Question

A solenoid of $1200$ tums is wound uniformly in a single layer on a glass tube $2\, m$ long and $02\, m$ in diameter The magnetic intensity at the center of the solenoid when a current of $2 A$ flows through it is:

• A. $2.4 \times 10^3 A m ^{-1}$
• B. $1.2 \times 10^3 A m ^{-1}$
• C. $1 Am ^{-1}$
• D. $2.4 \times 10^{-3} A m ^{-1}$

Answer 1

The Correct Option is B

The problem involves calculating the magnetic intensity at the center of a solenoid. To solve this, we use the formula for the magnetic field inside a solenoid:

\(B = \mu_0 \cdot n \cdot I\)

where:

• \(B\) is the magnetic field inside the solenoid.
• \(\mu_0\) is the permeability of free space, approximately \(4\pi \times 10^{-7} \, T \cdot m/A\).
• \(n\) is the number of turns per unit length of the solenoid.
• \(I\) is the current flowing through the solenoid.

Given:

• Total number of turns, \(N = 1200\).
• Length of the solenoid, \(L = 2 \, m\).
• Current, \(I = 2\, A\).

First, calculate the number of turns per unit length:

\(n = \frac{N}{L} = \frac{1200}{2} = 600 \, \text{turns/m}\)

The magnetic intensity, \(H\), inside the solenoid is given by:

\(H = n \cdot I\)

Substitute the values:

\(H = 600 \times 2 = 1200 \, A/m\)

Thus, the magnetic intensity at the center of the solenoid is \(1.2 \times 10^3 \, A/m\).

This matches the given correct option:

$1.2 \times 10^3 A m ^{-1}$