A. Four point charges are located at the corners of a square with sides of lengt

Question

A. Four point charges are located at the corners of a square with sides of length a. Two of the charges are +q, and two are ?q. Find the magnitude of the net electric force exerted on a charge +Q, located at the center of the square, for the following arrangement of charge: the charges alternate in sign (+q,?q,+q,?q) as you go around the square.

Express your answer in terms of the variables q, Q, a, and appropriate constants.

B.Find the magnitude of the net electric force exerted on a charge

+Q, located at the center of the square, for the following arrangement of charge: the two positive charges are on the top corners, and the two negative charges are on the bottom corners.

Explanation / Answer

here

distance from corner to center x = a*sqrt2; x^2 = 2a^2
Now all the sideways components of E will be nullified by the charge beside it

E (per charge in the downward direction) = k*q/(2a^2) * sin(45) [since E makes 45 degree with the sides of the square]

So total E (in the downward direction) = 4k*q/(2a^2)/sqrt(2)

if you consider the upward direction to be positive, then you'll need the minus sign as well

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