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: Understanding the Concept
Inside a long solenoid, the magnetic intensity is \(H=nI\), where \(n\) is the number of turns per unit length.

Step 2: Turns per metre
\[ n=\frac{1000}{4}=250\ \text{turns/m} \]

Step 3: Calculation
\[ H=nI=250\times4=1000\ \text{A/m}=10^3\ \text{A/m} \]

Step 4: Check the options
The diameter of 0.3 m is not needed because the solenoid is long compared with its width (4 m against 0.3 m). Using 1000 turns without dividing by length would give 4000 A/m, which is option (C), a common slip. The answer is option (D).

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