A charged ring of mass m = 50 gm, charge 2 coulomb and radius R = 2m is placed on a smooth horizontal surface. A magnetic field varying with time at a rate of (0.2 t) Tesla/sec is applied on to the ring in a direction normal to the surface of ring. Find the angular speed attained in a time `t_(1) = 10 sec`.

Answer

`200 rad//sec`

Explanation

`ointvec(E).vec(dl)=d/(dt)vec(B).vec(A)`
`E.2piR=A(dB)/(dt)`
`E.2piR=piR^(2)xx0.2t`
`E=0.2t`
`F=qE=0.4t`
`tau=RF=0.8t`
`I alpha=0.8t implies mR^(2) alpha=0.8t`
`alpha=(0.8t)/(50xx10^(-3)xx2^(2))=4t rad//sec^(2)`
`(domega)/(dt)=4t implies int_(0)^(omega)domega=4int_(0)^(10) t dt`
`implies omega=4(t^(2)/2)_(0)^(10)=200 rad//sec`