Q97 / 125 · BITSAT 2021 · Physics

A solenoid is $2 \mathrm{~m}$ long and $3 \mathrm{~cm}$ in diameter. It has 5 layers of winding of 1000 turns each and carries a current of $5 \mathrm{~A}$. What is the magnetic field at its centre ? Use the standard value of $\mu_{0}$.

  • A
    $1.57 \times 10^{-4} \mathrm{~T}$
  • B
    $2.57 \times 10^{-3} \mathrm{~T}$
  • Correct answer
    C
    $1.57 \times 10^{-2} \mathrm{~T}$
  • D
    $3.57 \times 10^{-6} \mathrm{~T}$

Solution

Length of solenoid, $l=2 \mathrm{~m}$ Total number of turns, $\mathrm{N}=5 \times 1000=5000$ Number of turns per unit length, $\mathrm{n}=\frac{\mathrm{N}}{l}=\frac{5000}{2}=2500 \mathrm{~m}^{-1}$ Current, I = 5A Now, B $=\mu_{0} \mathrm{nI}=4 \pi \times 10^{-7} \times 2500 \times 5 \mathrm{~T}$ $=1.57 \times 10^{-2} \mathrm{~T}$

Hence, the correct answer is option: 'C'.

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