Transcript motional emf

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
F = BA cos q = BA
B = m0nI = (4pX10-7)(1000)(10) =
A = (0.1)(0.1) =
Current in Ring
F = BA = (0.0126)(0.01) =
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) =
DV = IR or I = e/R = 1.26 X 10-4/10
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 DV = 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

X
L
v
B field
into
page
x
Dx in
time Dt
 The area of the loop
increases by LDx in time Dt

 DF/Dt = (BLDx)/Dt
 e = N(DF/Dt) = 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 best way to use inductance
to produce current?

This changing flux produces an emf in the
loop

Falling water, rising steam etc.
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 w

From Faraday’s Law:
The flux is equal to BA cos q

The change of F with time is thus BAw sin wt, so the
emf is:
e = NBAw sin wt
Frequency
How does the emf vary?

As the loop makes one complete
rotation (w goes from 0 to 2p
radians) the emf goes from 0, to
maximum +, to maximum -, and
back to zero again

1 turn per second (f=1) means 2p
radians per second (w=2p)
emax
Today’s PAL
Consider a generator that consists of a
single 1 meter by 1 meter loop of wire
with a resistance of 15 W 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, 21.9-21.11
Homework: Ch 21, P 14, 23, 30, 39