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Electromagnetic Induction. A changing magnetic field generates a current. Faraday’s Induction Law. Emf  electromotive force Induced emf ( ε )  voltage Induced emf is proportional to the area of the loop penetrated perpendicularly by the field.

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faraday s induction law
Faraday’s Induction Law
  • Emf electromotive force
  • Induced emf (ε)  voltage
  • Induced emf is proportional to the area of the loop penetrated perpendicularly by the field.
  • Simply put: ε is proportional to magnetic flux.

ε = -ΔΦ/Δt

ε measured in V


Each coil in a wire will experience an induced emf, so as you add coils…(N is number o’ coils)

ε = -N (ΔΦ/Δt)


One of the fundamental eqns of electromagnetism. Not really derived from prev formulas, more from observation.

example 1
Example 1
  • A circular flat coil of 200 turns of wire encloses an area of 100 cm2. The coil is immersed in a uniform perp magnetic field of 0.50 T that penetrates the entire area. If the field is shut off so that it drops to zero in 200 ms, what is the avg induced emf? Given that the coil has a resistance of 25 Ω, what current will be induced in it?
lenz s law
Lenz’s Law
  • The induced emf will produce a current that always acts to oppose the change that originally created it.
  • In human speak: whatever is caused (induced) by a flux changed over time must go against that change rather than add to it.
  • Why? Otherwise MAGIC happened. COE is violated.
example 2
Example 2
  • A bar magnet is moved rapidly toward a 45 loop coil of wire. As the magnet moves, the magnetic flux through the coil increases from 1.3 x 10-5 T•m2to 3.7 x 10-5T•m2 in0.25 s. What is the magnitude of the induced emf?
motional emf
Motional emf
  • If you have a moving charge (like through a wire) moved perp across a B at speed v,

FM = qvB sinϴ = qvB

example 3
Example 3
  • A 1.0 m long wire in a horizontal east-west orientation is dropped at a place where the Earths’ mag field is 2.0 x 10-5 T, due north. Determine the induced emf 4.0 s after release.