Question

For a short magnet, the magnetic field on the axial line at a distance 10 cm from its centre is \( 1.6 \times 10^{-7} \, T \). What is the magnetic field on its equatorial line at the same distance 10 cm from its centre?

• A. \( 4.8 \times 10^{-7} \, T \)
• B. \( 3.2 \times 10^{-8} \, T \)
• C. \( 1.6 \times 10^{-7} \, T \)
• D. \( 0.8 \times 10^{-7} \, T \)

Hint:

Axial field is always twice the equatorial field for a short magnet.

Answer 1

The Correct Option is D

Step 1: Magnetic field on axial line.
\[ B_{axial} = \frac{\mu_0}{4\pi} \frac{2M}{r^3} \]

Step 2: Magnetic field on equatorial line.
\[ B_{eq} = \frac{\mu_0}{4\pi} \frac{M}{r^3} \]

Step 3: Relation between fields.
\[ B_{axial} = 2 B_{eq} \]

Step 4: Given axial field.
\[ B_{axial} = 1.6 \times 10^{-7} \]

Step 5: Find equatorial field.
\[ B_{eq} = \frac{1.6 \times 10^{-7}}{2} \]

Step 6: Calculate.
\[ B_{eq} = 0.8 \times 10^{-7} \]

Step 7: Final Answer.
\[ \boxed{0.8 \times 10^{-7} \, T} \]