[email protected] Schuster 4-11 · 2019-10-20 · 3.11 Magnetostatics in a magnet...
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Electromagnetism PHYS20141 Paul.Campbell-3@manchester.ac.uk Schuster 4-11
Transcript of [email protected] Schuster 4-11 · 2019-10-20 · 3.11 Magnetostatics in a magnet...
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Lecture 9
- Potential formulation- Lorentz invariance & Lorentz transformations
for E & B- Static fields & special relativity
Remember
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Lorenz gauge
As in the static case the choice is not unique
This is called gauge freedom. It is described in the printed notes that one can always make the choice
which is known as the Lorenz gauge conditionPHYS20141 Electromagnetism4
Not a spelling mistake !
Lorentz transformations
Consider a z-directed LT
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Lorentz invariance
On the printed notes it is shown that Maxwell’sequations are invariant under LT
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Remember
Wire in z-direction with static line charge
Wire in z-direction with current I
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Consider the x-y planeS
No B-field
E-field Const |E|
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Consider the x-y planeS S’
No B-field
E-field Const |E| Const |E’|E’-field
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Consider the x-y planeS S’
No B-field
E-field Const |E| Const |E’|E’-field
B’-field
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3. EM in simple materials
3.1 Conductors3.2 Method of images3.3 Capacitance, relative permittivity & dielectrics3.4 Polarization & electric susceptibility3.5 Mechanisms for polarization3.6 Electrostatics in a dielectric3.7 Interfaces between dielectrics
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3. EM in simple materials
3.8 Inductance & relative permeability3.9 Magnetization & magnetic susceptibility3.10 Diamagnetism and paramagnetism3.11 Magnetostatics in a magnet3.12 Interfaces between magnets3.13 Ferromagnetism3.14 Ideal ferromagnetism3.15 Electromagnets and hysteresis
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Lecture 10
- Ohm’s law - Relaxation time- Method of images- Force on a particle near a conductor
Conductivity
conductivity [m-1]
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dl
dS
Example : a metal
Metal with one free electron per atom
- RMS velocity : <v2>1/2
- Mean free path : L- Time between collisions : - Drift velocity : vdrift
NB insulators have 10-15 m-1
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Relaxation time
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{8 x 10-19 s metal
8 x 103 s insulator
“Characteristic time for electrons to rearrange themselves”
Point charge near conductor
Physical picture :Conduction electrons are attracted to the surface of the conductor creating a surface charge density, s(NB tR = 0!)
Mathematical picture :Solve Poisson’s equation for subject to the boundary condition that (x,y,0)=0. NB this will be unique as shown in lecture 2
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Physical picture
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Mathematical problem
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Comparison of field lines
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Methods of images
Image charge
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Comparison of field lines
