Question

A square loop of side 22 cm is changed to a circle in a time of 0.4 s. The magnetic field is 0.2 t. The emf induced is

Answer 1

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Answer 2

The induced emf is 6.55 mV.

Explanation:

Given that,

Side of the square loop, x = 222 cm

It changed to a circle in 0.4 seconds

Magnetic field, B = 0.2 T

To find,

Induced emf.

Solution,

As the square loop is change to a circle such that the area of the square is converted to a circle such that,

Initial area, $A_1=x^2=(22\ cm)^2=0.0484\ m^2$

The perimeter of square = circumference of circle

$4\times 0.22=2\pi r$

r = 0.14 m

New area,

$A_2=\pi (0.14)^2=0.0615\ m^2$

Due to change in area an emf will be induced that is given by :

$\epsilon=-\dfrac{d\phi}{dt}$

$\phi$ = magnetic flux

$\epsilon=-\dfrac{d(BA)}{dt}$

$\epsilon=-B\dfrac{A_2-A_1}{dt}$

$\epsilon=-B\dfrac{A_2-A_1}{t}$

$\epsilon=-0.2\times \dfrac{0.0615-0.0484}{0.4}$

$\epsilon=-0.00655\ volts$

$\epsilon=-6.55\times 10^{-3}\ volts$

$\epsilon=-6.55\ mV$

So, the induced emf is 6.55 mV.

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Induced emf

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