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Unformatted text preview: ECE 329 Homework 3 Due: Feb 4, 2008, 5PM 1. Gauss’s law for magnetic field B states that the surface integral S B · d S = 0 over any closed surface S enclosing a volume V . a) Show that a magnetic vector field specified as B = 10 4 ( y ˆ x x ˆ y ) Teslas (or Wb/m 2 ) satisfies this constraint for a surface S defined to be the surface of a cube with volume V = L 3 m 3 having vertices at (0 , , 0) and ( L, L, L ) m — specifically compute S B · d S explicitly by summing parts of S B · d S for all six surfaces of volume V . b) How would the magnetic flux S B · d S over surface S change if volume V were displaced in z direction? in x direction? 2. Gauss’s law for electric field E states that S o E · d S = V ρdV over any closed surface S enclosing a volume V in which charge density is specified by ρ ( x, y, z ) C/m 3 . The surface integral on the left can be termed the “displacement flux” since o E is known as displacement vector and abbreviated as D = o E ....
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This note was uploaded on 04/14/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 FRANKE

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