Question

3. (20) A spherically symmetric charge distribution creates the following electric field (2) E E,r with 20 r r < a for 4meoa3 (3) E,= Q 4mor2 for r> a where Q and a are positive constants of suitable units. (a) Draw a graph of E, for 0 <r3a; please label your graph clearly (b) Calculate the charge distribution that generates this electric field. (c) Draw a graph of the charge distribution for 0 <r< 3a; please label your graph clearly. 4. (20) Method of images The figure shows a head-on view of a thick grounded conducting plate that spans the x-y plane. Above it are two point charges: 91 q has coordinates (-a, 0, b) and 92- has coordinates (a, 0, b), where q, a, and b are positive constants of b 9:-9 -a suitable units. (a) Two image charges are required to describe the potential for z > 0. Add the images charges to the figure and write down their charge values and positions. (b) Write down the potential for z> 0 and show that the potential satisfies the boundary condition at the surface of the conductor. (c) By symmetry, what direction do you expect the electric field to have for points on the 2-axis above the conductor? (d) (Leave for last) Calculate the electric field component you determined in (c) for points on the 2-axis above the conductor and find its limit when :b2a.

Answer 1

W23. Члбоо Baza fox untoa Aromat za 3A for Er rea Era or directly proportional to the distance. so graph will blinear for rca. for roa Ex & 1 or inversely proportional to the square of the distance. As distance increase electric field decreases rapidly. guap will be parabolic.

for rsa *D. E= 1 406 var 22 for change distribution volume charge dersity which is 60 for rea or zero for rosa

chog 2 * 60 ут 93 a 2 a 3 a
To calculate charge from charge density use divergence of spherical bodies.