A circular coil of one turn of radius `5.0cm` is rotated about a diameter with a constant angular speed of `80` revolutions per minute. A uniform magnetic field `B=0.0IT` exists in a direction perpendicular to the axis of rotation, the maximum emf induced, the average emf induced in the coil over a long period and the average of the squares of emf induced over a long period is

Options

A. `6.4xx10^(-4)V,zero,2.2xx10^(-7)V^(2)`
B. `6.6xx10^(-4)V,zero,2.0xx10^(-7)V^(2)`
C. `6.8xx10^(-4)V,zero,2.5xx10^(-7)V^(2)`
D. `6.4xx10^(-4)V,zero,2.0xx10^(-6)V^(2)`

Answer

B

Explanation

Let at any time, normal to loop makes an angle `theta` with magnetic field
`phi_(B)=NBS cos theta=NBScos omegat`
`e=-(dphi_(B))/(dt)=NBS omega sin omegat=e_(0) sin omegat`
`rArre_("max")=e_(0)=NBSomega=1xx0.01xxpi(5)^(2)xx10^(-4)xx(80xx2pi)/(60)`
`=6.6xx10^(10^(-4))V`
Over a long period, i.e. one time period, average of induced emf is
`bar(e)=(int_(0)^(T)edt)/(T)=0`
`bar(e^(2))=(int_(0)^(T)e^(2)dt)/(T)=(e_(0)^(2))/(2)=2.0xx10^(-7)V^(2)`