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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llltkl | College Teacher | (Level 3) Valedictorian

Posted on

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.
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