A total electric charge of 6.75 nC is distributed uniformly over the surface of a metal sphere with radius 20.0 cm. If the potential is zero at infinity, find the value of the potential at the following distances from the sphere (a) 10 cm, (b) 20 cm, and (c) 40 cm.

a) 60 V

b) 125 V

c) 125 V

Explanation:

Given

We are given the total electric charge q = 6.75 nC = 6.75x 10^-9 C distributed uniformly over the surface of a metal sphere with a radius of R = 20.0 cm = 0.020 m.  

Required

We are asked to calculate the potential at the distances

(a) r = 10.0 cm

(b) r = 20.0 cm

(c) r = 40.0 cm  

Solution

(a) Here, the distance r > R so, we can get the potential outside the sphere (r > R) where the potential is given by

V = q/4∈_o                       (1)

r is the distance where the potential is measured and the term 1/4∈_o equals  9.0 x 10^9 Nm^2/C^2. Now we can plug our values for q and r into equation (1) to get the potential V where r = 0.10 m  

V= 1*q/4∈_o*r

 =60 V

(b) Here the distance r is the same for the radius R, so we can get the potential inside the sphere (r = R) where the potential is given by  

V = 1*q/4∈_o*R                (2)    

Now we can plug our values for q and R into equation (2) to get the potential V where R = 0.20 m  

V = 1*q/4∈_o*R

    = 125 V

(c) Inside the sphere the electric field is zero therefore, no work is done on a test charge that moves from any point to any other point inside the sphere. Thus the potential is the same at every point inside the sphere and is equal to the potential on the surface. and it will be the same as in part (b)  

V= 125 V

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