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Unformatted text preview: EE1259: Electromagnetic assignment 1 EE1259 Assignment 5 ((Due on 9:30am, October 11, 2007) 1. Point charges Q and –Q are located at (0, d/2,0), and (0, -d/2, 0). Show that at point ( r, θ , φ ), where r>>d 2 4 r Qd V πε φ θ sin sin = Also, find the corresponding E r field 2. A sphere of radius a and dielectric constant ε r has a uniform charge density ρ , show that a. At the center of the sphere: ( ) 1 2 6 2 + = r r a V ε ε ε ρ b. Find the potential at the surface of the sphere. 3. Show that for two infinitely long line charges parallel to the z-axis, having uniform densities ρ L1 =2k πε C/m and ρ L2 =-2k πε C/m passing through (-1,0,0) and (1,0,0), respectively, the potential is given by ( ) ( ) k V 1 2 1 2 / ln , ρ ρ ρ ρ = Where r 2 and r 1 are distances to the point from the line charges 1 and 2, respectively. 4. A volume charge distribution is given in spherical coordinates by ⎩ ⎨ ⎧ > < = a r for a r for a r ) / ( 2 ρ ρ Find the work required to re-arrange the charge with uniform density within the region (r<a). Find the work required to re-arrange the charge with uniform density within the region (r<a)....
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This homework help was uploaded on 04/10/2008 for the course ECE 1259 taught by Professor Chen during the Fall '07 term at Pittsburgh.
- Fall '07