AP Physics C III.E – Electromagnetism

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

Three examples of a circular loop in a magnetic field

Faraday’s Law of Electromagnetic Induction

Motional EMF from Faraday’s Law

Using Lenz’ Law Determine the direction of the flux change Using the word “increase” describe the direction of an induced magnetic field that opposes the initial change Use RHR-2 to determine the direction of the induced current that opposes the change

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

y l r

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 rectangular loop of wire 10 cm by 4 cm has a total resistance of 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)

Ex. A circular loop of wire surrounds an ideal solenoid. The solenoid has 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...

EMF (ε L )induced in an inductor (self- inductance)

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. The inductor seeks to maintain the status quo. Notice, this is the 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.

LC - circuits

Maxwell’s Equations

Magnetic Poles

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

A circular parallel plate capacitor

The direction of the induced magnetic field

4. Ampere-Maxwell Law Note: 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.