A long solenoid is formed by winding 20 turns cm−1. The current which is necessary to produce a magnetic field of 20 mT inside the solenoid is approximately
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8.0 A
The field inside a long solenoid is uniform and depends only on the number of turns per unit length and the current:
\( \displaystyle B = \mu_0 nI \;\Rightarrow\; I = \frac{B}{\mu_0 n} \)
\( n = 20\,\mathrm{turns\,cm^{-1}} = 2000\,\mathrm{turns\,m^{-1}} \)
\( B = 20\,\mathrm{mT} = 2\times10^{-2}\,\mathrm{T} \)
\( \displaystyle I = \frac{2\times10^{-2}\,\mathrm{T}}{4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}} \times 2000\,\mathrm{m^{-1}}} \)
\( \displaystyle I = \frac{2\times10^{-2}}{2.51\times10^{-3}}\,\mathrm{A} \approx 7.96\,\mathrm{A} \approx 8.0\,\mathrm{A} \)
Note: A similar question was also asked in CUET (UG) 2024 on 19-07-2024 (Slot 1).