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A wire is wrapped N times over a solid s...

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.

Text Solution

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(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`
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