A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m3. What is the magnitude of the potential difference between the center and a point 4.0 cm away?

Explanation:

The given data is as follows.

   Radius of the sphere (R) = 10 cm = 0.01 m   (as 1 m = 100 cm)

   Distance from the center (r) = 4 cm = 0.04 m

   Charge density () = 100

                                  =   (As 1 nm = )

As the relation between charge and potential difference is as follows.

          Q =

              =

              =  

              =

Expression for electric field is as follows.

           E(r) =

Electric potential, V(r) =

               =

               =  

               =  

              = -3 V

Thus, we can conclude that the magnitude of the potential difference between the center and a point 4.0 cm away is -3 V.

t = 1/400 h   ⇔ 0.0025 h ⇔ 9s ⇔ 0.15 m

any of the answers are correct.