Question

Four charges +q , +q , -q and -q are placed at the four corners of a square of side a. Calculate the electric field at the centre of the square . Also calculate potential at the centre.

Answer 1

Since the centre is equidistant from all corners of the square.

V_A=V_B = kq/r

V_C = V_D = -kq/r

The potential at the centre will be zero.

To calculate electric field:

If the charges of the same sign are placed diagonally opposite, then the electric field is zero at the centre.

For the following arrangement:

AB=BC=CD=DA= a

⇒BD = (2)^1/2a

⇒OA = OB = OC=OD= BD/2 = a/(2)^1/2

The net field along OD, E' = E_A + E_D = 4kq/ a² along OD

The net field along OC, E'' =E_B + E_C = 4kq/a² along OC

Resultant electric field E =