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

(a) `tau = MB sin theta = Ni A B sin theta = Ni pi r^(2) B sin theta`
`tau` is minimum if `theta = 90^(@)`
`tau_(max) = Ni pi r^(2) B`
`= (50) (5) (pi) (2 xx 10^(-2))(0.2)`
`= 2pi xx 10^(-2) Nm`
(b) `tau = (tau_(max))/(2)`
`tau = tau_(max) sin theta'`
`(tau_(max))/(2) = tau_(max) sin theta' = rArr sin theta' = (1)/(2)`
`theta`' is the angle between normal to loop and magnetic field, normal to loop is perpendicular to plane of loop hence angle between plane of loop and magnetic field `= 90 - theta' = 60^(@)`.