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Three charges each of value q are placed...

Three charges each of value `q` are placed at the corners of an equilateral triangle. A fourth charge `Q` is placed at the centre of the triangle. If `Q = -q`:

A

`(qQ)/(4 pi epsi_(0)r^(2))`

B

`(qQ)/(4 pi epsi_(0)(r+a)^(2))`

C

`(Qqsqrt(9r^(2) - 3a^(2)))/(4 pi epsi_(0) x^(3))`

D

`(qQ)/(2 pi in_(0) (x^(2) + a^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C

`F=(Qq)/(4 pi e_0 r^2)` and net force on Q is `3F cos theta implies F_(net)=3. (Q q)/(4 pi e_0 r^2) cos theta`
Let G. centroid of `Delta ABC implies AB=a//sqrt3 implies h=sqrt(r^2-a^2//3)=sqrt((3r^2-a^2)/sqrt3)`
`implies cos theta =h/r=sqrt(3r^2-a^2)/(sqrt3 r)`
`implies F_(net) (sqrt3 Q q(sqrt(3r^2-a^2))/(4 pi e_0 r^3) = (Q q sqrt(9r^2-3a^2))/(4 pi e_0 r^3)`
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