AP Physics CIII.E – Electromagnetism

Motional EMF. Consider a conducting wire moving through a magnetic field.

Induced EMF

Magnetic Flux

Three examples of a circular loop in a magnetic field

Faraday’s Law of Electromagnetic Induction

and as t → 0

Motional EMF from Faraday’s Law

Using Lenz’s Law to determine the direction of the induced current. Multiple examples.

Ex. A circular loop whose surface is perpendicular to a magnetic field rotates at a constant angular speed through 45° in 0.5 s. a) What is the induced emf in the loop? b) What is the direction of the induced current?

Ex. A conducting rod of length l moves with constant velocity v along a pair of parallel conducting rails within a uniform magnetic field B. Find the induced emf and the direction of the induced current in the circuit.

Ex. A square loop of wire 2.0 cm on each side contains 5 tight turns and has a total resistance of Ω. The loop is placed 20 cm from a long, straight, current-carrying wire. If the current in the wire is increased at a steady rate of 20 A to 50 A in 2 s, determine the magnitude and direction of the current induced in the square loop. Assume the loop is at such a great distance from the wire, the magnetic field through the loop is uniform and equal to the field strength at the center.

Ex. A rectangular loop of wire 10 cm by 4 cm has a total resistance of 0.005 Ω. It is placed 2 cm from a long straight current carrying wire. If the current in the straight wire is increased at a steady rate from 20 A to 50 A in 2 s, determine the magnitude and direction of the current induced in the rectangular loop.

Induced Electric Fields (Faraday’s Law revisited)

This is Faraday’s Law in terms of an electric field

Ex. A circular loop of wire surrounds an ideal solenoid. The solenoid has 15 000 turns per meter and a radius of 2 cm. The radius of the circular loop is R = 4. 0 cm. If the current in the solenoid is increased at a rate of 10 A/s, what is the magnitude of the induced electric field at each position along the circular wire?

Inductance. Consider a long solenoid . . .

Inductance () or Henry, H

EMF (εL)induced in an inductor (self-inductance)

𝜀𝐿=−𝐿𝑑𝐼𝑑𝑡

So, self-induced EMF occurs in any solenoid where current is changing with

time

RL circuits and transient current (direction of the current)

The induced EMF opposes the change of current in the circuit. Therefore,

immediately after the switch is closed, the inductor acts as a broken wire. A

long time after the switch is closed, the inductor acts as a wire in the circuit. Notice, this is the exact opposite of

capacitors.

Graphs for induced EMF and current for an inductor.

Current and the time constant for an inductor

Energy stored in an inductor

Ex. For the circuit shown a) Find the current in the 10 Ω when the switch is open. b) Find the current in the 15 Ω resistor when the switch is first closed. c) Determine the current in the 10 Ω resistor when the switch has been closed a long time.

Maxwell’s Equations

Magnetic Poles

1. Gauss’ Law for magnetic fields – this equation shows all magnets

must have two poles

2. Gauss’ Law for electric fields (you know this one already)

3. Faraday’s Law for induction – the new and improved version. You

know this one too.

A changing magnetic flux induces an electric field. Will a changing electric flux

induce a magnetic field?

Maxwell’s Law of induction (this isn’t the fourth of his equations yet)

A circular parallel plate capacitor

The direction of the induced magnetic field

4. Ampere-Maxwell Law

4. Ampere-Maxwell LawNote: if there is current but no

changing electric flux, this equation reduces to Ampere’s Law. If there is changing flux but no steady current, this equation reduces to Maxwell’s

Law of induction.