign shows that the induced emf is generated in such a direction as to create an induced magnetic field that opposed the change in flux.

22.4 Faraday’s Law of Electromagnetic Induction

Example 5 The Emf Induced by a Changing Magnetic Field

A coil of wire consists of 20 turns each of which has an area of 0.0015 m2.A magnetic field is perpendicular to the surface. Initially, the magnitude of the magnetic field is 0.050 T and 0.10s later, it has increased to 0.060 T.Find the average emf induced in the coil during this time.

V 100.3

s 0.10

T 050.0T 060.00cosm 0015.020cos

coscos

3

2

t

BBNA

t

ABBAN

tN

o

o

E

22.5 Lenz’s Law

LENZ’S LAW

The induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change.

22.5 Lenz’s Law

LENZ’S LAW

The induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change.

Reasoning Strategy

1. Determine whether the magnetic flux that penetrates the coilis increasing or decreasing.

2. Find what the direction of the induced magnetic field must beso that it can oppose the change influx by adding or subtracting from the original field.

3. Use RHR-2 to determine the direction of the induced current.

22.5 Lenz’s Law

Conceptual Example 8 The Emf Produced by a Moving Magnet

A permanent magnet is approaching a loop of wire. The external circuit consistsof a resistance. Find the direction of theinduced current and the polarity of the induced emf.

22.5 Lenz’s Law

Conceptual Example 9 The Emf Producedby a Moving Copper Ring.

There is a constant magnetic field directed into the page in the shaded region. The fieldis zero outside the shaded region. A copperring slides through the region.

For each of the five positions, determine whetheran induced current exists and, if so, find itsdirection.