Question

A positive charge q is fixed at the point x = 0, y = 0, and a negative charge -2q is fixed at the point x = a, y = 0.

a) Derive an expression for the potential V at points on the x -axis as a function of the coordinate x . Take V to be zero at an infinite distance from the charges. (Express your answer in terms of the given quantities and appropriate constants).

V(x) =

b) At which positions on the x -axis is V = 0? (Enter your answers numerically separated by commas).

x/a =

c) What does the answer to part A become when x>>a ?

V =

d) Explain why this result is obtained.

Answer 1

a) Considering the image above

In general:

Is important to know that the denominator is the distance therefore must be positive

b) We have to solve V(x) = 0

simplifying

The solution are

and

c) When x >> a

so the electrical potential is:

d) When you have x>>a the d

the distance between charges is very small, and You can see both charges as a single point charge of net charge

So the electrical potential of this charge is:

Regards