A circular current coil with 100 turns and area `20 cm^(2)` is placed in a uniform magnetic field in such a manner that magnetic field lines are parallel to the plane of the coil. Torque experienced by the coil is` 0.1` Nm when a current of 1 A is passed through the coil. What is the magnitude of magnetic field intensity?

Explanation

Number of turns, ` N = 100`
Area of coil , `A = 20 cm^(2) = 20 xx 10^(-4) m^(2)`
Torque, ` tau = 0.1 ` Nm, Current , `I = 1 A`
As the magnetic field lines are parallel to the plane of coil. So, angle between area vector to the plane of coil and magnetic field i.e.
` theta = 90^(@)`
As ` tau = NIAB sin theta`
` B = tau/(NIA sin theta)`
` B = (0.1)/(100 xx 1 xx 20 xx 10^(-4) sin 90^(@))`
` B = 0.00005 xx 10^(4)`
` B = 0.5 ` T