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

Options

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

Answer

C

Explanation

`BC=2R sin (120/2)=sqrt(3)R`

`*`Electric field at O
`=1/(4pi in_(0))((2q//3)/R^(2))=q/(6pi in_(0)R^(2))`
along negative X-axis
`*` the potential energy of the system is non zero
`*` Force between B & C B
`=1/(4pi in_(0))((q//3)(-2q//3))/((sqrt(3)R)^(2))=-q^(2)/(54pi in_(0) R^(2))`
`*` Potential at O
`=1/(4pi in_(0))(q/3+q/3-(2q)/3)=0`