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In the figure below, a solid sphere, of radius a = 1.40 cm is concentric with a

ID: 1525567 • Letter: I

Question

In the figure below, a solid sphere, of radius a = 1.40 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 charge q_1 = +8.00 fc which is distributed uniformly through the sphere; the shell has a charge of q_2 = q_1. What is the magnitude of the electric field at radial distance r = 0? What is the magnitude of the electric field at radial distance r = a/4? What is the magnitude of the electric field at radial distance r = a? What is the magnitude of the electric field at radial distance r = 1.40a? What is the magnitude of the electric field at radial distance r = 2.10a? What is the magnitude of the electric field at radial distance r = 3.20a? What is the net charge on the inner surface of the shell? What is the net charge on the outer surface of the shell?

Explanation / Answer

(a)

at r = 0,

q = 0

so, electric field E = 0

(b)

at r = a/4

E = k*q*r / a^3

E = 9*10^9*8*10^(-15)*a/4 / a^3

E = 9*10^9*8*10^(-15) / 4*(0.014)^2

E = 9.18*10^(-2) N/C

(c)

at r = a

E = k*q / a^2

E = 9*10^9*8*10^(-15) / (0.014)^2

E = 36.73*10^(-2) N/C

(d)

at r = 1.4a (a<r<b)

E = k*q / r^2

E = 9*10^9*8*10^(-15) / (1.5*0.014)^2

E = 16.32 N/C

(e)

at r = 2.1a (b<r<c)

E = 0 (because q = 0)

(f)

at r = 3.2a

+q lies inside the shell and -q lies outside the shell.

so, qnet = 0

therefore, E = 0

(g)

for inner surface,

qi + q1 = 0

qi = -q1 = -8 fC

(h)

for outer surface,

qo = -q1 - q2 = -q1 + q1

qo = 0