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Assignment No. 1
THIRD YEAR PHYSICS
Electrodynamics Assignment 1
Q1. (Potential)
a) An infinite conducting plate has a current density of K= K xˆ A/m flowing in the x direction.
Find the B at a distance z1 above and below the conducting plate (above has coordinate z = z1,
below z = -z1). Using B    A calculate A above and below the conducting plate.
b) Write down Maxwell’s Equations in free space and use these equations to define the vector and
scalar potential in time dependent form. What makes potential arbitrary? What is a Lorentz and
Coulomb Gauge?
Q2 (Electric Fields in Matter)
a) A sphere of radius R carries a polarization, P(r) = r 2 ˆr , where rˆ is a unit vector in the radial
direction. Calculate the bound charges, b [C/m2] and b [C/m3]. (Hint: choose the co-ordinates
first)
b) If the applied field that created the polarization is E(r) = r 2 ˆr /(90), calculate D(r) inside the
material and the dielectric constant of the material.
Q3. (Magnetic Fields in Matter)
a) An infinitely long circular cylinder carries a uniform magnetization parallel to its axis of M =
k zˆ , where k is a constant and zˆ is the unit vector parallel to the cylinder axis. Calculate the
bound current densities Jb [A/m2] and Kb [A/m]. (Hint: choose the co-ordinates first)
b) Ignoring any applied field that caused the magnetization, find the magnetic flux density B due to
Jb and Kb inside and outside the cylinder using Ampere’s Law. Comment on the direction and
magnitude in relation to the magnetization.
c) If the magnetization M, was caused by an applied magnetic field intensity of H = k zˆ /9,
calculate the magnetic flux density B in the material, and relative permeability of the material.
(assume the material is linear with no hysteresis) Suggest how to generate and determine the
strength of the applied H field.
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