JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Electromagnetic Induction

A 30 cm long solenoid has 10 turns per cm and area of

5 cm^{2}

. The current through the solenoid coil varies from 2 A to 4 A is 3.14 s. The e.m.f. induced in the coil is

α \times 1 0^{- 5} V

. The value

α

is ______.

(A)60
(B)12✓ Correct
(C)120
(D)34

Answer: (B)

Solution

The self-inductance of the solenoid is

L = μ_{0} n^{2} A ℓ

, with

n = 1000 m^{- 1}

A = 5 \times 1 0^{- 4} m^{2}

and

ℓ = 0.3 m

, giving

L = 4 π \times 1 0^{- 7} \times (1 0^{3})^{2} \times 5 \times 1 0^{- 4} \times 0.3 = 6 π \times 1 0^{- 5} H

. The current changes at

\frac{d i}{d t} = \frac{4 - 2}{3.14} = \frac{2}{π} A/s

. The induced emf is

ε = L \frac{d i}{d t} = 6 π \times 1 0^{- 5} \times \frac{2}{π} = 12 \times 1 0^{- 5} V

. The value of

α

12

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Single correct option

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