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 theta sqrt((pi lambdagL)/(mu_(0)cos theta))`
B. `2 sin theta sqrt((pi lambdagL)/(mu_(0)cos theta))`
C. `2sqrt((pigL)/mu_(0) tan theta)`
D. `sqrt((pi lambdagL)/mu_(0) tan theta )`.

Answer

b

Explanation

Magnetic force between wires per unit length can be written as follows :
` F = (mu_(0) I^(2))/(2 pi (2 L sin theta)) `

If T is tension in string then
` T cos theta = lambda g `
` T sin theta = (mu_(0)I^(2))/(4 pi L sin theta) `
` (T sin theta)/(T cos theta ) = (mu_(0)I^(2))/(4 pi L lambda g sin theta ) `
` rArr " " I = 2 sin theta sqrt((pi L lambda g)/(mu_(0) cos theta )) `
Thus , option (b) is correct.