Question

(7) A conducting spherical shell of radius r is charged to a potential V. What is the value of the potential at a distance D from the surface of the sphere? (10 pts)

Answer 1

Given is:-

Radius of the conducting spherical shell = r

Potential = V

Now,

we know that

Given is: Radius of the conducting spherical shell = r Potential = V Now, we know that V = K q/r or V = q/4 pi elementof_0 r Solving for charge q we get q = 4 pi elementof_0 r (V) eq - 1 Now, By Gauss's law the potential at a distance D from the surface will be V' = 1/4 pi elementof_0 q/D by substituting the value of q from eq-1, we get V' = 1/4 pi elementof_0 4 pi elementof_0 r(V)/D which gives us V' = V r/D
or

Solving for charge q we get

eq-1

Now,

By Gauss's law the potential at a distance D from the surface will be

by substituting the value of q from eq-1, we get

which gives us