A circular loop of radius 20 cm and resistance \(2 \Omega\) is placed in a time varying magnetic field \(\overrightarrow{\mathrm{B}}=\left(2 \mathrm{t}^{2}+2 \mathrm{t}+3\right) \mathrm{T}\). At \(\mathrm{t}=0\), for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at \(\mathrm{t}=3 \mathrm{~s}\) is \(\frac{\alpha}{50} \mathrm{~A}\). The value of \(\alpha\) is \_\_\_\_ (Take \(\pi=22 / 7\))

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Electromagnetic Induction

A circular loop of radius 20 cm and resistance

2Ω

is placed in a time varying magnetic field

B = (2 t^{2} + 2 t + 3) T

. At

t = 0

, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at

t = 3 s

\frac{α}{50} A

. The value of

α

is ____ (Take

π = 22/7

)

Answer: 44

With the plane of the loop perpendicular to the field the flux is

ϕ = B π r^{2}

, and by Faraday's law the induced emf is

ε = \frac{d ϕ}{d t} = π r^{2} \frac{d B}{d t}

. Here

B = 2 t^{2} + 2 t + 3

, so

\frac{d B}{d t} = 4 t + 2

, and the induced current is

i = \frac{ε}{R} = \frac{π r ^{2}}{R} (4 t + 2)

. Substituting

r = 0.2 m

R = 2 Ω

and

π = \frac{22}{7}

t = 3 s

i = \frac{\frac{22}{7} ( 0.2 ) ^{2}}{2} (14) = \frac{22}{7} \times \frac{0.04}{2} \times 14 = \frac{44}{50} A

. Comparing with

i = \frac{α}{50} A

, the value of

α

44

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Integer answer