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Unformatted text preview: EE 1 - Homework #1 Solutions (1) R R 2 R d d =? (R, , and define the spherical coordinate system) Physically, the above integral is summing the unit vector R over the entire sphere. If we inspect the figure below, one can see that for every vector, there is exactly one other vector in the exact opposite direction with the same magnitude ( | R | = 1). Therefore, every vector will have one other that will cancel it out. The sum total would be equal to zero: Z Z 2 R d d = 0 . Mathematically, the same can be obtained by revealing the dependence of R on and . R = rsin + zcos = xcossin + ysinsin + zcos The integral would then be: Z Z 2 R d d = x Z Z 2 cossin d d + y Z Z 2 sinsin d d + z Z Z 2 cos d d =- xsin | 2 cos | + ycos | 2 cos | + zsin | = x (0- 0)(2) + y (1- 1)(- 2) + z (0- 0) = 0 ....
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This note was uploaded on 06/18/2008 for the course EE 1 taught by Professor Joshi during the Spring '08 term at UCLA.
- Spring '08