IP Four point charges, each of magnitude q, are located at the corners of a squa

Question

IP Four point charges, each of magnitude q, are located at the corners of a square with sides of length a. Two of the charges are +q, and two are q. The charges are arranged in the following way: (1) the charges alternate in sign (+q,q,+q,q) as you go around the square; (2) the top two corners of the square have positive charges (+q,+q), and the bottom two corners have negative charges (q,q).

Calculate the magnitute of electric field at the center of the square for the second case.

Express your answer in terms of some or all of the variables q, a, and appropriate constants.

Explanation / Answer

We have a square with positive charges at the top and negative charges at the bottom

The Ex at center will cancel due to symmetry

distance between each charge at center of square = 1/ 2( diagonal) = a sqroot (2)/ 2=

Ey =2x 4 (k) ( q^2) sin 45 / ( a^2 x 2 ) = 4k (q^2) sin 45 /a^2

sin 45 is apprx = 0.707

E= 25.45 x 10^9 ( q^2/a^2)

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