# Three charges, each of magnitude 5 nC, are at separate corners of a square of edge length 3 cm. The two charges at opposite corners are positive, and the other charge is negative. Find the force...

Three charges, each of magnitude 5 nC, are at separate corners of a square of edge length 3 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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### 1 Answer

The force diagram is shown in the attached figure.a=3 cm=0.03 m

The force due to each of the positive charges is:

`F_p=(k*q_1q_2)/a^2` (where `k =1/(4piepsilon_0)` )

`=(8.98755*10^9*5*10^-9*3*10^-9)/(0.03)^2 N`

`=1.5*10^-4 N`

Force due to the negative charge is:

`F_n=(kq_1*q_2)/(sqrt2a)^2`

=`(8.98755*10^9*5*10^-9*3*10^-9)/(sqrt2*0.03)^2 N`

`=7.5*10^-5`

The net vector sum along the diagonal is:

`F_(n et)=2F_p*cos45^o-F_n`

`=2*1.5*10^-4*1/sqrt2-7.5*10^-5`

`=1.37*10^-4 N`

Therefore, the force exerted by these charges on a fourth charge

*q*= +3 nC is 1.37*10^-4 N.