Inductors PH 203 Professor Lee Carkner Lecture 20

Finding emf   = -N(d  /dt)  But the magnetic flux depends on the changing current and the properties of the coil   = -L(di/dt)   where the constant of proportionality L is the inductance

Inductance  The unit of inductance is the henry,   Equating the two expressions for   = L(di/dt) = N(d  /dt) L = N(d  /di)   Inductance is a property of the circuit element  Like resistance or capacitance

Solenoid Inductance  To find L, we need a relationship between  and I for a solenoid   Flux in general:   = BA cos  or  = BA   B =  0 (N/l)i or i = Bl/(  0 N)   L = N(d  /di) = N  /i = NBA  0 N/Bl =  0 N 2 A/l L =  0 n 2 Al  Note:   N is number of turns, n is number of turns per meter

Inductors   In a circuit any element with a high inductance is represented by an inductor   We will assume that the rest of the circuit has negligible inductance   Symbol is a spiral:

Motional emf   If we make the loop larger or smaller, or move it in or out of a field, we will induce a potential   remember emf is a potential difference (or voltage)  How does motion in a field translate to voltage?

Motional emf - Derived  Consider a conductor of length L sliding on a frame with velocity v   but  x = v  t, so  A = Lv  t    /  t = B  A/  t = (BLv  t)/  t   = BLv X B field into page v x L  x in time  t AA

Motional emf -- Direction   If the area decreases, the flux decreases and thus the induced B field is in the same direction as the original

Motional emf Energy  How is energy related to motional emf?   The loop feels a magnetic force you have to overcome   The energy goes into the electrical energy of the current in the loop  P = i 2 R

Power and Motional emf  Since  = BLv and  = iR, we can write: i = BLv/R P = B 2 L 2 v 2 /R  Large loops with low resistance moving fast in a large magnetic field will have a lot of electrical energy and thus require more work input

Eddy Currents  Imagine a loop moving out of a magnetic field    If the object is not a loop, circular currents can still be induced which have the same effect  Called eddy currents

Eddy Braking  The field from the eddy currents will produce a force opposite the motion   Can produce magnetic braking  No physical contact with disk, so no wear 

Next Time  Read  Problems: Ch 30, P: 21, 29, 31, 48, 51

What is the direction of current in the loop from the PAL (seen from top down)? A)clockwise B)counterclockwise C)left D)right E)down

A ring undergoes thermal expansion while in a uniform magnetic field. If the current induced in the loop is clockwise, what is the direction of the magnetic field? A)left B)right C)into the page D)out of the page E)counterclockwise

A bar magnet held north pole up is dropped straight down through a face up coil of wire. What is the direction of the current in the coil as the magnet enters and leaves the coil? A)clockwise, counterclockwise B)counterclockwise, clockwise C)clockwise, clockwise D)counterclockwise, counterclockwise E)no current is induced