A solenoid of length $L$ and $N$ turns carries a current $I$. What is the magnetic field inside the solenoid far from the ends?

Solution

1. The number of turns per unit length is $n=\frac{N}{L}$.
2. Using Ampere's Law for an ideal solenoid, the magnetic field inside is $B={\mu }_{0}nI$.
3. Substituting $n$, we get $$\begin{array}{rl}B& ={\mu }_0\left(\frac{N}{L}\right)I\\ & =\frac{{\mu }_{0}NI}{L}\end{array}$$.
4. Hence the answer is (A).