JEE Main 2026 — Jan 23, Shift 2 — Physics solution

JEE Main2026Jan 23, Shift 2Physics

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 ______ mV.

A
6.6
B
13.2
C
8.25
D
1.32

Solution

Perimeter (constant length of wire): $L = 2 π r = 14 π$ cm. Side of resulting square: $s = \frac{14 π}{4} = \frac{7 π}{2}$ cm.

Initial area: $A_{1} = π r^{2} = 49 π$ cm $^{2}$ .

Final area: $A_{2} = s^{2} = \frac{49 π ^{2}}{4}$ cm $^{2}$ .

Change in area: $Δ A = A_{2} - A_{1} = \frac{49 π ^{2}}{4} - 49 π = 49 π (\frac{π}{4} - 1)$ cm $^{2}$ .

Converting cm $^{2}$ to m $^{2}$ : factor $1 0^{- 4}$ . Numerically $Δ A \approx 49 π (- 0.215) \approx - 33.1$ cm $^{2} = - 33.1 \times 1 0^{- 4}$ m $^{2}$ .

$∣ΔΦ∣ = B ∣Δ A ∣ = 0.2 \cdot 33.1 \times 1 0^{- 4} \approx 6.62 \times 1 0^{- 4}$ Wb.

$∣ EMF ∣ = \frac{∣ΔΦ∣}{Δ t} = \frac{6.62 \times 1 0 ^{- 4}}{0.5} \approx 1.32 \times 1 0^{- 3}$ V $= 1.32$ mV.

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