A plane spiral with a great number `N` of turns wound tightly to one another is located in a uniform magnetic field perpendicular to the spiral's plane.The outside radius of the spiral's turns is equal to a and inner radius is zero.The magnetic induction varies with time as `B=B_(0) sin omega t`, where `B_(0)` and `omega` are constants.The amplitude of `emf` induced in the spiral is `epsilon_(im)=1/xpia^(2) NomegaB_(0)`.Find out value of `x`.

Answer

C

Explanation

`depsilon=-(Ndr)/axxpir^(2)(dB)/(dt)`
here `(dB)/(dt)=B_(@)omega cos ,omegat depsilon=-N/a pi r^(2) B_(@) omega cos`
`epsilon=intdepsilon=(B_(@)omegapiN cos omega t)/a underset(@)overset(a)intr^(2)dr , epsilon=-(B_(@)omegapiN cos omega t)/a [r^(3)/3]_(@)^(a)`
`epsilon=-(B_(@)omegapiN cos omega t.a^(2))/3` , Amplitude `epsilon=1/3 pi a^(2) N omega B_(@)`
`x=3`