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. 0.5 mA
B. 1.0 mA
C. 1.5 mA
D. 3.0 mA

Answer

B

Explanation

Here , R = 10 cm` = 10 xx 10^(-2)m`
Number of turns , N = 500, Resistance ` = 2Omega`
Magnetic field , `B = 3 xx 10^(-5) T`
Initial flux through the coil , `phi_(B_("initial") ) = BA cos theta`
` = 3 xx 10^(-5) xx pi xx (10 xx 10^(-2) )^2 cos 0^@ = 3pi xx 10^(-7) Wb`
Final flux after rotation ,
`phi_(B_("final") ) = 3 xx 10^(-5) xx pi xx (10 xx 10^(-2) )^2 xx cos 180^@`
` = -3pi xx 10^(-7) Wb`
Emf induced in the coil , `epsi = - N (Delta phi_B)/(Delta t) = - N ((phi_(B_("final")) - phi_(B_("initial")) )/(Delta t ))`
` = - (500 xx (-3pi xx 10^(-7) -3pi xx 10^(-7) ) )/(0.5)`
` = (500 xx 6pi xx 10^(-7) )/(0.5) = 2 xx 10^(-3) V`
Induced current in the coil , `I = (2 xx 10^(-3) V)/(2Omega) = 10^(-3) A = 1 mA`