A long solenoid carries a current of 2 A. The magnetic field inside it is \(2\pi\times10^{-3}\ \mathrm{T}\). The number of turns per centimetre of its length is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 25
Inside a long solenoid the field is uniform and equals \(B=\mu_0nI\), where \(n\) is the number of turns per metre.
\( \begin{aligned} n &= \frac{B}{\mu_0 I} \\ &= \frac{2\pi\times10^{-3}}{4\pi\times10^{-7}\times2} \\ &= 2500\ \mathrm{turns\ per\ metre} \end{aligned} \)
One metre has 100 cm. Therefore, the solenoid has 25 turns per centimetre.
NCERT (2026-27):
The Solenoid – “Let n be the number of turns per unit length, then the total number of turns is nh. …”
\( B=\mu_0 nI \)\( \qquad (4.16) \)