Question

A short bar magnet has a magnetic moment of \(0.48 \, J {T}^{-1}\). The magnitude of magnetic field at a point at 10 cm distance from the centre of the magnet on its axis is

• A. \(0.96 \, \text{gauss}\)
• B. \(0.48 \, \text{gauss}\)
• C. \(1.92 \, \text{gauss}\)
• D. \(1.44 \, \text{gauss}\)

Hint:

To find magnetic field along the axis of a magnetic dipole, use \( B = \frac{\mu_0}{4\pi} \cdot \frac{2M}{r^3} \). Don’t forget to convert units properly—especially meters to centimeters and Tesla to gauss!

Answer 1

The Correct Option is A

Step 1: Use the formula for magnetic field on the axial line of a short dipole. \[ B = \frac{\mu_0}{4\pi} \cdot \frac{2M}{r^3} \] where: \( M = 0.48 \, \text{J T}^{-1} \) 
\( r = 10 \, \text{cm} = 0.1 \, \text{m} \) 
\( \frac{\mu_0}{4\pi} = 10^{-7} \, \text{T m A}^{-1} \) 
Step 2: Substitute the values. \[ B = 10^{-7} \cdot \frac{2 \times 0.48}{(0.1)^3} = 10^{-7} \cdot \frac{0.96}{0.001} = 10^{-7} \cdot 960 = 9.6 \times 10^{-5} \, \text{T} \] Step 3: Convert tesla to gauss.
\[ 1 \, \text{T} = 10^4 \, \text{gauss} \Rightarrow B = 9.6 \times 10^{-5} \times 10^4 = 0.96 \, \text{gauss} \] Step 4: Select the correct option.
The magnetic field is \(0.96 \, \text{gauss}\), which matches option (1).