A circular coil of radius `10cm` and `25` turns is rotated about its vertical diameter with an angular speed of `40rads^(-1)`, in a uniform horizontal magnetic field of magnitude `5xx10^(-2)T`. Calculate the maximum emf induced in the coil. Also find the maximum current in the coil if the resistance of the coil is `15Omega`.

Explanation

Given `r=10cm=0.1m`
`N=25`, `omega=40rads^(-1)`, `B=5xx10^(-2)T`
`R=1.5Omega`, `e=?`, `I=?`
we know that `e_(max)=BANomega`, `A=pi r^(2)`
`=5xx10^(-2)xx3.14xx(0.1)^(2)xx25xx40`
`=15.7xx10^(-2)xx10^(-2)xx10^(3)`
`e_(max)=1.57` volt and `e_(rms)=1.11` volt
Hence maximum current induced `=I_(max)=(e_(max))/(R )`
i.e., `I_(max)=(1.57)/(15)=0.105A` and `I_(rms)=0.0742A`