hw4 - Phys 3327 Fall 10 HW 4 Due Wednesday 9/29/10 in...

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Phys 3327 Fall 10 HW 4 Due Wednesday 9/29/10 in lecture Homework 4 Laplace Equation (2) Ex. 4.1: Depolarizing Factor Consider an infnitely long dielectric cylinder o± radius a and dielectric constant ± . The cylinder is placed in an electric feld E 0 directed perpendicular to the cylinder’s axis. a) Find the electrostatic potential Φ at all points outside and inside the cylinder. b) Find the corresponding electric feld E . c) Show that the feld inside the cylinder can be written as a superposition o± the applied feld and the incremental feld produced by the polarization induced on the electric cylinder, E = E 0 - 4 πL P , where P is the polarization in the cylinder and L is the ”depolarizing ±actor”. What value does L take? Note: The difference between the actual feld E inside the cylinder and the applied feld E 0 is known as the ”depolarizing feld”. Ex. 4.2: Demagnetizing feld For an arbitrary stationary current density j ( r ), the vector potential A ( r ) reads A ( r )= ± V
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hw4 - Phys 3327 Fall 10 HW 4 Due Wednesday 9/29/10 in...

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