Consider a system of three charges q/3 ,q/3 and 2q/3 placed at points A, B and C respectively , as shown in the figure .Take O to be the centre of the circle of radius R and angle `CaB = 60^(@)`

Options

A. The electric field at point O is `q/(8piepsilon_(0)R^(2))` directed along the negative x - axis .
B. The potential energy of the system is zero
C. The magnitude of the force between the charges at C and B is ` (q^(2))/(54piepsilon_(0)R^(2))`
D. The potential at point O is `q/(12 piepsilon_(0)R)`

Answer

C

Explanation

The electric field due to A and B at O are equal and opposite producing a resultant which is zero . The electric field at due to C is E ` = 1/(4piin_(0)) (2q//3)/(R^(2))`
` = q/(6piin_(0)R^(2))`
` :. ` option (a) is not correct . The elctric potential at O is :

`V_(O) = K [(+q//3)/R] +K [(+q//3)/R] +K [(-2q//3)/R] =0`
` :. ` option (d) is wrong
In `Delta ABC (AC)/(AB) = sin 30^(@) rArr AC = (AB)/2 = R `
Also `(BC)/(AB) = sin 60^(@) rArr BC = (sqrt(3)AB)/2 = sqrt(3)R`
Potential energy of the system
`K = [((q//3)(2//3))/(2R)] +K [ ((q//3)(-2q//3))/R] +K [((q//3)(-2q//3))/(sqrt(3)R)] `
` = (kq^(2))/(9R) [1/2-2 2/(sqrt(3))] != 0 `
`:. ` Option (b) is wrong
Magnitude of force between B and C is
`F = 1/(4piin_(0)) ((2q//3)(q//3))/((sqrt(3)R)^(2))`
` = (q^(2))/(54piin_(0)R^(2))`.