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

Answer 2

The magnetic flux that passes through the circular loop is 0.00848 Wb.

What is the magnetic flux?

The magnetic flux is defined as the measurement of the total magnetic field which passes through a given area.

Given that the magnetic flux that passes through the square loop is 6.68 × 10-3 Wb.

Let's consider that r is the radius of the circle and a is the side of the square.

The magnetic flux through the square loop is given below.

$\phi_s = Ba^2$

Where B is the magnetic field.

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

$4a = 2\pi r$

$r = \dfrac {2a}{\pi}$

The magnetic flux through the circular loop is given below.

$\phi = BA$

Where A is is the cross-sectional area of the circular loop.

$\phi = B \pi r^2$

$\phi = B \pi (\dfrac {2a}{\pi})^2$

$\phi = B\pi \times \dfrac {4a^2}{\pi^2}$

$\phi = Ba^2 \dfrac {4}{\pi}$

$\phi = \phi_s \dfrac {4}{3.14}$

$\phi = 6.68 \times 10^{-3} \times 1.27$

$\phi = 0.00848 \;\rm Wb$

Hence we can conclude that the magnetic flux that passes through the circular loop is 0.00848 Wb.

To know more about the magnetic flux, follow the link given below.

https://brainly.com/question/15359941.