JEE Main 2025 Jan 29 Shift 2, Physics Q21: Magnetic Field due to Electric Current

JEE Main2025Jan 29, Shift 2Physics

The magnetic field inside a $200$ turns solenoid of radius $10$ cm is $2.9 \times 1 0^{- 4}$ Tesla. If the solenoid carries a current of $0.29$ A, then the length of the solenoid is __________ $π$ cm.

Your answer

Solution

Treat the solenoid as long, so $B = μ_{0} n I = μ_{0} \frac{N}{L} I$ .

$L = \frac{μ _{0} N I}{B} = \frac{( 4 π \times 1 0 ^{- 7} ) ( 200 ) ( 0.29 )}{2.9 \times 1 0 ^{- 4}}$

$= \frac{4 π \times 58 \times 1 0 ^{- 7}}{2.9 \times 1 0 ^{- 4}} = 80 π \times 1 0^{- 3} m = 8 π cm$ .

$∴$ The blank is $8$ .

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JEE Main 2025 Jan 29 Shift 2, Physics Q21: Magnetic Field due to Electric Current

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