Question

In the figure a solid sphere of radius a = 3.20 cm is concentric with a spherical conducting shell of inner radius b = 2.00a and outer radius c = 2.40a. The sphere has a net uniform charge q1 = +3.75 fC; the shell has a net charge q2 = –q1. What is the magnitude of the electric field at radial distances (a) r = 0 cm, (b) r = a/2.00, (c) r = a, (d) r = 1.50a, (e) r = 2.30a, and (f) r = 3.50a? What is the net charge on the (g) inner and (h) outer surface of the shell?

Answer 1

From gauss's law,

E.dA = q / eo

E . 4pi*r^2 = qen / eo

E = q / 4*pi*r^2*eo

(a)

at r = 0,

qenclose = 0

so, E = 0

(b)

At r = a/2

E = kqr / a^3 = kq / 2a^2

E = 9*10^9*3.75*10^(-15) / 2*(0.032)^2

E = 1.64*10^(-2) N/C

(c)

At r = a,

E = kq / r^2

E = 9*10^9*3.75*10^(-15) / (0.032)^2

E = 3.29*10^(-2) N/C

(d)

at r = 1.5a

E = kq / r^2

E = 9*10^9*3.75*10^(-15) / (1.5*0.032)^2

E = 1.46*10^(-2) N/C

(e)

r = 2.3a

E = 0

(f)

at r = 3.5a

E = 0

(g)

Charge on inner surface,

qin = -q = -3.75 fC

Charge on outer surface,

qout = -q + q

qout = 0