1. Classical Theory of Electromagnetic Radiation
Chapter 24
Classical Theory of Electromagnetic Radiation

2. Maxwell’s Equations Four equations (integral form) : Gauss’s law
Gauss’s law for magnetism
Faraday’s law
Ampere-Maxwell law
Add Lorentz to complete the list of fundamental equations of electricity and magnetism
Lorentz eq – defines the meaning of electric and magnetic field in terms of their effect on charge
+ Lorentz force

3. Fields Without Charges
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

4. A Simple Configuration of Traveling Fields
Key idea: Fields travel in space at certain speed
Disturbance moving in space – a wave?
1. Simplest case: a pulse (moving slab)
very high and deep slab – fields only inside
Is it consistent with Maxwell’s law?
Note: strictly speaking fields don’t move, they just change in time

5. A Pulse and Gauss’s Laws
Pulse is consistent with Gauss’s law
very hign and deep slab – fields only insude
Is it consistent with Maxwell’s law?
Pulse is consistent with Gauss’s law
for magnetism

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

7. A Pulse and Ampere-Maxwell Law=0

8. A Pulse: Speed of Propagation
E=Bv
E=cB
Spectacular result: Maxwell predicts speed of light for electromagnetic pulse in mid-1800 – but no one at this time could guess the electromagnetic nature of light, though the speed of light was already known.
He got speed of light theoretically from constants epsilon and mu which are easy to measure in experiment
Based on Maxwell’s equations, pulse must propagate at speed of light

9. Clicker In a time Dt, what is DFmag?
A) 0; B) BvDt; C) BhvDt; D) Bxh; E) B(x+vDt)h

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

11. 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:
Fmag/Fele = qvB/qE = vB/cB=v/c

12. Direction of Propagation
Direction of speed is given
by vector product

13. Electromagnetic Radiation
Last shown

14. Electromagnetic Spectrum
Microwave: not because it is used in microwave, but because it has ~micron wavelength
Visible – the whole spectrum from blue to red – the frequency barely changes twice!

16. Maxwell’s Theory of Electromagnetism
( )
Light is electromagnetic wave!
Challenge: Design an electric device which emits and detects electromagnetic waves
1865
Even result that electromagnetic pulses and waves can propogate in space was new and not well accepted.
Maxwell’s theory was based on unusual mechanical ideas about the luminiferous ether and has not been universally accepted. Moreover, Michelson assisted by Morley, performed remakarbly clever experiment that proved the non-exsistence of this ether.
In 1884 Maxwell eqs were redirived by Hertz without assumption of ether, these are the ones we know now as Maxwell’s eqs, Maxwell original eqs did not look like that (different form)

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

18. Accelerated Charges Transverse pulse propagates at speed of light
Since E(t) there must be B
Direction of v is given by: E B v
No magnetic field out of the circle
Ordinary (steady) magnetic field out of page inside – same as radiative.
But this is does not need to be the case – acceleration matters – if it moves up and then slows down – different direction.

19. Accelerated Charges: 3D

20. Magnitude of the Transverse Electric Field
We can qualitatively predict the direction.
What is the magnitude?
Vectors a, r and E always in one plane
Magnitude can be derived from Gauss’s law
Field ~ -qa
Derivation is too complex for this course
Kink in the electric field
Much slower than 1/r2 – makes it possible to affect matter that is very far from the accelerated charges – that is why we see very distant stars.
1. The direction of the field is opposite to qa
2. The electric field falls off at a rate 1/r

21. Exercise a
An electron is briefly accelerated in the direction shown. Draw the electric and magnetic vectors of radiative field. E B
1. The direction of the field is opposite to qa
2. The direction of propagation is given by
Derivation is too complex for this course
Kink in the electric field
Much slower than 1/r2 – makes it possible to affect matter that is very far from the accelerated charges – that is why we see very distant stars.
Quali

22. Exercise
An electric field of 106 N/C acts on an electron for a short time. What is the magnitude of electric field observed 2 cm away?
2 cm
E=106 N/C B
Erad a
1. Acceleration a=F/m=qE/m= m/s2
2. The direction of the field is opposite to qa
3. The magnitude:
E= N/C
4. The direction of propagation is given by
What is the magnitude of the Coulomb field at the same location?

23. 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? B A A D C + C