Consider three charges `q_(1),q_(2), q_(3)` each equal to q at the vertices of an equilateral triangle of side l. What is the force on a charge Q (with the same sign as q) placed at the centroid of the triangle, as shown in figure ?

Explanation

Situation given in the statement is depicted in following figure.

Here O is the centroid of an equilateral triangle `triangleABC` .
Hence, OA = OB = OC = r ... (1)
Electric repulsive forces exerted by `q_(1),q_(2), q_(3)` on `q_(4)` have same magnitudes each equal to F because,
`F_(41) = F_(42) = F_(43) =F = k(Qq)/r^(2)`......(2)
Suppose, `vecF^(.) = vecF_(42) + vecF_(43)`
`therefore F. = sqrt(F^(2) + F^(2) + 2F F cos (120^(@))` `(therefore F_(42) = F_(43) = F)`
`=sqrt(2F^(2) + 2F^(2) (-1/2))`
(`therefore` Angle between `vecF_(42)` and `vecF_(43)` is `theta = 120^(@)`)
`=sqrt(F^(2))`
=F.............(3)
If resultant force exerted on `q_(4) =Q` is `vecF_(4)` then
`vecF_(4) = vecF_(41) + vecF_(42) + vecF_(43)`
`=vecF_(41) + vecF^(.)`
`=F(-hatj) + F(hatj)`
`therefore vecF_(4)=vec0`