Question

A bar magnet has pole strength of 15 A m and magnetic length 1 cm. What is the magnetic induction produced by it at a distance of 50 cm from either pole? (Given: \( \dfrac{\mu_0}{4\pi} = 10^{-7} \, \text{Wb A}^{-1}\text{m}^{-1} \))

• A. \(1.2 \times 10^{-6} \, \text{Wb m}^{-2}\)
• B. \(2.4 \times 10^{-5} \, \text{Wb m}^{-2}\)
• C. \(0.12 \times 10^{-6} \, \text{Wb m}^{-2}\)
• D. \(24 \times 10^{-5} \, \text{Wb m}^{-2}\)

Hint:

At large distances, a bar magnet behaves like a pair of magnetic poles.

Answer 1

The Correct Option is C

Step 1: Formula for magnetic field due to a pole.
\[ B = \frac{\mu_0}{4\pi} \cdot \frac{m}{r^2} \]
Step 2: Substituting values.
\[ m = 15 \, \text{A m}, \quad r = 0.5 \, \text{m} \]
Step 3: Calculation.
\[ B = 10^{-7} \times \frac{15}{(0.5)^2} \] \[ B = 10^{-7} \times \frac{15}{0.25} = 60 \times 10^{-7} \]
Step 4: Result.
\[ B = 0.12 \times 10^{-6} \, \text{Wb m}^{-2} \]
Step 5: Conclusion.
The magnetic induction produced is \(0.12 \times 10^{-6} \, \text{Wb m}^{-2}\).