A positive charge + q is located at the point x =0, y = a and a negative charge

Question

A positive charge +q is located at the point x =0, y =a and a negative charge q is located at the point x =0, y =+a .

Part A

Derive an expression for the potential V at points on the y -axis as a function of the coordinate y . Take V to be zero at an infinite distance from the charges

Part B

What are the answer to part A if the two charges are interchanged so that +q is at y = +a and q is at y = a ?

Part C

What are the answer to part B if the two charges are interchanged so that +q is at y = +a and q is at y = a ?

Please show organized steps.

Explanation / Answer

A)   V(y) = (1/4)*q*[ -{1/(y-a)}+{1/(y+a)}] = (1/4)*q*[(-y-a+y-a)/(y²-a²)] or
V(y) = -(1/4)*(2aq)*[1/(y²-a²)]

B) and C) With q at (0, a) and -q at (0, -a)
V(y) = (1/4)*q*[ {1/(y-a)}-{1/(y+a)}] = (1/4)*(2aq)*[1/(y²-a²)] for any y

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