A charge is located at and a charge is located at . Thus the separation between the two charges is .
The total electric field on the axis can be written as
(a) What is the direction of the total electric field at any point on the axis where ?
(b)What is as a function of for ? Express your answer in terms of, if necessary, , , and the constant (if needed, enter pi for , epsilon_0 for ).
(c) Consider now the limit where , so that
Express, in this limit, in terms of, if necessary, , and . The quantity is called the dipole moment.