Question

The inner loop has an area of $5\times {10}^{-4}{m}^2$ and a resistance of $2\Omega$(figure). The larger circular loop is fixed and has a radius of $0.1m$. Both the loops are concentric and coplanar. The smaller loop is rotated with an angular velocity $\omega$ and $s^{-1}$ about its diameter. The magnetic flux with the smaller loop is

• A. $2\pi \times {10}^{-6}Wb$
• B. $\pi \times {10}^{-9}Wb$
• C. $\pi \times {10}^{-9}\cos \omega tWb$
• D. zero

Answer 1

Answer: (C)

$\pi \times {10}^{-9}\cos \omega tWb$

Magnetic field at the center $=\frac{{\mu }_{0}i}{2R}=\frac{4\pi \times {10}^{-7}}{2\times 0.1}=2\pi \times {10}^{-6}$

Flux $=BA=2\pi \times {10}^{-6}\times 5\times {10}^{-4}{m}^2=\pi \times {10}^{-9}Wb$

As the smaller coil is rotating flux varies as $\varphi cos\left(\omega t\right)$