A circular coil of radius 10 cm, 500 turns and resistance 2 Omega is placed with its plane prependicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through `180^(@)` in 0.25 s. Estimate the magnitude of the e.m.f and current induced in the coil. Horizotal component of earth's magnetic field at the place is `3 xx 10^(-5) T`.

Options

A. `3.9xx10^(-3)A`
B. `2.9xx10^(-3)A`
C. `1.9xx106(-3)A`
D. `4.9xx10^(-3)A`

Answer

C

Explanation

Initial flux,
`phi_(1)=B_(H)A costheta=3.0xx10^(-5)xx(pixx10^(-2))xxcos0^(@)`
`=3pixx10^(-7)Wb`
Final flux after the rotation of coil
`phi_(f)=3.0xx10^(-5)xx(pixx10^(-2))xxcos 180^(@)`
`=-3pixx10^(-7)Wb`
hence induced emf,
`e=-N(Deltaphi)/(Deltat)=-(N(phi_(f)-phi_(1))/(t)`
`=-(500(-3pixx10^(-7)-3pixx10^(-7)))/(0.25)=3.8xx10^(-3)V`
`I=(e)/(R )=(3.8xx10^(-3)V)/(2Omega)=1.9xx10^(-3)A`