Verified Solution • 2025–26 Session moderate

QPages 277-278: Q11: HC Verma: Concepts of Physics - Volume 2 Permanent Magnets Pages 277-278: Q11 Solution: The magnetic moment of the assumed dipole at the earth's centre …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently confuse the magnetic field formula at the poles with that at the equator, omitting the factor of 2 required for the end-on position. Always use $B = \frac{\mu_0}{4\pi} \frac{2M}{r^3}$ for poles and $B = \frac{\mu_0}{4\pi} \frac{M}{r^3}$ for the equator.

The magnetic moment of the assumed dipole at the earth's centre is

8.0 \times 10^{22} \text{ A m}^2

. Calculate the magnetic field B at the geomagnetic poles of the earth. Radius of the earth is 6400 km.

Step-by-Step Verified Solution

**Answer:**

B = 60 \mu\text{T}

. **Step-by-Step Explanation:** Given:

M = 8.0 \times 10^{22} \text{ A m}^2

,

R = 6400 \text{ km} = 6.4 \times 10^6 \text{ m}

. At geomagnetic poles (end-on):

B = \frac{\mu_0}{4\pi} \frac{2M}{R^3} = 10^{-7} \times \frac{2 \times 8 \times 10^{22}}{(6.4 \times 10^6)^3} = 6 \times 10^{-5} \text{ T} = 60 \mu\text{T}

[citation:12].

All Questions in this Chapter

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