Chapter 23 Induced Emf’s

Induced emf A current can be produced by a changing magnetic field First shown in an experiment by Michael Faraday A primary coil is connected to a battery A secondary coil is connected to an ammeter

Faraday’s Experiment The purpose of the secondary circuit is to detect current that might be produced by the magnetic field When the switch is closed, the ammeter deflects in one direction and then returns to zero When the switch is opened, the ammeter deflects in the opposite direction and then returns to zero When there is a steady current in the primary circuit, the ammeter reads zero

Faraday’s Conclusions An electrical current is produced by a changing magnetic field The secondary circuit acts as if a source of emf were connected to it for a short time It is customary to say that an induced emf is produced in the secondary circuit by the changing magnetic field

INDUCTION Michael Faraday (1791 – 1867) …it appeared very extraordinary, that as every electric current was accompanied by a corresponding intensity of magnetic action at right angles to the current, good conductors of electricity, when placed within the sphere of this action, should not have any current induced through them, or some sensible effect produced equivalent in force to such a current.

Primary Coil Secondary coil G ?

Lenz’s Law Summary of Experimental Findings Vind = - A (dB/dt) EMF is induced in the secondary coil Only when the magnetic field through it changes. Lenz’s Law EMF induced is bigger if the area of coil is bigger. EMF is induced always in the opposite direction of change in magnetic field. Vind = - A (dB/dt) = - d/dt  = A B : magnetic flux

Magnetic Flux The emf is actually induced by a change in the quantity called the magnetic flux rather than simply by a change in the magnetic field Magnetic flux is proportional to both the strength of the magnetic field passing through the plane of a loop of wire and the area of the loop

 = A B┴ B A B┴ B B// = (0.3 x 0.2)(0.175 sin(40)) = 0.06 x 0.112 = 0.0067 T.m2 0.3 m 0.2 m B = 0.175 T 40 B B// B┴

Vind = - d/dt Vt = -3 d/dt - + Net number of loops - + Example 23.2 150 turn loop with a 0.75 cm2 cross-section Magnetic field: 0 T  0.25 T in 3.6 s What is the induced current in the coil? 5 Ohm

Faraday’s Law and Electromagnetic Induction The instantaneous emf induced in a circuit equals the time rate of change of magnetic flux through the circuit If a circuit contains N tightly wound loops and the flux changes by Φ during a time interval t, the average emf induced is given by Faraday’s Law:

Faraday’s Law and Lenz’ Law The change in the flux, Φ, can be produced by a change in B, A or θ Since ΦB = B A sin θ The negative sign in Faraday’s Law is included to indicate the polarity of the induced emf, which is found by Lenz’ Law The polarity of the induced emf is such that it produces a current whose magnetic field opposes the change in magnetic flux through the loop That is, the induced current tends to maintain the original flux through the circuit

Applications of Faraday’s Law – Ground Fault Interrupters The ground fault interrupter (GFI) is a safety device that protects against electrical shock Wire 1 leads from the wall outlet to the appliance Wire 2 leads from the appliance back to the wall outlet The iron ring confines the magnetic field, which is generally 0 If a leakage occurs, the field is no longer 0 and the induced voltage triggers a circuit breaker shutting off the current

Applications of Faraday’s Law – Electric Guitar A vibrating string induces an emf in a coil A permanent magnet inside the coil magnetizes a portion of the string nearest the coil As the string vibrates at some frequency, its magnetized segment produces a changing flux through the pickup coil The changing flux produces an induced emf that is fed to an amplifier

FB = -evB Motional EMF FE = -eE B E - eE = evB E = vB Vind = LE = LvB x x x x x x - - - - - v - eE = evB E = vB Vind = LE = LvB