A solenoid of length 0.4 m and having 500 turns of wire carries a current of 3 amp. A thin coil having 10 turns of wire and of radius 0.01 m carries a current of 0.4 amp. The torque (in Nm) required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid is (`mu_(0) = 4pi xx 10^(-7)` V-s/A-m)

Options

A. `6xx10^(6)` N-m
B. `6xx10^(-6)` N-m
C. `7.5 xx10^(-6)` N-m
D. `4.2 xx10^(-6)` N-m

Answer

B

Explanation

For the solenoid B=`mu_(0)nI`
`=4pi xx10^(-7)xx(500)/(0.4)xx3`
`=1.5 pi xx10^(-3)T`
Dipole moment of the coil (M)
`therefore M=4pixx10^(-4) Am^(2)`
Torque required =MB sin 90 =MB
`=4pi xx10^(-4) xxx1.5 pi xx10^(-3)`
`=6xx10^(-6) N-m`