Electrical Engineering 117A - Fall 1996 - Midterm 1 - Problem 1 Problem 1 Electrostatics and Dielectrics A point charge q is located in free space a

# Electrical Engineering 117A - Fall 1996 - Midterm 1 -...

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Problem 1 Problem 1. Electrostatics and Dielectrics. A point charge q is located in free space a distance d from a semi-infinite block of dielectric of relative dielectric constant kappa = epsilon / epsilon0. The electrostatic potential for this system is ( (x, y, z) = q/4pi*epsilon0[1/sqrt((x+d) 2 +y 2 +z 2 )) + (1-kappa)/(1+kappa) * 1/sqrt((x+d) 2 +y 2 +z 2 ))], = (q/4pi*epsilon0)(2/1+kappa)1/sqrt((x+d) 2 +y 2 +z 2 )) 10 pts (a) Find the electric field E in the dielectric block region x > 0. 10 pts(b) Find the bound surface charge density sigma-b [C/m2] at the surface x = 0. 10 pts(c) Find the electrostatic force acting on the charge q (both magnitude and direction). 1 PM (1 of 4)1/27/2007 4:35:4
Problem 1 Problem 2. Magnetostatics Faraday's Law An infinite cylindrical solenoid of radius b whose axis lies along the z-axis is partially filled with a concentric ferrite (nonconducting) rod having a radius a < b and permeability u > u0. A low frequency surface current K = phi K0 cos wt [A/m] flows in the phi-direction on the surface of the solenoid at r = b.

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