A circular coil of radius $r=0.1\text{ m}$ is placed in a magnetic field $B=0.2\text{ T}$. If the plane of the coil is perpendicular to the field, what is the magnetic flux $\Phi$ through the coil?

Solution

1. The formula for magnetic flux is $\Phi =BA\cos (\theta )$.
2. Since the plane is perpendicular to the field, the angle between the area vector and field is $0^{\circ }$, so $\cos (0)=1$.
3. Calculate the area: $$\begin{array}{rl}A& =\pi r^2\\ & =\pi (0.1{)}^2\\ & =0.01\pi {\text{ m}}^2\end{array}$$.
4. Calculate the flux: $$\begin{array}{rl}\Phi & =0.2\times 0.01\pi \\ & =0.002\pi \text{ Wb}\end{array}$$.
5. Hence the answer is (A).