Chapter 24 Classical Theory of Electromagnetic Radiation

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) Note: strictly speaking fields don’t move, they just change in time 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

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

Clicker 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: F mag /F ele = qvB/qE = vB/cB=v/c

Direction of speed is given by vector product Direction of Propagation

Electromagnetic Radiation

Electromagnetic Spectrum

Light is electromagnetic wave! Challenge: Design an electric device which emits and detects electromagnetic waves ( ) Maxwell’s Theory of Electromagnetism

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

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

Accelerated Charges: 3D

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 Vectors a, r and E always in one plane

An electron is briefly accelerated in the direction shown. Draw the electric and magnetic vectors of radiative field. 1. The direction of the field is opposite to qa  aa E 2. The direction of propagation is given by B Exercise

An electric field of 10 6 N/C acts on an electron for a short time. What is the magnitude of electric field observed 2 cm away? 2 cm E=10 6 N/C 1. Acceleration a=F/m=qE/m= m/s 2 a 2. The direction of the field is opposite to qa  E rad 3. The magnitude: E= N/C 4. The direction of propagation is given by B What is the magnitude of the Coulomb field at the same location? Exercise

Question A proton is briefly accelerated as shown below. What is the direction of the radiative electric field that will be detected at location A? + A A B C D