Four charges , all of the same magnitude , are placed at the four corners of a square . At the centre of the square , the potential is `V` and the field is `E`. By suitable choice of the signs of the four charges ,which of the following can be obtained?
(i) `V = 0 , E = 0`
(ii) `V = 0 , E != 0`
(iii) `V != 0 , E = 0`
(iv) `V != 0 , E != 0`

Options

A. `(i),(ii)`
B. `(i),(iii)`
C. `(ii),(iii)`
D. all

Answer

D

Explanation

At `O`:
(i) `Q_(1) = Q_(3) = Q, Q_(2) = Q_(4) = -Q`
`E = 0 , V = 0`
(ii) `Q_(1) = Q_(2) = Q , Q_(3) = Q_(4) = -Q`
`V = 0 , E!= 0`
(iii) `Q_(1) = Q_(2) = Q_(3) = Q_(4) = Q`
`V!= 0 , E = 0`
(iv) `Q_(1) = Q_(2) = Q_(3) = Q , Q_(2) = -Q`
`V != 0 , E!= 0`