Three identical point charges, each of mass m and charge q, hang from three strings as shown in fig. The value of q in term of m, L, and q is

Options

A. `q=sqrt((16//5)pi epsilon_(0)mg L^(2)sin^(2)theta tan theta)`
B. `q=sqrt((16//15)pi epsilon_(0)mg L^(2)sin^(2)theta tan theta)`
C. `q=sqrt((15//16)pi epsilon_(0)mg L^(2)sin^(2)theta tan theta)`
D. none of these

Answer

A

Explanation

`F_(e)=F_(2)+F_(3)`
`=(kq^(2))/((L sin theta)^(2))+(2kq^(2))/((2L sin theta)^(2))`
`F_(e)=5/4 (kq^(2))/(L^(2) sin^(2) theta)` …(i)
`T sin theta=Fe` …(ii)
`T cos theta = mg` (iii)
from (i), (ii) and (iii)
`q=sqrt((16)/(5)pi epsilon_(0)L^(2)sin^(2)theta tan theta)`