Question

A wire $88$ cm long bent into a circular loop is placed perpendicular to the magnetic field of flux density $2.5Wb{m}^{-2}$. Within $0.5$ s, the loop is changed into a square and flux density is increased to $3.0Wb{m}^{-2}$. The value of e.m.f. induced is

• A. $0.018V$
• B. $0.016V$
• C. $0.020V$
• D. $0.012V$

Answer 1

The correct option is A $0.018V$

Answer is A.
The magnetic flux $\varphi =B\times A$ depends on the magnetic field, the area
of the loop, and their relative orientation.
In this case, the wire 88 cm long bent into a circular loop is placed perpendicular to the magnetic field and Within 0.5 s, the loop is changed into a square.
Magnetic Flux when in a circular loop:
Circumference of the loop = $2\times 3.14\times r=88cm$.
So, radius of the loop r = 14 cm.
Magnetic field $\varphi =B\times A=2.5\times 3.14\times 0.14\times 0.14=0.154Wb$.
Magnetic Flux when in a square:
Circumference of the square = $4r=88cm$
So, length of the side of the square is $\frac{88}{4}=22cm$.
Magnetic feild ${\varphi }^{\prime }=B\times A=3\times 0.22\times 0.22=0.1452Wb$.
The total induced emf is $\frac{0.154-0.1452}{0.5}=0.018V$.
Therefore, the value of e.m.f induced is 0.018 V.