Question

A square loop of side 22cm is changed to a circle in time 0.4s. the Maine field present is 0.2 T. the emf induced is?

Answer 1

induced emf is the negative of rate of change of magnetic flux.

i.e., emf = - $\frac{d\phi}{dt}$

= - $B\frac{dA}{dt}$

a/c to question,

A square loop of side 22cm is changed into a circle.

so, perimeter of square = circumference of circle

or, 4 × 22cm = 2 × 22/7 × r

or, r = 14cm

now, area of circle = πr²

= 22/7 × 14 × 14

= 44 × 14 = 616 cm²

and area of square loop = (side length)²

= (22cm)² = 484 cm²

so, dA = 616cm² - 484 cm² = 132 cm²

now, induced emf = - 0.2T × (132 × 10^-4 m²)/0.4sec

= - 66 × 10^-4 Volts

= -6.6 mV

hence, option (1) is correct choice.