Unit 5: Electromagnetism

Day 1: Faraday’s Law of Induction

Objectives:

• Induced EMF• Electromagnetic Induction• Magnetic Flux• Faraday’s law of Induction• Lenz’s Law & it’s Applications

Induced EMF

• Michael Faraday built a circuit that would produce a current in a secondary winding of a transformer by allowing a current to flow through the primary winding. The result was a magnetic field produced in the primary winding

• The core intensified the magnetic field which produced a current spike in the secondary winding

• Faraday concluded that the changing magnetic field through the primary coil is what was responsible for the current pulse in the secondary

• The current pulse in the secondary coil is called the induced current

• If the output current fed a load resistor R, then the induced voltage would be E=IR, called the induced EMF

• These experiments led to the development of Faraday’s theories of Electromagnetic Induction

• Further experiments doing the opposite, yielded similar results

• Moving a magnet through a coil also produces a current pulse in a wire. Again, Faraday concluded that it was due to the change in magnetic field that caused the current pulse

Magnetic Flux• Out of Faraday’s investigations, the development of the

concept of magnetic flux developed (similar to electric flux)

for any surface A, made of infinitely small segments dA, of arbitrary shape:

cosBAABB

dABABB

Magnetic Flux

• The number of flux lines per unit area is proportional to the strength of the magnetic field

• In a loop or coil of wire, the number of B-Field lines passing through or are enclosed by the loop, is the magnetic flux

dABABB

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2

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Faraday’s Law of Induction• Faraday identified that it was the change in the magnetic

field in a coil, that induced an EMF in the circuit (coil)

• This is Faraday’s Law of Induction• If more than one loop is in the coil, then the induced EMF

is:

• Note: • The induced current in the circuit will therefore be:

where R = the resistance of the coil of wire

dt

d B

dt

dN B

dABorAdBeitherd B

RI

Lenz’s Law• The negative sign in Faraday’s Law in Induction is an

indication of the direction of the induced EMF.

• The current produced by the induced EMF moves in a direction so that the magnetic field created by the induced current, opposes the original change in flux

This is Lenz’s Law

Explanation of Lenz’s Law1. Given a closed conducting loop with B-Field flux lines through the loop

2. Determine whether the magnetic flux is increasing or decreasing. This will determine the direction of the conventional induced current

3. The induced current produces (or induces) a magnetic field which opposes the original externally applied magnetic field direction

Explanation of Lenz’s Law

4. Use the RHR to determine the direction of the induced current & induced EMF from the induced magnetic field

Example: Pulling a Coil Through a Magnetic Field

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J

d

U

d

WF

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clockwiseAV

RI

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B

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1.0

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