Question

A circular loop (radius of 20 cm) is in a uniform magnetic field of 0.15 T. What angle(s) between the normal to the plane of the loop and the field would result in a flux with a magnitude of ?

Answer 1

Answer:

The angle other than 90 degrees would result in magnetic flux of non zero magnitude.

Explanation:

The magnetic flux through a given closed area is equal to $\underset{B}{\rightarrow}.\underset{A}{\rightarrow}$.

    Where $\underset{B}{\rightarrow}$ is the magnitude of magnetic flux through loop .

                $\underset{A}{\rightarrow}$ is the area vector of the given loop .

      We know that $\underset{B}{\rightarrow}.\underset{A}{\rightarrow}$ = $\left | A \right |\left | B \right |\cos \theta$,

 Where $\theta$ is the angle made by magnetic field with area vector.

   Area vector of a closed loop is always normal to the plane of the loop .

So from above equation we can deduce that

                  $\theta = \cos^{-1}\frac{\phi }{\left | A \right |\left | B \right |}$      

      $\phi$ is the magnitude of magnetic flux which is non zero when $\theta$ not equal to 90 degrees.