Question

In a region of uniform magnetic induction $B={10}^{-2}tesla$, a circular loop of radius 30 cm and resistance ${\pi }^2$ ohm is rotated about an axis which is perpendicular to the direction of B and which forms a diameter of the loop. If the loop rotates at 200 rpm , the maximum amplitude of the alternating current induced in the loop is

• A. $4{\pi }^{2}mA$
• B. 30 mA
• C. 6 mA
• D. 200 mA

Answer 1

The correct option is C 6 mA

Maximum Amplitude of AC $i_0=\frac{V_0}{R}=\frac{\omega NBA}{R}=\frac{\left(2\pi v\right)NB\left(\pi r^2\right)}{R}$
$\Rightarrow i_0=\frac{2\pi \times \frac{200}{60}\times 1\times {10}^{-2}\times \pi \times (0.3{)}^2}{{\pi }^2}=6mA$