A circular coil of radius 10 ~cm, 500 turns and resistance 2 is...

A circular coil of radius

10 \mathrm{~cm}, 500

turns and resistance

2 \Omega

is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through

180^{\circ}

0.25 \mathrm{~s}

. The current induced in the coil is (Horizontal component of the earth's magnetic field at that place is

3.0 \times 10^{-5} \mathrm{~T}

)

Options

A. $1.9 \times 10^{-3} \mathrm{~A}$

Initial magnetic flux through the coil,

\begin{aligned} \phi_i & =B_H A \cos \theta=3.0 \times 10^{-5} \times\left(\pi \times 10^{-2}\right) \times \cos 0^{\circ} \\ & =3 \pi \times 10^{-7} \mathrm{~Wb}\end{aligned}

Final magnetic flux after the rotation

\begin{aligned} \phi_f & =3.0 \times 10^{-5} \times\left(\pi \times 10^{-2}\right) \times \cos 180^{\circ} \\ & =-3 \pi \times 10^{-7} \mathrm{~Wb}\end{aligned}

Induced emf,

\varepsilon=-N \frac{d \phi}{d t}=-\frac{N\left(\phi_f-\phi_i\right)}{t}

\begin{aligned} & =-\frac{500\left(-3 \pi \times 10^{-2}-3 \pi \times 10^{-7}\right)}{0.25} \\ & =\frac{500 \times\left(6 \pi \times 10^{-7}\right)}{0.25}=3.8 \times 10^{-3} \mathrm{~V} \\ & I=\frac{\varepsilon}{R}=\frac{3.8 \times 10^{-3} \mathrm{~V}}{2 \Omega}=1.9 \times 10^{-3} \mathrm{~A}\end{aligned}