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A thin circular disk of radius R carries a uniform positive surface charge density σ. If the disk is set into steady rotation about its symmetry axis with angular speed ω, its magnetic dipole moment is

1. (a) πR⁴σω / 2
2. (b) πR⁴σω
3. (c) πR⁴σω / 4
4. (d) 2πR⁴σω

Correct answer: (c) πR⁴σω / 4

Solution

For a ring radius r: dq = sigma*2pi r dr, current di = dq*omega/2pi = sigma*omega*r dr, dm = di*pi r^2 = pi*sigma*omega*r^3 dr. Integrating 0 to R gives m = pi*sigma*omega*R^4/4.

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