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Consider a system of three charges (q)/(...

Consider a system of three charges `(q)/(3),(q)/(3) and -(2q)/(3)` placed ar point 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^(@)`. Choose the incorrect options

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

A

The electrical field at point O is `(q)/(8 pi epsi_(0)R^(2))`

B

The potential energy of the system is zero

C

The magnitude of the force between the charges at point C and B is `(q^(2))/(5 4pi epsi_(0) R^(2))`

D

The potential at point O is `(q)/(12pi epsi_(0) R)`

Text Solution

Verified by Experts

The correct Answer is:
C
Distance `BC=ABsin60^(@)=(2R)(sqrt3)/(2)=sqrt(3)R" "therefore" "|Fe_(BC)|=(1)/(4piepsi_(0))((q//3)(2q//3))/((sqrt(3)R)^(2))=(q^2)/(54piepsi_(0)R^(2))`
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