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Electromagnetic Induction

- Electricity from Magnetism

Induced Current

- When a conductor is moved in a magnetic field,

current can be induced (caused) - Faradays Original Experiment

Many Ways to Produce EMF

- Many forms of changing magnetic field can produce

Emf (current) - Magnet or coil or both can move
- Field can turn on or off due to closing or

opening a switch

Faradays Law (I)

- Induced emf is proportional to the rate of change

of magnetic flux FB passing through a loop of

area A - FB BAcosq

q is angle between B and a line perpendicular to

the face of the loop

Flux applet

Courtesy Dept. of EE Surrey University

Nature of Magnetic Flux

- FB BAcosq is a scalar
- Above formula comes from dot product of B and A

whereas - F Bqvsinq comes from cross or vector product

B x v - Unit of magnetic flux is tesla-meter2 or weber

Ways of Changing Flux

- Move coil into or out of field
- Change area of coil
- Rotate coil so number of field lines changes
- Change field strength
- Ways Flux will not change
- Rotate coil around field line doesnt change

number of field lines - Slide coil at constant angle within field

Faradays Law (II)

- Magnetic flux is also proportional to total

number of field lines passing through loop - When q 00 magnetic flux FB BA (A is area

of loop perpendicular to magnetic field) - When q 900 magnetic flux is zero no field

lines pass through loop. Mathematically - Emf -N D FB/ Dt
- N is number of loops

Almost calculus

- D FB/ Dt is time rate of change of flux

Simple example

- A square loop of side a enters a region of

uniform magnetic field B in time Dt one second.

Write an expression for the voltage induced

during that interval - Emf -N D FB/ Dt -a2B/1 second -a2B

Current direction?

- How do we know in what direction, clockwise or

counterclockwise the induced current will flow? - Energy conservation plays a role
- Energy in the current and voltage must come from

somewhere - How this works is called Lenzs Law

Lenzs Law

- Minus sign in Faradays Law reminds us that
- Induced current produces its own magnetic field
- This field interacts with original field to make

a force - Work must be done against this force to produce

induced current or conservation of energy will be

violated

An induced emf always gives rise to a current

whose magnetic field opposes the original change

in flux Applet

How Current Varies

- Link (demonstrates Lenzs Law with bar magnet and

loop)

In Other Words

- Physical motion that induces current must be

resisted by magnetic forces - Something has to do work to induce the current,

otherwise energy conservation is violated

What is Direction of Current?

loop

Current clockwise

Field in this region toward us

What is Direction of Current?

loop

Field in this region away from us

Current counter clockwise

Changing Area What is the direction of induced

current?

- Field away from us xxx
- Field toward us . . .

Answer to 1. CW. Induced field away to restore

existing field

Answer to 2. CCW. Field toward us to restore

existing field

Loop area shrinks

What if Loop Area Increases?

- Answers reverse
- 1 CCW
- 2 CW

Another Example of Lenzs Law

- When field is increasing, induced field opposes

it - When field is decreasing, induced field acts in

the same direction

Diagram courtesy Hyperphysics web site

Example Square coil side 5.0 cm with 100 loops

removed from 0.60T uniform field in 0.10 sec.

Find emf induced.

- Find how flux FB BA changes during Dt 0.10

sec. - A
- Initial FB
- Final FB zero
- Change in flux is
- Emf -(100)(-1.5 x 10-3 Wb)/(0.10 s)

2.5 x 103 m2

1.5 x 10-3 Wb

-1.5 x 10-3 Wb

1.5 volts

Example, continued

- If resistance of coil is 100 ohms what are

current, energy dissipated, and average force

required? - I emf/R 1.5v/100 ohms
- E Pt I2Rt
- F work required to pull coil out/distance

energy dissipated in coil/distance W/d

15mA

2.25 x 10-3 J

0.050 N

Use d 0.05 m since no flux change until one

edge leaves field

EMF in a Moving Conductor

Courtesy P Rubin, university of Richmond

Moving Rod Changes Area of Loop

- Let rod move to right at speed v
- Travels distance Dx v Dt
- Area increases by DA LDxL v Dt
- By Faradays law
- Emf D FB/ Dt BDA/Dt BLvDt/Dt BLv
- B, L and v must be mutually perpendicular

Alternate Derivation of emf BLv

- Force on electron in rod moving perpendicular to

magnetic field strength B with speed v is FqvB

acting downward - Produces emf with top of rod
- CCW conventional current as rod slides to right
- Work to move a charge through rod against

potential difference is - W Fd qvBL. Emf is work per unit charge BLv

Blv Example Voltage across an airplane wing

- Airplane with 70 m wing travels 1000 km/hr

through earths field of 5 x 10-5 T. Find

potential difference across wing. Is this

dangerous? - Emf Blv
- Could such a potential difference be used to

reduce the aircrafts need for fuel?

(5.0 x 10-5 T) (70m) (280 m/s) 1.0volt

The Generator

Generators and alternators work by rotating a

coil in a magnetic field. They produce

alternating current.