Q90 / 110 · VITEEE 2022 · Physics
In a region of uniform magnetic induction \(\mathrm{B}=10^{-2}\) tesla, a circular coil of radius \(30 \mathrm{~cm}\) and resistance \(\pi^2 \mathrm{ohm}\) is rotated about an axis which is perpendicular to the direction of \(B\) and which forms a diameter of the coil. If the coil rotates at \(200 \mathrm{rpm}\) the amplitude of the alternating current induced in the coil is
- A\(4 \pi^2 \mathrm{~mA}\)
- B\(30 \mathrm{~mA}\)
- Correct answerC\(6 \mathrm{~mA}\)
- D\(200 \mathrm{~mA}\)
Solution
\(I_0=\frac{E_0}{\mathrm{R}}=\frac{\mathrm{nBA} \omega}{\mathrm{R}}\)
Given, \(\mathrm{n}=1, \mathrm{~B}=10^{-2} \mathrm{~T}\),
\(\mathrm{A}=\pi(0.3)^2 \mathrm{~m}^2, \mathrm{R}=\pi^2\)
\(\mathrm{f}=(200 / 60)\) and \(\omega=2 \pi(200 / 60)\)
Substituting these values and solving, we get \(\mathrm{I}_0=6 \times 10^{-3} \mathrm{~A}=6 \mathrm{~mA}\)
Hence, the correct answer is option: 'C'.