A solenoid of length `0.4m` and having `500` turns of wire carries a current of `3amp`.Calculate the torque requred to hold a coil (having radius `0.02 cm` current `2A` and turns `50`)in the middle of the solenoid with its axis perpendicular to the axis of the solenoid.`(pi^(2)=10)`

Options

A. 14.5
B. 10.3
C. 12.5
D. 16.3

Answer

C

Explanation

Magnetic field due to a solenoid, `B= mu_(0) ni`
`:.` Torque acting on the second coil,
`tau= MB sin 90^(@)= (N_(2) i_(2) A_(2))B= N_(2) i_(2) xx A xx mu_(0)n xx i`
`rArr tau =(500) xx 3 xx pi (0.02)^(2) xx 4pi xx 10^(-7) xx 50xx 2`
`rArr tau= 2400 xx 10^(-11)`
Given: `tau = (3)/(x) xx 10^(-7) Nm, :. (3)/(x) xx 10^(-7) = 2400 xx 10^(-11)`
`rArr x= 12,5`