Two long current carrying thin wires , both with current `I`, are held by insulating threads of length `L` and are in equilibrium as shown in the gigure , With threads making an angle ` theta` with the vertical . If wires have mass ` lambda` per unit length then the value of `I` is :

Options

A. `sin thetasqrt((pilambdagL)/(mu_0cos theta))`
B. `2 sin theta sqrt((pilambdagL)/(mu_0cos theta))`
C. `2sqrt((pigL)/(mu_0))tan theta`
D. `sqrt((pilambdagL)/(mu_0))tan theta`

Answer

B

Explanation

let l be the length of a wire under study. In equilibrium state
`Tcos theta=mg=lambda lg` or `l=(Tcos theta)/(lambdag)` …(i)
`Tsin theta=F=(mu_0)/(4pi)(2I_1I_2)/(r)l`

`=(mu_0)/(2pi)(Iil)/((2Lsin theta))xx(Tcos theta)/(lambdag)`
or `I=2sin thetasqrt((piLlambdag)/(mu_0cos theta))`