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 Fig. The cross sectinal area of the coil is `S = 1.0 cm^(2)`, the length of the arm `OA` of the balance beam is `l = 30 cm`. When there is no current in the coil the balance is irl equilibrium. On passing a current `I = 22 mA` through the coil the equiibrium is restroed by putting the additional counterweight of mass `Delta m = 60 mg` ont he balnace pan. Find the magnetic induction at the spot where the coil is located.

Explanation

We known that the torque acting on a magentic dipole.
`vec(N) = vec(p_(m)) xx vec(B)`
But `vec(p_(m)) = i S hat(n)`, where `hat(n)` is the normal on the plane of the loop and is directed in the direction of advancement of a right handed screw, if we rotate the sense of current in the loop.
On passing a current through the coll, this torque acting on the torque acting on the magnetic dipole, is conterbalanced by the moment of addional weight, about `O`. Hence, the direction of current in the loop must be in the direction, shown in the figure.
`vec(p_(m)) xx vec(B) = -vec(l) xx Delta m vec(g)`
or, `N i S B = Delta mgl`
So, `B = (Delta mgl)/(N i S) = 0.4 T` on putting the values.