# Document

```Introduction
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Vending machine
Electricity generator and motor
Electric guitar
Train brake
Wireless battery charger
Airport metal detector
Transformer
CD player and tape cassette
Sunglass
Sail on sunlight
Photos
More
Brief review of E &amp; M
• Gauss’s law
Qin
FE = &Uacute; E • dA =
e0
What is Gauss’s law for magnetic field?
†
• Ampere’s law
dQ
&Uacute; B • ds = m0 I = m0 dt
• Lorentz force law
†
†
F = qE + qV &yen; B
†
FB =
&Uacute; B • dA
dFB
e = -N
dt
The emf induced in a circuit is directly
proportional to the time rate of change of
magnetic†flux through the circuit.
FB =
†
†
†
†
&Uacute; B • dA = B • A = BA cosq
d
e = - (BAcosq )
dt
• B =B(t)
• A = A(t)
• q = q(t)
• Any combinations
d
- cos wt = w sin wt
q = wt
dt
e = BAw sin wt
If there are N turns, what is the emf ?
†
†
Example 31.1
A coil consists of 200 turns of wire having a total
resistance of 2.0 W. Each turn is a square of side
18 cm, and a uniform magnetic field directed
perpendicular to the plane of the coil is turned on.
If the field changes linearly from 0 to 0.50 T in
0.8s, what is the magnitude of induced emf in the
coil, and what is induced current?
dF B
| e |= N
dt
F B = AB cosq = AB cos 0 = AB
dF B d(AB)
dB
=
=A
dt
dt
dt
†
N = 200, A = (0.18m)2 ,
| e |= 4.1V
|e |
I=
= 2.0A
R
†
dB 0.50T - 0T
=
dt
0.80s
Motional emf
qE = qvB
E = vB
e = DV = El = Blv
†
†
Does†a current flow? Is there a
voltage?
Lenz’s law
The polarity of induced emf is such that it tends
to produce a current that creates a magnetic
flux (Lorentz force) to oppose the change in
magnetic flux through the area enclosed by the
current loop (the motion of a conductor)
Example 31.2
Blv
R R
Blv
B 2l 2 v
FB = IlB =
(lB) =
R
R
†
e = Blv
†
e
I=
=
Application of Lenz’s
law
Find the direction of the current induced in
the ring.
Eddy Current:
Application of Lenz’s law
†
Induced electric field
and electrostatic field
• Induced electrical field
produced by changing
magnetic flux
dF B
e = - dt
e = &Uacute; E • ds
dF B
e = &Uacute; E • ds = - dt ≠ 0
†
Nonconservative
Induce electric field in vacuum
• Electrostatic field produced by stationary
charges
&Uacute; E • ds = 0
Conservative
†
DV = 0
Example 31.8
B = 0, r &gt; R
B = m0 nI, r &lt; R
2
†
for r&gt;R
F B = BpR
F B = Bpr 2
for r&lt;R
B = m0 nI = m0 nI max cos wt
† E • ds = E(2 pr) E • ds = - dF B E(2 pr) = - dF B
&Uacute;
&Uacute;
dt
dt
†
2
m
nI
w
R
† E = 0 max
sin wt
for r&gt;R
2r
† maxw
†
m0 nI
E=
r sin wt
for r&lt;R
2
Maxwell’s Equations
Q
&Uacute;&Uacute; E • dA = e
0
&Uacute;&Uacute; B • dA = 0
dF B
&Uacute; E • ds = - dt
dF E
&Uacute; B • ds = m0 I + e0m0 dt
F = qE + qV &yen; B
†
```