Question

A solenoid of 1000 turns is wound uniformly on a glass tube 4 m long and \(0.3\) m in diameter. The magnetic intensity at the centre of the solenoid when a current of 4 A flows through it is

• A. \(2\times 10^{+3} \text{A/m}\)
• B. \(16\times 10^{+3} \text{A/m}\)
• C. \(4\times 10^{+3} \text{A/m}\)
• D. \(10^{+3} \text{A/m}\)

Hint:

Magnetic intensity inside a long solenoid is H = nI.

Answer 1

The Correct Option is D

Step 1: Approach
Use Ampere's law for a long solenoid.

Step 2: Result
$B=\mu_0nI$ and $H=B/\mu_0=nI$. Here $n=\dfrac{1000}{4}=250$ m$^{-1}$, so $H=250\times4=1000$ A/m.

Step 3: Answer
Option (D).

Final Answer:
With 250 turns per metre and 4 A, H = nI = 1000 A/m, option (D). \[ \boxed{10^{3}\ \text{A/m}} \]