JEE Main 2026 Apr 8 Shift 2, Physics Q15: Inductance

JEE Main2026Apr 8, Shift 2Physics

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
$12$
C
$120$
D
$34$

Solution

Self-inductance of a solenoid: $L = μ_{0} n^{2} A ℓ$ , where $n = 1000$ turns/m, $A = 5 \times 1 0^{- 4}$ m $^{2}$ , $ℓ = 0.3$ m.

EMF magnitude: $∣ ε ∣ = L \frac{∣ d i ∣}{d t} = μ_{0} n^{2} A ℓ \cdot \frac{d i}{d t}$ .

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

$∣ ε ∣ = (4 π \times 1 0^{- 7}) (1 0^{6}) (5 \times 1 0^{- 4}) (0.3) \cdot \frac{2}{π}$

$= 4 \times 1 0^{- 7 + 6 - 4} \cdot 0.3 \cdot 2 \cdot \frac{1}{1} \cdot 5 = 4 \cdot 5 \cdot 0.3 \cdot 2 \times 1 0^{- 5} = 12 \times 1 0^{- 5}$ V.

$∴$ $α = 12$ .

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JEE Main 2026 Apr 8 Shift 2, Physics Q15: Inductance

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