• Study Resource
• Explore

# Download Electromagnetic Induction

Survey
Was this document useful for you?
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Metadyne wikipedia, lookup

Lorentz force wikipedia, lookup

Aharonov–Bohm effect wikipedia, lookup

Electromagnet wikipedia, lookup

Magnetic monopole wikipedia, lookup

Field (physics) wikipedia, lookup

Maxwell's equations wikipedia, lookup

Superconductivity wikipedia, lookup

Electromagnetism wikipedia, lookup

History of electromagnetic theory wikipedia, lookup

Magnetic field wikipedia, lookup

Neutron magnetic moment wikipedia, lookup

Time in physics wikipedia, lookup

Transcript
```Faraday’s Law and Inductance
Faraday’s Law
• A moving magnet can exert a force on a
stationary charge.
Remember:
• Faraday’s Law of Induction
d m
  N
dt
 
 m   B dA
• Induced emf is directly proportional to the
change in the magnetic flux.
Collapsing Field
• Ex. What is the induced emf in a 100 turn
coil with an area of 0.035 m² when the
magnetic field decreases linearly from 2.5 T
to 0 T in 10 seconds?
B
Moving Loop
• Ex. For a rectangular loop moving through
a magnetic field, plot the total flux, emf,
and force on the loop with respect to time.
v
l
w
d
B l = 20 cm
w = 20 cm
v = 5 m/s
B = 0.75 T
d = 60 cm
R=1W
Motional EMF
• For a moving conductor in a
magnetic field
qE  qvB
or
R
V  lvB
With a resistor attached the
current is
lvB
I
R
l
v
Lenz’s Law
• Polarity of the induced emf is such that it
produces a current that will create a
magnetic flux to oppose the change in
magnetic flux through the loop.
As the loop enters the field
the downward flux increases.
Therefore, the current flows I
in the loop to generate an
upward flux to cancel the
change.
v
Induced EMF
• A changing magnetic field always generates
an electric field.
 
d m
 E  ds   dt
• This electric field is non-conservative and
time varying.
Generators &
Motors
• AC Generator - A spinning loop in a magnetic
field generates an AC voltage.
 m  BA cost 
  NBA sin t 
• Eddy Currents - Currents generated within a
conductor due to changes in the magnetic field.
Induced EMF
• Self induced emf is due to a
change in current.
d m
dI
  N
 L
dt
dt
• Inductance, L
N m
L
I
• Units, henry (H) which is a
V·s/A
Solenoid
• From Ampere’s Law
 
 B  ds  B  l  N0 I
• If the cross sectional area
of the solenoid is A, then
N 0 IA
m  B  A 
• Inductance is then
l
N m N 2  0 A
L

I
l
ds
l
Solenoid (cont.)
• Ex. What is the inductance of a solenoid of
500 turns where the length is 0.05 m and the
diameter of the coil is 0.04 m?
A  r   (0.02m)  1.26 10 m
2
2

3
2

N 2 0 A (500) 2 4 107 N / A2 (1.26 103 m2 )
L

l
(0.05m)
L  7.9 10 3 H
RL Circuits
• After the switch is closed,
Kirchoff’s rules gives
R

dI
  IR  L  0
dt
• Solution is
I (t ) 


1 e
R
 Rt / L
  I 1  e 
t / 
0
• If power supply is shorted out, then
I (t )  I 0 e
t /
L
L

R
RL Circuit Current
• How much current is
flowing in a 10W 0.1H 1.0I0
RL circuit 15 ms after
0.5I0
it is hooked up to a
10V power supply?
0.1H

 10ms
10W

Current Flow
0

10V
15ms / 10 ms
I (t ) 
1 e
 0.78 A
10W

2
3
4
Energy in the
Magnetic Field
• Power is voltage times current, but also the
rate at which work is done.
dI
P  I     IL
dt
dU m
dW
P

dt
dt
dU m
dI
 IL
dt
dt
• Energy Density of a solenoid:
Um
B2
um 

A  l 2 0
U m  LI
1
2
2
Important E & M
Equations
• Maxwell’s Equations
  Q
 E  dA 
0
 
B

d
A

0

• Lorentz Force
 
d m
 E  ds   dt
 
d e
 B  ds  0 I   0 0 dt


 
F  qE  qv  B
```
Related documents