Three small balls, with charges of +q, - 2q, and + 3q, can be placed on the x-ax

Question

Three small balls, with charges of +q, - 2q, and + 3q, can be placed on the x-axis in three different configurations, as shown in the figure below. In each case, one of the balls is at x = - a, one is at x = + a, and the third is at x = + 2a. Recall that the electrostatic potential energy is defined to be zero when charged particles are infinitely far from one another. (a) What is the electrostatic potential energy for Configuration 1? (Use the following as necessary: k, q, and a.) (b) What is the electrostatic potential energy for Configuration 2? (Use the following as necessary: k, q, and a.) (c) What is the electrostatic potential energy for Configuration 3? (Use the following as necessary: k, q, and a.)

Explanation / Answer

(a)

U = U12 + U23 + U13

U = k/a [q(-2q)/2 + (-2q)(3q)/1 + (3q)q/3]

U = kq^2/a (-1 -6 + 1) = -6 k q^2/a

Hence, U = -6 k q^2/a

(b)U = U12 + U23 + U13

U = k/a [(-2q)(q)/2 + (q)(3q)/1 + (3q)(-2q)/3]

U = k q^2/a (-1 + 3 -2) = 0

Hence, U = 0

(c)U = U12 + U23 + U13

U = k/a [(q)(3q)/2 + (3q)(-2q)/1 + (-2q)(q)/3]

U = k q^2/a (3/2 - 6 -2/3) = -31/6 k q^2/a

Hence, U = -31/6 kq^2/a

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