ABCD is a square of side 1m. Charges of `+3nC, -5nC and +3nC` are placed at the comers A, B and C respectively. Calculate the work done in transferring a charge of `12mu c` from D to the point of intersection of the diagonals?

Explanation

Diagonal = BD= AC= 1.414m Half of diagonal = AO = BO= CO= 0.707m. Electric potential due system of charges
`V= (1)/(4pi in_(0)) [(q_(1))/(r_(1)) + (q_(2))/(r_(2)) + (q_(3))/(r_(3))]`
Electric potential at the centre O of square
`V= 9 xx 10^(9) [(3 xx 10^(-9))/(0.707) -(5 xx 10^(-9))/(0.707) + (3 xx 10^(-9))/(0.707)]`
`V_(0)= 12.7298V`
Electric potential at the corner D of square
`V= 9 xx 10^(9) [(3 xx 10^(-9))/(1)- (5 xx 10^(-9))/(1.414) + (3 xx 10^(-9))/(1)]`
`V_(D)= 22.176V`
Work done to transfer `12mu C` charge from D to 0
`W=q[V_(D)-V_(0)] 12 xx 10^(-6) [22.176- 12.7298]`
`W= 1.1335 xx 10^(-4)J`