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