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Conisder a system of three charges q//3,...

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^@`

A

The electric field at point `O` is ` q/(8 pi varepsilon_(R)^(2)` directed anong the negative x-axis

B

The potential enrtgy of the system is zero

C

The magnitude of the force between the charges at C and B is ` q^2 /( 53 pi varepsilon_(R)^(2)`.

D

The potential at point `O` is ` q/( 12 pi varepsilon_(R)`.

Text Solution

Verified by Experts

The correct Answer is:
C
Refer to the following figure
In `Delta ABC, `60^@ ( 60^@ (alpha) + alpha =180^2 rArr alpha = 30^@`
` B C = sqrt (( 2 R)^2 - R^2) sqrt 3 R`
(a) `vec E_o = vec E_A + vec E_C`
Since` vec E_A =- vec E_B`
` ve e_o = vec E_c = (K (2q //3))/(R^2 (- hat i)`
.
(b)` U= (K 9 -2 q //3) (q //3))/(sqrt 3T) + (K (- 2q) (q //3)/R + (K (q//3) (q//3))/(2R) != 0`
(c) The magnitude of the force bhetween charges at `B` and `C` is .
`F= 1/( 4 pi varepsilon_0) . (q/3 xx (2q)/3)/(R sqrt 3)^@ = q^2 /(54 pi varepsilon_0R^@)`
(d) `V_o = (K (-2 q//3))/R + (K(q//r))/R + (K(q q//3))/a=0`
Hence choice `C` is correct .
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