hw2 - ECE 3025 A Problem Set #2 Solutions 1. Let D = 4xyax...

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ECE 3025 A Problem Set #2 Solutions 1. Let D =4 xy a x +2( x 2 + z 2 ) a y +4 yz a z C / m 2 and evaluate surface integrals to Fnd the total charge enclosed in the rectangular parallelepiped 0 <x< 2, 0 <y< 3, 0 <z< 5 m: Of the 6 surfaces to consider, only 2 will contribute to the net outward flux. Why? ±irst consider the planes at y = 0 and 3. The y component of D will penetrate those surfaces, but will be inward at y = 0 and outward at y = 3, while having the same magnitude in both cases. These fluxes will thus cancel. At the x = 0 plane, D x = 0 and at the z = 0 plane, D z = 0, so there will be no flux contributions from these surfaces. This leaves the 2 remaining surfaces at x = 2 and z = 5. The net outward flux becomes: Φ= ! 5 0 ! 3 0 D " " x =2 · a x dy dz + ! 3 0 ! 2 0 D " " z =5 · a z dx dy =5 ! 3 0 4(2) ydy +2 ! 3 0 4(5) ydy = 360 C 2. Use Gauss’s law in integral form to show that an inverse distance Feld in spherical coordinates, D = A a r /r , where A is a constant, requires every spherical shell of 1 m thickness to contain
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This note was uploaded on 10/28/2008 for the course ECE 3025 taught by Professor Citrin during the Spring '08 term at Georgia Institute of Technology.

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hw2 - ECE 3025 A Problem Set #2 Solutions 1. Let D = 4xyax...

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