Four point charges `q_(A) =2 muC, q_(B) = -5 muC, q_(C) =2 muC`, and `q_(D) = -5 muC` are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of `1 muC` placed at the centre of the square ?

Explanation

Situation given in the statement is depicted ii the following figure.

Magnitude of Coulombian force exerted of `q_(0)` by `q_(A)` is,
`F_(OA) = k(q_(0)q_(A))/r^(2)` (From A to O) …………..(1)
Magnitude of Coulombian force exerted on `q_(0)` by `q_(C)`, is
`F_(OC) =k(q_(0)q_(C))/r^(2) = k(q_(0)q_(A))/r^(2) (therefore q_(C) = q_(A))`
From C to O ..........(2)
From eqn (1) and (2)
`vecF_(OA) = -vecF_(OC)`...........(3)
Magnitude of Coulombian force exerted on `q_(0)` by `q_(B)` is
`F_(OB) = k(q_(0)q_(B))/r^(2)` (From O to B)...........(4)
`F_(OB) = -F_(OB)`..........(6)
Now, resultant Coulombian force exerted on `q_0` by remaining charges is,
`vecF_(O) = vecF_(OA) + vecF_(OB) + vecF_(OC) + vecF_(OD) = vecO`
`therefore F_(O) =0`