A solenoid of length 0.5 m has a radius of 1 cm and is made up of ' m ' number of turns. It carries a current of 5 A. If the magnitude of the magnetic field inside the solenoid is 6.28 × 10⁻³ T then the value of m is __________. Numerical answer type. Work it out, then open the answer.

Answer: 500. B = (μ₀ m I)/(L) ⇒ m = (BL)/(μ₀ I). m = 6.28 × 10⁻³ × 0.54π × 10⁻⁷ × 5 = 3.14 × 10⁻³6.28 × 10⁻⁶. m = 500 turns.

A solenoid of length 0.5 m has a radius of 1 cm and is made up of ' m… | JEE Main 2024 (5 Apr, Shift 2)

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Ampere's Law, Cylinders, Solenoid & Toroid

A solenoid of length $0.5\text{ m}$ has a radius of $1\text{ cm}$ and is made up of ' $\mathrm{m}$ ' number of turns. It carries a current of $5\text{ A}$ . If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3}\text{ T}$ then the value of $\mathrm{m}$ is __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 500

$B = \dfrac{\mu_0 m I}{L} \Rightarrow m = \dfrac{BL}{\mu_0 I}$ .
$m = \dfrac{6.28 \times 10^{-3} \times 0.5}{4\pi \times 10^{-7} \times 5} = \dfrac{3.14 \times 10^{-3}}{6.28 \times 10^{-6}}$ .
$m = 500$ turns.

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