A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is…

Given: radius of the circular loop is r = 7 cm = 0.07 m, magnetic field is B = 0.2 T, and time taken is t = 0.5 s. Find: the induced EMF when the circular loop is converted into a square loop. Initial area of the circle is A1 = r^2 = 227(0.07)^2 = 154 10^-4 m^2 Perimeter of the original loop is L = 2 r = 44 cm So the side of the square is a = 11 cm Final area of the square is A2 = a^2 = (0.11)^2 = 121 10^-4 m^2 Change in magnetic flux is = B(A2 - A1) = 0.2(121 - 154) 10^-4 = -6.6 10^-4 Wb Hence the magnitude of induced EMF is = | | t = 6.6 10^-40.5 = 13.2 10^-4 V Therefore, = 1.32 10^-3 V = 1.32 mV The correct option is D.

A circular loop of radius 7 cm is placed in uniform magnetic fiel… — Solution | JEE Physics

MCQEasyJEE 2026Faraday's Laws of EMI

A circular loop of radius $7 \, \text{cm}$ is placed in uniform magnetic field of $0.2 \, \text{T}$ directed perpendicular to plane of loop. The loop is converted into a square loop in $0.5 \, \text{s}$ . The EMF induced in the loop is ___ $\text{mV}$ .__

A
$13.2$
B
$8.25$
C
$6.6$
D
$1.32$

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: radius of the circular loop is $r = 7 \, \text{cm} = 0.07 \, \text{m}$ , magnetic field is $B = 0.2 \, \text{T}$ , and time taken is $\Delta t = 0.5 \, \text{s}$ .

Find: the induced EMF when the circular loop is converted into a square loop.

Initial area of the circle is

A_1 = \pi r^2 = \frac{22}{7}(0.07)^2 = 154 \times 10^{-4} \, \text{m}^2

Perimeter of the original loop is

L = 2\pi r = 44 \, \text{cm}

So the side of the square is

a = 11 \, \text{cm}

Final area of the square is

A_2 = a^2 = (0.11)^2 = 121 \times 10^{-4} \, \text{m}^2

Change in magnetic flux is

\Delta \Phi = B(A_2 - A_1) = 0.2(121 - 154) \times 10^{-4} = -6.6 \times 10^{-4} \, \text{Wb}

Hence the magnitude of induced EMF is

\epsilon = \frac{|\Delta \Phi|}{\Delta t} = \frac{6.6 \times 10^{-4}}{0.5} = 13.2 \times 10^{-4} \, \text{V}

Therefore,

\epsilon = 1.32 \times 10^{-3} \, \text{V} = 1.32 \, \text{mV}

The correct option is D.

Common mistakes

Using the area of the circle and square correctly but forgetting that induced EMF depends on change in flux per unit time. This is wrong because $\epsilon = \frac{|\Delta \Phi|}{\Delta t}$ , not just $|\Delta \Phi|$ . After finding the flux change, always divide by $0.5 \, \text{s}$ .
Taking the square side as $7 \, \text{cm}$ instead of using the same perimeter. This is wrong because the wire length remains unchanged during reshaping. First compute the perimeter of the circle, then use that perimeter to find the side of the square.
Ignoring unit conversion between cm and m. This is wrong because magnetic flux must be calculated in SI units to get EMF in volts. Convert $7 \, \text{cm}$ to $0.07 \, \text{m}$ and $11 \, \text{cm}$ to $0.11 \, \text{m}$ before calculating areas.

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