A small coil `C` with `N=200` turns is mounted on one end of a balance beam and introduced between the poles of an electromagnet as shown in figure. The cross sectional area of coil is `A=1.0 cm^(2)`, length of arm `OA` of the balance beam is `l=30 cm`. When there is no current in the coil the balance is in equilibrium. On passing a current `I=22 mA` through the coil the equilibrium is restored by putting the additional counter weight of mass `Deltam=60 mg` on the balance pan. Find the magnetic induction at the spot where coil is located.

Options

A. `0.4T`
B. `0.3T`
C. `0.2T`
D. `0.1T`

Answer

A

Explanation

On passing current through the coil, it acts as a magnetic dipole. Torque acting on magnetic dipole is counter balanced by the moment of additional weight about position `O`. Torque acting on a magnetic dipole `tau=MB sintheta=(NiA)B sin 90^(@)=NiAB`
Again `tau= ForcexxLever arm=Deltamgxxl`
`implies NiAB= Deltamgl`
implies `B=(Deltamgl)/(NiA)=(60xx10^(-3)xx9.8xx30xx10^(-2))/(200xx22xx10^(-3)xx1xx10^(-4))=0.4 T`