Motors Physics 102 Professor Lee Carkner Lecture 20

Ring in Solenoid  If the current flows clockwise through the solenoid, the B field inside is straight down  To get maximum flux, the ring should face up (same direction as solenoid)  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) = T  A = (0.1)(0.1) = 0.01 m 2

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

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   The area of the loop increases by L  x in time  t  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

Generators  What is the most efficient way to use inductance to produce current?   This changing flux produces an emf in the loop  Turn the loop with an external source of work   A machine that converts work into emf is called a generator

Alternating Current  Which way does the current flow?  As the loop turns the flux points in one direction and then the other   If the loop is turned quickly, the changes in direction can occur rapidly   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:  = N(  /  t)   The cos  term changes with time and can be related to the angular frequency  (radians/second)  The change of  with time is thus BA  sin  t, so the emf is:  = NBA  sin  t

Sinusoidal Variations   As the loop makes one complete rotation (  t goes from 0 to 2  radians) the emf goes from 0, to maximum +, to maximum -, and back to zero again   The current through the loop goes one way and then the other, sometimes is weak and sometimes is strong  max

Frequency   The number of these cycles made per second is the frequency f =  /2   1 turn per second (f=1) means 2  radians per second (  =2  )   NBA  is the maximum emf  sin  t tells us where we are in the cycle between positive and negative maximums

Power Generation  A potential difference causes current to flow  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 Currents

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

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 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