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

To find the magnetic intensity at the center of a solenoid, we can use the formula for the magnetic field inside an ideal solenoid:

\(B = \mu_0 n I\)

Where:

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

Given:

• The number of turns \(N = 1200\)
• The length of the solenoid \(L = 2 \, \text{m}\)
• The current \(I = 2 \, \text{A}\)

First, calculate the number of turns per unit length:

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

Now, substitute the values into the formula for magnetic intensity (or magnetic field, \(H\)):

\(H = n I = 600 \times 2 = 1200 \, \text{A/m}\)

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

Therefore, the correct answer is: $1.2 \times 10^3 A m ^{-1}$.