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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 /(90), 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. Page 1