Problem 27.

In a certain region of space, the electric potential is , where A, B, and C are positive constants.

(a)  Calculate the x-, y-, and z-components of the electric field.

(b) At which points is the electric field equal to zero?

Solution

(a) By definition the x-,y- and z-components of electric field are

(b) The electric field is zero if all its components are zero. Therefore:

From these equations we can find: