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
0
E dA encE
q
B dA 0B ��������������
No magnetic charges
Practice: P2 (p.883)
Ampere: current I B field
0 encB ds i ����������������������������
Faraday: dB/dt E field
Bd
dt
B dAd
E dsdt
����������������������������
Lenz’s law tells DIRECTION of
Induced emf opposes change in flux:
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?
Bd
dt
Practice with Lenz’s law
In what direction does current flow, in each loop
Generators & Transformers
cos sind
BA t NBA tdt
N
1 2
1 2
2
1
1 1 2 2
2
1
:
________
________
B
B
d
dtshared flux
d V V
dt N N
V
V
Power I V I V
I
I
V N
AC power depends on transformers
Step-up transformer: higher voltage, lower current
Step-down: lower voltage, higher current
Induced magnetic fields: dE/dt B
BdE ds
dt
����������������������������
Recall Faraday: changing magnetic flux E field
Symmetry: changing electric flux B
0 0Ed
B dsdt
����������������������������
Practice: P 5, 10 (p.884)
Ampere-Maxwell Law
What can cause a magnetic field B?
Ampere: Current IB:
Maxwell: changing EB: 0 0Ed
B dsdt
����������������������������
0 enci B ds ����������������������������
0 0 0E
enc
dB ds i
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
