A 50 turn circular coil of radius 2.0 cm carrying a current of 5.0 A is rotated in a magnetic field of strength 0.20 T. (a) What is the maximum torque that acts on the coil? (b) in a particular position of the coil, the torque acting on it is half of this maximum. What is the angle between the magnetic field and the plane of the coil?

Explanation

`n = 50 , r = 0.02 m`,
`I = 5 A and B = 0.20 T`
`tau is maximum when sin theta = 90^@`
` tau _(max) = nia b sin 90^@ = mb`
`= 50 xx 5 xx 3.14 xx 4 xx10^(-4) xx 2 xx 10^(-1)`
`= 6.28 xx 10^(-2)N m`
Given `tau = (1)/(2) xx tau _(max)`
`rArr sin sin theta = (1)/(2)` or `sin theta = 30 ^@`
`= angle between area vartor and magnetic field`.
So angle between magnetic field and the plane of the coil
`= 90^@ - 30^@ = 60^@`.