Motors Physics 102 Professor Lee Carkner Lecture 21

Ring in Solenoid   To get maximum flux, the ring should face up (parallel with the coils)  We need to find the flux through the loop before and after the current is switched off   = BA cos  = BA  B =  0 nI = (4  X10 -7 )(1000)(10) =  A = (0.1)(0.1) =

Current in Ring   = BA = (0.0126)(0.01) =  In 1 second the flux goes to 0   = (1.26 X ) - (0) = 1.26 X   t = 1   = -N(  /  t) = (1)(1.26 X ) =   V = IR or I =  /R = 1.26 X /10  I =

Lenz’s Law

Direction of Current (PAL)  If the solenoid has clockwise current what is direction of induced current?   The flux goes from down to zero  Ring tries to counteract change and get original flux back 

Motional emf  Instead of changing the magnetic field, what if we change the loop?   called motional emf   How does motion in a field translate to voltage?

Induced Potential  Suppose we have a straight wire moving in a magnetic field   We can relate the deflection force to the electric force   qE = qvB or E = vB  Since  V = Ed, if L is the length of the wire:   Potential induced in a wire of length L moving at velocity v through a magnetic field B

Motional emf - Derived   The area of the loop increases by L  x in time  t    /  t = (BL  x)/  t   = N(  /  t) = BLv X B field into page v x L  x in time  t

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

Generators  What is the best way to use inductance to produce current?   This changing flux produces an emf in the loop   Falling water, rising steam etc.  Generator converts work into emf

Alternating Current  Which way does the current flow?   Thus the current flows in one direction and then the other   e.g. household current is at 60 Hz, or 60 cycles per second  This is called alternating current

emf From a Generator  Consider a loop of wire rotating in a magnetic field with angular speed    From Faraday’s Law:   The flux is equal to BA cos    The change of  with time is thus BA  sin  t, so the emf is:  = NBA  sin  t

Frequency  How does the emf vary?   As the loop makes one complete rotation (  goes from 0 to 2  radians) the emf goes from 0, to maximum +, to maximum -, and back to zero again   1 turn per second (f=1) means 2  radians per second (  =2  )  max

Today’s PAL  Consider a generator that consists of a single 1 meter by 1 meter loop of wire with a resistance of 15  in a magnetic field of 2 T  How many times per second must you rotate the loop to produce a maximum current of 12 amps?

Power Generation   Produced (in general) in two ways:   Chemical reactions separate charges so that one terminal is + and one is -   A changing magnetic field separates charges

An Alternating Current Generator

Motors  If you run a generator backwards it becomes a motor   Motor converts emf to work   This reduces the emf of the loop and is called back emf  Example: A motor initially has 120 volts, but if the motor produces a back emf of 70 volts, then the total emf is 50 volts

Force on Eddy Curents

Eddy Currents   As the field through the loop drops, it induces a field in the same direction   If the object is not a loop, circular currents can still be induced which have the same effect   Net effect:  Metal objects moving through a magnetic field will be slowed 

Next Time  Read 21.7,  Homework: Ch 21, P 14, 23, 30, 39