JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Magnetic Effects of Current

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

Answer: 8

Solution

For a long solenoid carrying current

i

with

N

turns over length

ℓ

, the field inside is

B = μ_{0} \frac{N}{ℓ} i ⟹ ℓ = \frac{μ _{0} N i}{B}

ℓ = \frac{( 4 π \times 1 0 ^{- 7} ) ( 200 ) ( 0.29 )}{2.9 \times 1 0 ^{- 4}} = \frac{232 π \times 1 0 ^{- 7}}{2.9 \times 1 0 ^{- 4}} = 80 π \times 1 0^{- 4} m = 8 π c m

The length of the solenoid is

8 π

cm.

JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Integer answer

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