A closely wound solenoid of 2000 turns and area of cross section `1*6xx10^-4m^2`, carrying a current of `4*0A` is suspended through its centre allowing it to turn in a horizontal plane. What is the magetic moment associated with the solenoid? What are the force and torque on the solenoid if a uniform horizontal field of `7*5xx10^-2T` is set up at an angle of `30^@` with the axis of the solenoid?

Answer

`1*28Am^2`; `F=0`, `tau=0*048Nm`

Explanation

Here, `N=2000`, `A=1*6xx10^-4m^2`, `I=4*0A`
`M=NIA=2000xx4*0xx1*6xx10^-4`
`=1*28Am^2`
Net force experienced by the magnetic dipole in uniform horizontal field, `F=0`
The magnitude of torque exerted by the magnetic field `vecB` on the solenoid is
`tau=MBsintheta`
`=1*28xx7*5xx10^-2xxsin30^@=0*048Nm`
The torque tends to align the axis of the solenoid, i.e., its magnetic moment `vecM` along the field `vecB`.