In the figure there are two fixed point charges, -q located at x = -2a, and +2q

Question

In the figure there are two fixed point charges, -q located at x = -2a, and +2q located at x = +2a. There are also six positions, labeled A through F, at various distances from the two point charges. Assume the electric potential V is 0 at a distance of infinity. Express algebraic answers in terms of q, a, and fundamental constants. Simplify all answers to this problem. Determine the electric potential, V, at the point labeled B. Imagine a negative probe charge is moved from infinity to point B. Is the electric potential energy, U, associated with the negative probe charge greater when the probe charge is located at infinity, or greater when it is located at point B? Explain. Is your answer consistent with the sign of the electric potential you calculated in part (a)? Assume the negative probe charge has charge -q. Calculate the change in kinetic energy when the charge moves from infinity to point B. (Neglect gravity.) Does your result show kinetic energy increased, decreased, or remained the same?

Explanation / Answer

a)

Vb = -k q/a + k q/(5a) = - (0.8) k q/a

b)

at infinity , electric potential energy = 0

at the position on the graph, potential energy = k (-q) (2q)/(4a) < 0

hence it is greater at infinity

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