What is the potential at the centre of a square of each side 1.0 meter, when four charges `+1xx10^(-8)C, -2xx10^(-8) C, +3xx10^(-8)C and +2xx10^(-8)C` are placed at the four corners of the square.

Options

A. `5.09xx10^(2) V`
B. `5.09xx10^(3) V`
C. `5.09 V`
D. `8.23xx10^(2) V`

Answer

A

Explanation

As is clear from Fig

`OA = OB = OC = OD = (sqrt(2))/(2) = (1)/(sqrt(2)) m`
Potential at `O`
`V = (Sigma q)/(4pi in_(0) r)`
`= (9xx10^(9)(1xx10^(-8) -2xx10^(-8)+3xx10^(-8) + 2xx10^(-8)))/(1//sqrt(2))`
`= 9xx10^(9)xx4xx10^(-8) sqrt(2) = 5.09xx10^(2) V`