a) Sho infinite length is E Id b) Using your re ,A/d. 4. A Question 2: (18 point

Question

a) Sho infinite length is E Id b) Using your re ,A/d. 4. A Question 2: (18 points) Consider an infinitely long conducting hollow cylinder of inner radius a, outer radius b, and net charge per unit length 32. This cylinder is surrounded by another larger conducting cylinder with inner radius c, outer radius d, and net charge per unit length 2 The outer radius (d) of the larger cylinder is double that of smaller cylinder (b). a) (12 points) Give the charge per unit length on each cylinder surface. (Note: there are four surfaces in all at radii a through d.) In each case, explain the reason for your choice. insulating rubber material. What charge will reside on each of the four surfaces now? Explain your answers. b) (6 points) The area between these two cylinders is now filled with an uncharged

Explanation / Answer

given

infinitely long hollow conductinf shell

radii= (a,b,c,d)

for inner shell, charge density = 3*lambda

for outer cylinder, charge density = 2*lambda

d = 2b ( given)

a. for the inner most surface at r = a

charge densoty = 0

(as all the charge will accumulate on the outer surface to satisfy gauss' law)

for r = b

charge density = 6*lambda ( to make up for the 0 charge density on the inner surface, this has to have double that to make up for the average charge per unit length)

for r= c

charge density = x

now from gauss law

x + 3*lambda = 0

hence

x = -3*lanbda

for r = d

charge density = y

x + y = 4*lambda

hence

y = 7*lambda

b. when the area between these is filled with uncharged rubber insulator, there will be no change in the charge distribution and it will still reacoomodate accordong to gauss; law

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