Four point charges have the same magnitude of 8.40x10-12 C and are fixed to the

Question

Four point charges have the same magnitude of 8.40x10-12 C and are fixed to the corners of a square that is 4.0 cm on a side. Three of the charges are positive and one is negative. Determine the magnitude of the net electric field that exists at the center of the square. ___________N/C
Four point charges have the same magnitude of 8.40x10-12 C and are fixed to the corners of a square that is 4.0 cm on a side. Three of the charges are positive and one is negative. Determine the magnitude of the net electric field that exists at the center of the square. ___________N/C

Explanation / Answer

q = 8.40 x 10^-12 C, a = 4.0 cm, find the magnitude of the net electric at the center of the square. There is a diagonal with 2 positive charges q. By symmetry, the electric fields at the center due to these 2 charges cancel each other. There is one positive q and one negative q at the another diagonal. The electric fields at the center due to these 2 charges have same magnitude and same direction. So E = 2*kq/[a*sqrt(2)]^2 = kq/a^2 = 4.73*10^-3 N/C

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