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Three particles, each of mass m and carr...

Three particles, each of mass m and carrying a charge q each, are suspended from a common point by insulating mass-less strings each of length L. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side a, calculate the charge q on each particle. Assume `Lgtgta`.

Text Solution

Verified by Experts

The correct Answer is:
`3.17xx10^(-9) C`

`F_(B)=2F cos 30^(@)=(2Kq^(2))/a^(2)xxsqrt(3)/2=(sqrt(3)Kq^(2))/a^(2)`
For Charge at B: `2r cos 30^(@)=a`

`r=a/sqrt(3)`
`T sin theta=F_(B)`
`T cos theta=mg`
`tan theta=F_(B)/(mg)`
`rArr (sin theta)/(cos theta)=(99xx10^(-2))/(sqrt(3)xx10^(-2))=(sqrt(3)xx9xx10^(9)xxq^(2))/((3xx10^(-2))2)xx1/(10^(-3)xx10)`
`rArr q=3.17xx10^(-9)C`
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Knowledge Check

  • Two identical charged spheres suspended from a common point by two massless strings of lengths I, are initially at a distance d(d ltlt l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between as:

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