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## Q. 10.8

A uniform magnetic field is perpendicular to a loop of radius 1 cm. Find the value of the magnetic field such that the magnetic flux through the loop is equal to $\Phi_{0}$.

Strategy In general, flux of a magnetic field is a scalar product of the magnetic field with the area, or $\Phi_{0}=B A \cos \theta$, where A is the area of the loop and θ is the angle between the field vector and a vector normal to the loop. Because the magnetic field is perpendicular to the loop, $\cos \theta=1, \text { and so } \Phi_{0}=B A$.

## Verified Solution

Solving for the magnetic field and using the given size of the loop,

\begin{aligned}B=\Phi_{0} / A &=\left(2.068 \times 10^{-15} T \cdot m ^{2}\right) /\left[\pi\left(10^{-2} m \right)^{2}\right] \\&=6.58 \times 10^{-12} T\end{aligned}

This exceptionally small value is an indication of the small size of the quantum fluxoid.