Question

A circular coil of diameter $21\, cm$ is placed in a magnetic field of induction $10^{-4} T$. The magnitude of flux linked with coil when the plane of coil makes an angle $30^{\circ}$ with the field is

• A. $ 1.44\times 10^{-6}\,Wb $
• B. $ 1.732\times 10^{-6}\,\,Wb $
• C. $ 3.1\times 10^{-6}\,\,Wb $
• D. $ 4.2\times 10^{-6}\,\,Wb $

Answer 1

Answer: (B)

Magnetic flux, $\phi=\int \vec{B} \cdot \overrightarrow{d A}=B A \cos \theta$,
where $\theta$ is angle between normal to the area $d A$ with magnetic field $B$.
Here, $\theta=\left(90^{\circ}-30^{\circ}\right)$
$60^{\circ}$ and $\phi=10^{-4} \times \pi\left[\frac{21}{2} \times 10^{-2}\right]^{2} \times \cos 60^{\circ}$
$=1.732 \times 10^{-6} Wb$