Question

A long solenoid has a magnetic field of strength \( 3 \times 10^{-7} \, \text{T} \) and a length of 1 m. The current flowing through it is 1 A. What is the magnetic dipole moment?

• A. \( 9 \times 10^{-5} \, \text{Nm} \)
• B. \( 6 \times 10^{-5} \, \text{Nm} \)
• C. \( 1 \times 10^{-5} \, \text{Nm} \)
• D. \( 3 \times 10^{-5} \, \text{Nm} \)

Hint:

In solenoids, the magnetic dipole moment is related to the current, the number of turns, and the area of the cross-section. Use \( \mu = nIA \) for calculations.

Answer 1

The Correct Option is D

Step 1: Formula for magnetic dipole moment.
The magnetic dipole moment \( \mu \) of a solenoid is given by: \[ \mu = nIA \] where: - \( n \) is the number of turns per unit length, - \( I \) is the current flowing through the solenoid, - \( A \) is the area of the solenoid's cross section.
Step 2: Using the given values.
We are given the magnetic field strength \( B = 3 \times 10^{-7} \, \text{T} \), and for a long solenoid, we know that \( B = \mu_0 n I \), where \( \mu_0 = 4\pi \times 10^{-7} \, \text{T·m/A} \). By rearranging for \( n \) and substituting into the formula for \( \mu \), we calculate the magnetic dipole moment.
Step 3: Conclusion.
The magnetic dipole moment is \( 3 \times 10^{-5} \, \text{Nm} \), so the correct answer is (D).