A 30 cm long solenoid has 10 turns per cm and area of 5 . The current through the solenoid coil varies from 2 A to 4 A is 3.14 s

Question

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 $α \times 10^{- 5} V$ . The value $α$ is ______. [2026]

Smart Achievers · Accepted Answer

(2)

$< ε > = L \frac{Δ I}{Δ t} (magnitude)$

$α \times 10^{- 5} = (\frac{μ_{0} N^{2} A}{ℓ}) \frac{(I_{2} - I_{1})}{t}$

$α \times 10^{- 5} = \frac{4 π \times 10^{- 7} \times (300) (300) \times 5 \times 10^{- 4}}{30 \times 10^{- 2}} \times \frac{2}{3.14}$

$α \times 10^{- 5} = 120 \times 10^{- 6} \Rightarrow α = 12$

Solution

Q.
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 $α \times 10^{- 5} V$ . The value $α$ is ______. [2026]

1 60

2 12

3 120

4 34

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