Flux and nonconducting shells A charged particle is suspende

Flux and nonconducting shells. A charged particle is suspended at the center of two concentric spherical shells that are very thin and made of nonconducting material. Figure (a) shows a cross section. Figure (a) gives the net flux phi through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by phi_s = 7.5 Times 10^5 N middot m^2/C. What is the charge of the central particle? What are the net charges of shell A and shell S?

Solution

From Guass\'Law,

Electric flux from closed surafce = Qin / e0

for r < rA

Qin = q (where q is charge on central charge)

flux = q / e0 = 0.4 @s

q / (8.854 x 10^-12) = 0.4 x 7.5 x 10^5

q = 2.66 x 10^-6 C Or 2.66 uC

b) for rA < r < rB

flux = (q + qA)/e0 = -0.8(@s)

(2.66 x 10^-6 + qA) / (8.854 x 10^-12) = - 0.8 x 7.5 x 10^5

qA = - 7.97 x 10^-6 C Or - 7.97 uC

c) for r > rB

flux = (q + qA + qB)/e0 = 1.2@s

(2.66 x 10^-6 - 7.97 x 10^-6 + qB) / (8.854 x 10^-12) = 1.2 x 7.5 x 10^5

qB = 13.28 x 10^-6 C Or 13.28 uC