# PHYS208 10/31 Class

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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. 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.

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 is constructed similar to electric 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.

Adpated from HRW, Fig. 31-4 and 29-4

Solution