Four point charges have equal magnitudes. Three are positive, and one is negativ

Question

Four point charges have equal magnitudes. Three are positive, and one is negative, as the drawing shows. They are fixed in place on the same straight line, and adjacent charges are equally separated by a distance d. Consider the net electrostatic force acting on each charge. Calculate the ratio of the largest to the smallest net force magnitude.

Four point charges have equal magnitudes. Three are positive, and one is negative, as the drawing shows. They are fixed in place on the same straight line, and adjacent charges are equally separated by a distance d. Consider the net electrostatic force acting on each charge. Calculate the ratio of the largest to the smallest net force magnitude.

Explanation / Answer

For each of the four charges, apply Coulomb's Law to the three remaining charges (total of 12 calculations) then just add them up and look at largest/smallest.

A-B repels with force 1

A-C repels with force 1/4

A-D attracts with force 1/9 etc...

repeat for BCD keeping direction based on relative position in mind.

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