Question:
Four equal point charges, +3microcolumb, are placed at the four corners of a Square of each side 40cm. Find the magnitude of force on any one of the charges.
Answer:
Consider, force F1 F2 and F3 are acting on charge q1
Then,
F2 = F3 = 1/4πε0 x q12/r2 = 9 x 109 x (3 x 10-6)2/ (0.4)2 = 0.51N
If this force will place diagonal from q1 to q4
Then magnitude will be
F2cos45° + F2cos45° = 2 x 0.51/√2 = 0.72N
So for F4 force will be
F4 = 9 x 109 x (3 x 10-6)2/ (0.4 c √2)2 = 0.25N
Hence the resultant force will be = 0.72N + 0.25N = 0.97N
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