What are the magnitude and direction of the electric field at center of the square in Fig, if `q = 1.0xx10^(-8) C and a = 5.0 cm ?

Answer

`(7.2 sqrt(2) xx10^(4)) N//C at 45^(@)` to OA`

Explanation

`OA = OB = OC = OD = r = (5xx10^(-2))/(sqrt(2)) m`.
`E_(1) = E_(2) = (q xx 1)/(4pi in_(0) r^(2)) = ((1xx10^(-8))xx1xx9xx10^(9))/((5xx10^(-2)// sqrt(2))^(2))`
`= 7.2xx10^(4) N//C`
`/_ AOB = 90^(@)`
`:.` Net electric field at 0 `= sqrt(E_(1)^(2) + E_(2)^(2)) = E_(1) sqrt(2)`
`= (7.2 sqrt(2) xx10^(4)) N//C at 45^(@)` to OA