Consider four point charges arranged in a square with sides of length L. Three of the point charges have charge q and one of them has charge −q. What is the magnitude of the electric force on the −q charge due to the three q charges?

Explanation:

Given

Three charges of magnitude q is placed at three corners and fourth charge is placed at last corner with -q charge

Force due to the charge placed at diagonally opposite end on -q charge

where  Distance between the two charges

negative sign indicates that it is an attraction force

Now remaining two charges will apply the same amount of force as they are equally spaced from -q charge

The magnitude of force by both the  charge is same but at an angle of

thus combination of two forces at 2 and 3 will be

Now it will add with force due to 1 charge

Thus net force will be

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