Four point charges, each of magnitude 18.64 uC, are placed at the corners of a s

Question

Four point charges, each of magnitude 18.64 uC, are placed at the corners of a squard 56.2 cm on a side. If three of the charges are positive and on eis negative, find the magnitude of the force experienced by the negative charge. The value of Coulomb's constant is 8.98755 x 10^9 N*m^2/C^2. Answer in units of N.

I know the answer is 18.9257, but I want to know how to solve this problem.

I tried solving it somehow, but I got around the answer of 17. I need help solving this, because I don't understand how to solve this. I just found the answer online and got it correct on the assignment. I want to know how to solve it in case it my appear in the physics midterm.

Explanation / Answer

Here ,

length of side , a = 56.2 cm = 0.562 m

length of diagonal , d = a * sqrt(2)

d = 0.562 * sqrt(2)

d = 0.795 m

for the force between charge on sides

F1 = k * q^2/a^2

F1 = 9*10^9 * (18.64 *10^-6)^2/0.562^2

F1 = 9.9 N

for the force between diagonally oposite particles

F2 = k * q^2/d^2

F2 = 9*10^9 * (18.64 *10^-6)^2/0.795^2

F2 = 4.95 N

Now , for the net force on the negative charge

Fnet = 2 * F1 * cos(45) + F2

Fnet = 2 * 9.9 * cos(45) + 4.95

Fnet = 18.95 N

the net force acting on the negative charge is 18.95 N

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