HW84_4 - Problem 3 a) What is the unit of fictitious...

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Electromagnetics School of Electrical and Computer Engineering University of Tehran Homework 4 Fall Semester 1384 Due 84/8/16 Problem 1 a) Consider the product of a scalar field ) ( r r ψ by a constant vector a r , and obtain ) ( 2 a v r . b) Assume that ) ( r C r r is a divergence-less vector field with finite extent. Now, we define the vector field ) ( r F r r by: v d r C r r r F V = ) ( 1 ) ( r r r r r r Evaluate the vector Laplacian of ) ( r F r r , that is ) ( 2 r F r r r . Does the choice of the volume V affect the result? Problem 2 In free space on the 0 = y plane, an electric current flows in the z -direction. The current is uniform with a density of 1 A/m . a) We wish to describe this current with the help of J r (volume current density) instead of K r (surface current density). Give an expression for J r . b) Obtain B r and H r produced by this current everywhere in space.
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Unformatted text preview: Problem 3 a) What is the unit of fictitious magnetic charge m q ? Explain. a) In free space, the region a x &lt; , a y &lt; , L z ≤ ≤ of the rectangular coordinate system is occupied by z-directed, microscopic magnetic dipoles such that the magnetization vector inside this region is given by z M M o ˆ = r . ( o M is a constant.) Determine the scalar magnetic potential produced by these dipoles on the z-axis. Problem 4 The magnetization vector in the region b r a ≤ ≤ &lt; , L z ≤ ≤ of a cylindrical coordinate system is assumed to be o M r a M ϕ ˆ = r with o M as a constant. Use a) equivalent currents and b) fictitious magnetic charges to determine B r and H r everywhere in free space. M. Shahabadi...
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