MIDTERM 3 UTC Thu-Nov 15, 7:00PM - 9:00PM Course Summaries Unit 1, 2, 3 Provided TA session Monday Homework Review (attendance optional) Bring pencils, calculators (memory cleared)

Chapter 24 Classical Theory of Electromagnetic Radiation

Maxwell’s Equations Gauss’s law for electricity Gauss’s law for magnetism Complete Faraday’s law Ampere’s law (Incomplete Ampere-Maxwell law)

No current inside Current pierces surface Ampere’s Law

Time varying magnetic field leads to curly electric field. Time varying electric field leads to curly magnetic field? I ‘equivalent’ current combine with current in Ampere’s law Maxwell’s Approach

Works! The Ampere-Maxwell Law

Four equations (integral form) : Gauss’s law Gauss’s law for magnetism Faraday’s law Ampere-Maxwell law + Lorentz force Maxwell’s Equations

Time varying magnetic field makes electric field Time varying electric field makes magnetic field Do we need any charges around to sustain the fields? Is it possible to create such a time varying field configuration which is consistent with Maxwell’s equation? Solution plan: Propose particular configuration Check if it is consistent with Maxwell’s eqs Show the way to produce such field Identify the effects such field will have on matter Analyze phenomena involving such fields Fields Without Charges

Key idea: Fields travel in space at certain speed Disturbance moving in space – a wave? 1. Simplest case: a pulse (moving slab) A Simple Configuration of Traveling Fields

Pulse is consistent with Gauss’s law for magnetism A Pulse and Gauss’s Laws

Since pulse is ‘moving’, B depends on time and thus causes E Area does not move emf E=Bv Is direction right? A Pulse and Faraday’s Law

=0 A Pulse and Ampere-Maxwell Law

E=Bv Based on Maxwell’s equations, pulse must propagate at speed of light E=cB A Pulse: Speed of Propagation

Question At this instant, the magnetic flux  mag through the entire rectangle is: A)B; B) Bx; C) Bwh; D) Bxh; E) Bvh

Question In a time  t, what is  mag ? A) 0; B) Bv  t; C) Bhv  t; D) Bxh; E) B(x+v  t)h

Question emf =  mag /  t = ? A) 0; B) Bvh; C) Bv; D) Bxh; E) B(x+v)h

Question A)Eh; B) Ew+Eh; C) 2Ew+2Eh; D) Eh+2Ex+2Ev  t; E)2Ev  t

Question What is E? A) Bvh; B) Bv; C) Bvh/(2h+2x); D) B; E) Bvh/x

Exercise If the magnetic field in a particular pulse has a magnitude of 1x10 -5 tesla (comparable to the Earth’s magnetic field), what is the magnitude of the associated electric field? Force on charge q moving with velocity v perpendicular to B:

Direction of speed is given by vector product Direction of Propagation

Electromagnetic pulse can propagate in space How can we initiate such a pulse? Short pulse of transverse electric field Accelerated Charges

1.Transverse pulse propagates at speed of light 2.Since E(t) there must be B 3.Direction of v is given by: E B v Accelerated Charges

We can qualitatively predict the direction. What is the magnitude? Magnitude can be derived from Gauss’s law Field ~ -qa  1. The direction of the field is opposite to qa  2. The electric field falls off at a rate 1/r Magnitude of the Transverse Electric Field

Field of an accelerated charge vT A B Accelerates for t, then coasts for T at v=at to reach B. cT ct No charge

Field of an accelerated charge vT A B cT ct