Four point charges are fixed at the corners of a square of side length

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

a

. Starting at the top left corner and moving clockwise, the charges are

+q

-q

+q

, and

-q

respectively. (1) Calculate the total electric potential energy

U_{\text{alt}}

of this charge configuration in terms of

k

q

, and

a

. Show all work. (2) Indicate whether assembling this arrangement from infinite separation would require net input of energy, release energy, or require no net energy. Support your conclusion quantitatively using the value of

U_{\text{alt}}

you obtained. (3) Compare the numerical magnitude of

U_{\text{alt}}

with the magnitude of the potential energy for four identical

+q

charges placed at the same square corners. Discuss briefly what this comparison suggests about the relative electrostatic stability of the two arrangements.

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