A circular coil of radius 2.00 cm has 50 turns. A uniform magnetic field B= 0.200 T exists in the space is a direction parallel to the axis of the loop. The coil is now rotated about a diameter through an angle of `60.0^@`. The operation takes 0.100 s. (a) find the average emf induced in the coil. (b) if the coil is a closed one(with the two ends joined together) and has a resistance of `4.00 Omega`. calculate the net charge crossing a cross- section of the wire of the coil.

Explanation

Here N=50, vecB=0.200T`
`r=2.00cm,`
`=0.02m,`
`theta=60^(@), =0.100s.`
`(a) e=(Nd phi)/(dt)=(NxxB.A)/(T)`
`=(NB.A cos 60^(@))/t`
`=(50xx2xx10^(-1)xx pi (0.02)^2)/(0.1)`
`=5xx4xx10^(-3)xx pi`
`=2 pixx 10^(-2)V= 6.28xx10^2V`
`(b) i=e/R=(6.28xx10^(-2))/4`
`1.57xx10^(-2)A.`
`Q=it=1.57xx10^(-2)xx10^(-1)`
`=1.57xx10^(-3)C.`