Faraday’s Law and Inductance

Faraday’s Law A moving magnet can exert a force on a stationary charge. Faraday’s Law of Induction Induced emf is directly proportional to the change in the magnetic flux. Remember:

Collapsing Field Ex. What is the induced emf in a 100 turn coil with an area of m² when the magnetic field decreases linearly from 2.5 T to 0 T in 10 seconds? B

Moving Loop Ex. For a rectangular loop moving through a magnetic field, plot the total flux, emf, and force on the loop with respect to time. w l v Bl = 20 cm w = 20 cm v = 5 m/s B = 0.75 T d = 60 cm R = 1  d

Motional EMF For a moving conductor in a magnetic field or With a resistor attached the current is R v l

Lenz’s Law Polarity of the induced emf is such that it produces a current that will create a magnetic flux to oppose the change in magnetic flux through the loop. v I As the loop enters the field the downward flux increases. Therefore, the current flows in the loop to generate an upward flux to cancel the change.

Induced EMF A changing magnetic field always generates an electric field. This electric field is non-conservative and time varying.

Generators & Motors AC Generator - A spinning loop in a magnetic field generates an AC voltage. Eddy Currents - Currents generated within a conductor due to changes in the magnetic field.

Induced EMF Self induced emf is due to a change in current. Inductance, L Units, henry (H) which is a V·s/A

Solenoid From Ampere’s Law If the cross sectional area of the solenoid is A, then Inductance is then ds l

Solenoid (cont.) Ex. What is the inductance of a solenoid of 500 turns where the length is 0.05 m and the diameter of the coil is 0.04 m?

RL Circuits After the switch is closed, Kirchoff’s rules gives Solution is R L  If power supply is shorted out, then

RL Circuit Current How much current is flowing in a 10  0.1H RL circuit 15 ms after it is hooked up to a 10V power supply? 0  0.5I 0 1.0I 0 Current Flow

Energy in the Magnetic Field Power is voltage times current, but also the rate at which work is done. Energy Density of a solenoid:

Important E & M Equations Maxwell’s Equations Lorentz Force