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

Options

A. The electric field at point `O is (q)/(8 pi epsilon_(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))/(54 pi epsilon_(0) R^(2))`
D. The potential at point `O` is `(q)/(12 pi epsilon_(0) R)`

Answer

3

Explanation

(1) Electric field at `O`:
Electric field due to `(q)/(3) ,(q)/(3)` are equal and opposite.
`E_(o) = (1)/(4 pi in_(0)) .(2q//3)/(R^(2)) = (q)/(6 pi in_(0) R^(2))` along the `-ve x`-axis
(1) is wrong
(2) `U = (1)/(4 pi in_(0)) [ ((q)/(3) .(q)/(3))/(2 R) + ((q)/(3) . -(2q)/(3))/(R ) + ((q)/(3) .-(2q)/(3))/(sqrt(3) R)] != 0`
(3) `F = (1)/(4 pi in_(0)) .((q)/(3) .(2q)/(3))/((sqrt(3) R)^(2)) = (q^(2))/(54 pi in_(0) R^(2)) , O.K.`
(4) `V_(o) = (1)/(4 pi in_(0)) [ (q//3)/(R ) + (q//3)/(R ) + (-2q//3)/(R) ] = 0`