Consider the arrangement of point charges described in Exercise (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. (b) At which position on the y-axis is V = 0? (c) Graph V at points on the y-axis as a function of y in the range from y = −2a to y = +2a. What does the answer to part (a) become when y > a? Explain result is obtained.
Exercise:
A positive charge q is fixed at the point x = O, y = O, and a negative charge −2q is fixed at the point x = a, y = O. a) Show the positions of the charges in a diagram. (b) 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. (c) At which positions on the x-axis is V = O? (d) Graph V at points on the x-axis as a function of x in the range from x = −2a to x = +2a. (e) What does the answer to part (b) become when x ≫ a? Explain why this result is obtained.
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