Winter wk 8 – Thus.24.Feb.05
Review Ch.30 – Faraday and Lenz laws
Ch.32: Maxwell Equations!
• Gauss: q E
• Ampere: I B
• Faraday: dB/dt E (applications)
• Maxwell: dE/dt B
Magnetism in matter
Energy Systems, EJZ
Gauss: charge q  E field
E 
No magnetic
charges
Practice: P2 (p.883)
E

dA


B 
qenc
0
B

dA

0

Ampere: current I B field

B  ds   0ienc
Faraday: dB/dt  E field
dB
 
dt
d
B  dA    E  ds

dt
Lenz’s law tells DIRECTION of 
Induced emf opposes change in flux:
dB
 
dt
Induced current Ii creates an induced field Bi to
oppose any change in the external flux.
In what direction does current flow, in each diagram?
Practice with Lenz’s law
In what direction does current flow, in each loop
Generators & Transformers

d
 N BA cos    t   NBA sin  t 
dt
dB
 V  N
dt
shared flux :
d  B V1 V2
 
dt
N1 N 2
V2
 ________
V1
Power  I1V1  I 2V2
I2
 ________
I1
AC power depends on transformers
Step-up transformer: higher voltage, lower current
Step-down: lower voltage, higher current
Induced magnetic fields: dE/dt  B
Recall Faraday: changing magnetic flux  E field
dB
   E  ds
dt
Symmetry: changing electric flux  B
dE
 0 0
  B  ds
dt
Practice: P 5, 10 (p.884)
Ampere-Maxwell Law
What can cause a magnetic field B?
 0ienc   B  ds
Ampere: Current IB:
Maxwell: changing EB: 0 0 d  E   B  ds
dt
dE
B

ds





i
0
0
0
enc

dt
Practice with magnetic induction
Q1 (p.882): Is E increasing or decreasing?
Q2: Which loop has the greatest magnetic
circulation?
Maxwell Eqns  EM waves
Next week we will combine the Maxwell
equations to
• Derive electromagnetic waves
• Derive the speed of light
Magnetism in matter
Earth’s B field is due to currents
in the molten outer core
Electron spin ~ current loop 
magnetic moment =IA
Magnetic materials have regions
of aligned electron spin
Probs. 67, 72, 73