Transcript A Brief History of Planetary Science

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
F = BA cos q = BA
B = m0nI = (4pX10-7)(1000)(10) = 0.0126 T
A = (0.1)(0.1) = 0.01 m2
Current in Ring
F = BA = (0.0126)(0.01) = 1.26 X 10-4 Wb
In 1 second the flux goes to 0
DF = (1.26 X 10-4) - (0) = 1.26 X 10-4
Dt = 1
e = -N(DF/Dt) = (1)(1.26 X 10-4) = 1.26 X 10-4 V
DV = IR or I = e/R = 1.26 X 10-4/10
I = 1.26 X 10-5 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
DA
X
L
v  The area of the loop increases by
LDx in time Dt
 but Dx = vDt, so DA = LvDt

B field
into
page
x

Dx in
time Dt
 DF/Dt = BDA/Dt = (BLvDt)/Dt
 e = BLv
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 w

From Faraday’s Law:
e = N(DF/Dt)

The cos q term changes with time and can be related
to the angular frequency w (radians/second)
The change of F with time is thus BAw sin wt, so the
emf is:
e = NBAw sin wt
Sinusoidal Variations
emax

As the loop makes one complete rotation (wt goes
from 0 to 2p 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
Frequency

The number of these cycles made per second is the
frequency f = w/2p
1 turn per second (f=1) means 2p radians per second
(w=2p)

NBAw is the maximum emf
sin wt 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, 21.9-21.11
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)
B)
C)
D)
E)
clockwise
counterclockwise
left
right
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)
B)
C)
D)
E)
clockwise, counterclockwise
counterclockwise, clockwise
clockwise, clockwise
counterclockwise, counterclockwise
no current is induced