Transcript Inductors PH 203 Professor Lee Carkner Lecture 20

Inductors
PH 203
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 (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) = 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
Applied Induction

You connect a source of motion to a magnet

The changing flux produces a changing current

Can easily amplify and move the current
Many applications in music
Microphone
Electric Guitar
Induction Devices
Microphone

Speaker

Electric guitar
Pickup magnet magnetizes string, the motion of
which induces current

Tape recorders and players
The tape is magnetized such that when it passes
the tape heads it induces a current
How Does Induction Work?

If we move the wire through a B field
the electrons now have a velocity

This deflection produces an imbalance
of charge

Finding emf

e = -N(dF/dt)
But the magnetic flux depends on the changing
current and the properties of the coil

e = -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 e
e = L(di/dt) = N(dF/dt)
L = N(dF/di)

Inductance is a property of the circuit element
Like resistance or capacitance
Solenoid Inductance
To find L, we need a relationship between F and I
for a solenoid

Flux in general:
F = BA cos q or F = BA

B = m0(N/l)i or i = Bl/(m0N)

L = N(dF/di) = NF/i = NBAm0N/Bl = m0N2A/l
L = m0n2Al
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
DA
X
L
v
B field
into
page
x
 Consider a conductor of length L
sliding on a frame with velocity v

Dx in
time Dt
 but Dx = vDt, so DA = LvDt

 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
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 = i2R
Power and Motional emf
Since e = BLv and e = iR, we can write:
i = BLv/R
P = B2L2v2/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
Force on
Eddy
Currents
Eddy Currents
Imagine a loop moving out of a magnetic field
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
Called eddy currents

Metal objects moving through a magnetic field will
be slowed

Next Time
Read 30.8-30.12
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)
B)
C)
D)
E)
clockwise
counterclockwise
left
right
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)
B)
C)
D)
E)
left
right
into the page
out of the page
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)
B)
C)
D)
E)
clockwise, counterclockwise
counterclockwise, clockwise
clockwise, clockwise
counterclockwise, counterclockwise
no current is induced