A wire is wrapped N times over a solid sphere of mass m which is place on a smooth horizontal surface. A horizontal magnetic field of induction `vec B` is present. Find the (a) torque (b) angular acceleration experienced by the sphere. Assume that the mass of the wire is negligible compared to the mass of the sphere.

Explanation

(a) The net torque acting on the sphere is

`vectau=vecmuxxvecB=(NiAhatj)xx(Bhati)=-NiABhatk` where `A=piR^2`
or `vectau=-NpiR^2iBhatk`
(b) `vecalpha=(vectau)/(I_c)` (`:'` the sphere is free to rotate, it must rotate about
the centroidal axis)
`=(-NpiR^2iB)/(2/5mR^2)hatk (because I_c=2/5mR^2)`
`=(5NpiiB)/(2m)hatk`