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Faraday's Law / Lenz's Law

Quote of the Day

By the way, where do we stand with Maxwell's Equations?

Early in the semester we investigated current flow in a conductor created by application of an electric potential difference across its end. In the past few days, we have investigated the creation of magnetic fields by current distributions. Thus we might say that an electric field can be used to create a magnetic field.

Can a magnetic field produce an electric field?

DEMONSTRATION: Induced Currents
Needed: Nested solenoids, power supply, and projection ammeter.
[Faraday's law]
solenoid on, moving in   current induced
solenoid on, moving out   current reversed
solenoid not moving   no current
power supply reversed   currents reversed

power supply switched on   current induced
power supply switched off   current reversed
power supply steady   no current
power supply unsteady   current induced

Other observations: a relatively small current in the inner solenoid, pulled out of the outer solenoid quickly, can induce a current as large as a relatively large current in the inner solenoid pulled out slowly.

Careful experiment would show that the current induced in the outer solenoid is proportional to the rate at which the magnetic flux linking the turns of the solenoid changes.

Faraday's Law of Induction

[Faraday's law]

The magnitude of the emf induced about a closed loop is proportional to the rate at which the magnetic flux through that loop changes with time.

(Discovered by J. Henry in 1830.) Induced current is set up in a closed conducting loop by an induced emf. This emf is induced by the change of the magnetic flux through the loop. The induced emf appears only when the number of lines of B through loop are changing. The number of lines of B linking loop is not of primary concern, rather the rate of change of number of lines through the loop (the flux) is directly related to the induced emf.

[magnetic flux] Magnetic flux is constructed similar to electric flux:

[magnetic flux]

with the integral over a surface A bounded by a closed loop. For a uniform B field over a planar (flat) surface, the magnetic flux is simply BA. The SI unit of magnetic flux is the weber, but is not a widely used unit; T-m2 is fine for our purposes. Note that no additional proportionality constant is needed in Faraday's law when SI units are used consistently.

Lenz's Law

An induced current has a direction such that the magnetic field due to the induced current opposes the changed in the magnetic flux that induces the current.

[bar magnet approaching loop]

[bar magnet approaching loop]

Adpated from HRW, Fig. 31-4 and 29-4

Concept Check

Quiz 7: Current Distributions

Solution


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Last updated Nov. 2, 1997.
Copyright George Watson, Univ. of Delaware, 1997.