Question

A square loop of wire consisting of a single turn is perpendicular to a uniform magnetic field. The square loop is then re-formed into a circular loop, which also consists of a single turn and is also perpendicular to the same magnetic field. The magnetic flux that passes through the square loop is 6.68 × 10-3 Wb. What is the flux that passes through the circular loop?

Answer 1

Answer:

0.0085 Wb

Explanation:

a = Side of square

r = Radius of circle

$\phi_s$ = Magnetic flux through square loop = $6.68\times 10^{-3}\ Wb$

Magnetic flux is given by

$\phi=BA$

For square

$\phi_{s}=Ba^2$

The length of the square will be equal to the circumference of the circle

$4a=2\pi r\\\Rightarrow r=\frac{2a}{\pi}$

For circle

$\phi_{c}=B\pi r^2\\\Rightarrow \phi_{c}=B\pi \left(\frac{2a}{\pi}\right)^2\\\Rightarrow \phi_c=Ba^2\frac{4}{\pi}\\\Rightarrow \phi_c=\phi_s\frac{4}{\pi}\\\Rightarrow \phi_c=6.68\times 10^{-3}\frac{4}{\pi}\\\Rightarrow \phi_c=0.0085\ Wb$

The flux that passes through the circular loop is 0.0085 Wb