Three charges, each of magnitude 9 nC, are at separate corners of a square of ed

Question

Three charges, each of magnitude 9 nC, are at separate corners of a square of edge length 1 cm. The two charges at opposite corners are positive, and the other charge is negative. Find the force exerted by these charges on a fourth charge q = +3 nC at the remaining (upper right) corner. (Assume the +x axis is directed to the right and the +y axis is directed upward.)

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Explanation / Answer

Ft = F14 + F24 + F34

F14 = kq1q4/r14^2 = 9*10^9*9*10^-9*3*10^-9/(0.01^2) = 0.00243 j

F34 = kq3q4/r34^2 = 9*10^9*9*10^-9*3*10^-9/(0.01^2) = 0.00243 i

F24 = kq2q4/r24^2

r24 = 0.01i + 0.01 j

r(cap)24 = (0.01i + 0.01j)/sqrt(0.01^2 + 0.01^2) = 0.707 i + 0.707 j

F24 = 9*10^9*9*10^-9*3*10^-9(0.707 i + 0.707 j)/sqrt(0.01^2 + 0.01^2)

F24 = [9*9*3*10^-9*0.707/0.01414]i + [9*9*3*10^-9*0.707/0.01414]j

F24 = 8.59*10^-4 i + 8.59*10^-4 j

Since charge is negaative

F24 = -8.59*10^-4 i - 8.59*10^-4 j

Ft = 0.00243 i + 0.00243 j - 8.59*10^-4 i - 8.59*10^-4 j

Fx = 15.71*10^-4 i

Fy = 15.71*10^-4 j

Let me know if you find any mistake.

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