A conducting loop of area `5.0 cm^2` is placed in a magnetic field which varies sinusoidally with time as `B = B_0 sin omegat` where `B_0` = 0.20 T and `omega = 300 s^(-1)`. The normal to the coil makes an angle of `60^@` with the field. Find (a) the maximum emf induced in the coil, (b) the emf induced at `t = (pi/900)s` and (c) the emf induced at ` t = (pi/600)s`.

Explanation

Here `A=5 cm^2=5xx10^(-4) m^2`
`B=B_0 sin omega t=0.2sin (300t)`
` theta=60^(@)`
`(a) Max e.m.f induced in the coil`
`e=(-d theta )(dt)=(d/t)(BA cos theta)`
`=d/t(B_0 sin omega t xx5xx10^(-4)xx1//2)`
`=B_0xx5/2xx10^(-4) (d)/(dt) (sin omega t)`
`=(B_05)/2 10^(-4) cos omega t.omega`
`=(0.2xx5)/(2)xx300xx10^(-4)xxcos omega t`
`=15xx10^(-3)cost omegat.`
`e_(max)=15xx10^(-3)=0.015 V.`
`(b) Induced emf at t = ((pi)/(900))s`
`=e= 15xx10^(-3)cos omega t`
`=15xx10^(-3)xx cos (300xx(pi)/(900))`
`=15xx10^(-3)xx(1/2)`
`=(0.015)/(20=0.0075=7.5xx10^(-3) V`
`(c ) Induced emf at t=(pi)/(600)s`
`e=15xx10^(-3)xxcos(300xx(pi)/(600))`
`=15xx10^(-3)xx0=0V`