Question

The magnetic field intensity 'H' at the centre of a long solenoid having 'n' turns per unit length and carrying a current 'I', when no material is kept in it, is

• A. $\frac{1}{nI}$
• B. $\frac{n}{I}$
• C. $nI$
• D. $n^2 I$

Hint:

Always keep your unit relations straight: Magnetic induction $B$ depends on the medium properties ($\mu_0$), whereas magnetic intensity $H$ is independent of the medium and depends strictly on the current configuration geometry ($nI$)!

Answer 1

The Correct Option is C

Step 1: Recall the field inside a solenoid.
For a long solenoid the magnetic flux density is $B=\mu_0 nI$.

Step 2: Relate $B$ and $H$.
With nothing inside (vacuum or air), $B=\mu_0 H$, so $H=\frac{B}{\mu_0}$.

Step 3: Combine.
\[ H=\frac{\mu_0 nI}{\mu_0}=nI \]
\[ \boxed{nI} \]