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 No magnetic charges Practice: P2 (p.883)

Ampere: current I  B field

Faraday: dB/dt  E field

Lenz’s law tells DIRECTION of  Induced emf opposes change in flux: Induced current I i creates an induced field B i 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

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 Symmetry: changing electric flux  B Practice: P 5, 10 (p.884)

Ampere-Maxwell Law What can cause a magnetic field B? Ampere: Current I  B: Maxwell: changing E  B:

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