Electromagnetic InductionElectricity from Magnetism

Induced Current

When a conductor is moved in a magnetic field, current can be induced (caused)

Faraday’s 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

Faraday’s Law (I)

Induced emf is proportional to the rate of change of magnetic flux passing through a loop of area A

BAcos

Courtesy Dept. of EE Surrey University

is angle between B and a line perpendicular to the face of the loop

Flux applet

Nature of Magnetic Flux

BAcosis a scalarAbove formula comes from “dot product” of B and A whereas

F =Bqvsincomes from “cross” or vector product B x vUnit of magnetic flux is tesla-meter2 or weber

Ways of Changing Flux

Move coil into or out of fieldChange area of coilRotate coil so number of field lines changesChange field strength

Ways Flux will not change Rotate coil around field line – doesn’t

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

Faraday’s Law (II)

Magnetic flux is also proportional to total number of field lines passing through loopWhen = 00 magnetic flux A (A is area of loop perpendicular to magnetic field)When = 900 magnetic flux is zero; no field lines pass through loop. Mathematically

Emf = -N t N is number of loops

Almost calculus

t 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 t = one second. Write an expression for the voltage induced during that intervalEmf =-N t = -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 roleEnergy in the current and voltage must come from somewhereHow this works is called Lenz’s Law

Lenz’s Law

Minus sign in Faraday’s Law reminds us that

Induced current produces its own magnetic fieldThis field interacts with original field to make a forceWork 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 Lenz’s Law with bar magnet and loop)

In Other Words

Physical motion that induces current must be resisted by magnetic forcesSomething has to do work to induce the current, otherwise energy conservation is violated

What is Direction of Current?

Field in this region toward us

loop

Current clockwise

Changing Area – What is the direction of induced current?

Loop area shrinks

1. Field away from us xxx

2. 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

What if Loop Area Increases?

Answers reverse1 CCW2 CW

Another Example of Lenz’s Law

When field is increasing, induced field opposes itWhen 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 changes during t = 0.10 sec.

•A =

•Initial

•Final = zero

•Change in flux is

•Emf = -(100)(-1.5 x 10-3 Wb)/(0.10 s) =

2.5 x 10–3 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 x = v t

•Area increases by A = Lx=L v t

•By Faraday’s law

•Emf = t = BA/t = BLvt/t = 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 F=qvB 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 earth’s 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 aircraft’s need for fuel?

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

The GeneratorGenerators and alternators work by rotating a coil in a magnetic field. They produce alternating current.