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Unformatted text preview: ECE 329 Homework 3 Due: Sept 14, 2010, 5PM 1. In free space, find E if the scalar potential is V ( x,y,z ) = xz 2 V. What is the static charge density ρ ( x,y,z ) ? 2. Given that E = x ˆ x + y ˆ y − 4 ˆ z V/m, determine the potential V ( x,y,z ) if V (0 , , 0) = 0 . 3. Coulomb’s field of a charge Q stationed at the origin of a right-handed Cartesian coordinate system can be expressed as E = Q 4 πϵ o r 2 ˆ r = Q 4 πϵ o r 2 ( x,y,z ) r , where r 2 ≡ x 2 + y 2 + z 2 and r ≥ . a) Verify that ∇ × E = 0 by showing that when ∇ × E is expanded as usual, all of its Cartesian components cancel out exactly. b) Assuming that the electrostatic potential V associated with E is zero at r = ∞ , show that V = Q 4 πϵ o r . Hint: In this spherically symmetric situation, E = −∇ V = − ∂V ∂r ˆ r . 4. Consider a static charge distribution consisting of two infinitesimally thin, parallel sheets of charge in the z = 0 and z = 2 planes. The bottom sheet (at z = 0 ) has an unknown surface charge density...
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This note was uploaded on 11/06/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08