CHAPTER-30 Induction and Inductance

Ch 30-2 Two Experiments  First Experiment: An ammeter register a current in the wire loop when magnet is moving with respect to loop.  Faster motion causes more current  By changing the polarity of magnet facing the coil plane, changes the current direction  Second Experiment: An ammeter register a current in the left-hand wire loop just as switch s is opened or closed. No motion of coil is involved  Emf induced in the loop when something is changing in the loop

Ch 30-3 Faraday’s Law of Induction  Faraday’s Law : An emf  is induced in the loop in the previous experiments when the number of magnetic field lines that passes through the loop is changing.  Magnetic Flux through a loop:  B =  B.dA=  B dA cos   B =BA(B  A, B uniform)  Unit of  B : Weber (Wb) 1 Wb= 1T.m 2  Faraday’s Law:  = - d  B /dt = - d(B.A)/dt The magnitude of the emf  induced in a conducting loop is equal to rate at which the magnetic flux is changing through that loop with time Faraday’s Law:  = -N d  B /dt= - d(B.A)/dt N is number of coils Three cases:  B changing with time  = -N A cos  (dB /dt)  Coil Area A changing with time  = -N B cos  (dA /dt)  Angle between B- direction and coil-plane is changing with time  = -N AB (d (cos  ) /dt)

Ch 30-4 Lenz’s Law- definition of direction of induced current in the loop Lenz’s Law: An induced emf has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current  Opposition to Pole movement:  Opposition to Flux change:

Ch 30-4 Lenz’s Law- definition of direction of induced current in the loop Opposition to Flux change

Ch 30-5 Induction and Energy Transfer  A closed conducting loop is pulled out of a magnetic field at constant velocity v. While loop is moving a current I is induced in the loop and the loop segments still within magnetic field experiences forces F1, F2 and F3.  As the loop moves towards right, flux through the coil decreases, induced current will be clockwise   = B d(A)/dt= B d(Lx)/dt =BLdx/dt=BLv i=  /R=BLv/R; Power Disipated P dis =i 2 R=B 2 L 2 v 2 /R  Rate of doing work P=|F 3 |v F 3 =iLB=B 2 L 2 v/R; P=|F 3 |v= (B 2 L 2 v/R) x v =B 2 L 2 v 2 /R

Suggested problems from Chapter 30