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