A long solenoid is formed by winding 40 turns/cm. The current required to produce a magnetic field of 22 mT inside the solenoid will be (Take \( \mu_0 = 4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}} \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4.4 A
The field inside a long solenoid is uniform and depends on the number of turns per unit length \( n \):
\( \displaystyle B = \mu_0\,n\,I \;\Rightarrow\; I = \frac{B}{\mu_0\,n} \)
\( n = 40\,\mathrm{cm^{-1}} = 4000\,\mathrm{m^{-1}} \)
\( B = 22\,\mathrm{mT} = 22\times10^{-3}\,\mathrm{T} \)
\( \displaystyle I = \frac{22\times10^{-3}}{4\pi\times10^{-7} \times 4000} = \frac{22\times10^{-3}}{5.03\times10^{-3}} \approx 4.4\,\mathrm{A} \)