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QPages 230-234: Q61: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q61 Solution: Consider a solid sphere of radius and mass that has a charge…

⚠️ Common Exam Traps & Conceptual Pitfalls

When computing the magnetic moment of a uniformly charged rotating sphere, students frequently drop the prefactor ½ in the definition $\mu=\tfrac12\int \mathbf r\times\mathbf J\,dV$, or they replace the volume current by a surface current. This omission removes the essential factor that balances the $\tfrac{2}{5}$ moment‑of‑inertia term, leading to an incorrect $\mu$‑to‑$L$ ratio.

Consider a solid sphere of radius

r

and mass

m

that has a charge

q

distributed uniformly over its volume. The sphere is rotated about its diameter with an angular speed

\omega

. Show that the magnetic moment

\mu

and the angular momentum

l

of the sphere are related as

\mu = \frac{q}{2m} l

.

Step-by-Step Verified Solution

**Answer:**

\mu = \frac{q}{2m} L

. **Step-by-Step Explanation:** For a rotating solid sphere, integrate over volume. The result is the same universal ratio.

All Questions in this Chapter

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