A circular coil of radius 8cm, 400 turns and resistance `2Omega` is placed with its plane perpendicular to the horizantal component of the earth's magnetic fiedl. It is rotated about its vertical diameter through `180^(@)` in 0.30 s. Horizontal component of earth magnitude of current induced in the coil is approximately

Options

A. `4xx10^(-2)A`
B. `8xx10^(-4)A`
C. `8xx10^(-2)A`
D. `1.92xx10^(-3)A`

Answer

B

Explanation

Initial flux through the coil
`phi_(i)=BAcos theta`
`=3xx10^(-5)xxpixx(8xx10^(-2))xxcos 0^(@)`
`=192pixx10^(-9)Wb`
Final flux after the rotation
`phi_(f)=3xx10^(-5)xxpi(8xx10^(-2))^(2)cos 180^(@)`
`=-192pixx10Wb`
`:.` Teh magnitude of induced emf is
`epsi=N|(dphi|)/(dt)=(N|phi_(f)phi_(i)|)/(dt)`
`=(400xxx(384pxx10^(-9)))/(0.30)=1.6xx10^(-3)V`
Current `I=(epsi)/(R)=(1.6xx10^(-3))/(2)=8xx10^(-4)A`