A spherical conducting shell with inner radius 3.0cm and outer radius 3.5cm is c

Question

A spherical conducting shell with inner radius 3.0cm and outer radius 3.5cm is centered on the origin. The shell has been given a total charge of +6.0 mu C. At the origin, inside of the shell, there is a point charge of magnitude -2.0 mu C. Use the shell theorem and the behavior of the electric field in conductors to answer the following questions: How much total charge resides on the inner surface of the shell? How much total charge must reside on the outer surface of the shell? What is the surface charge density on the outer surface of the shell?

Explanation / Answer

(A) Qcentre + Qinner = 0

-2 uC + Qinner= 0

Qinner = 2 uC

(b) Qinner + Qouter = 6uC

2uC + Qouter = 6uC

Qouter = 4uC

(c) surface area of outer surface = 4 x pi x R0^2

= 4 x pi x 0.035^2 = 0.0154 m^2

surface charge density = Q / A = 259.84 x 10^-6 C / m^2

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