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A ring carrying uniform charge has radius 10 cm and spins about its own axis with a frequency of 10⁴ revolutions per second. At a point on the axis, 20 cm from the centre, the ratio of the electric-field energy density to the magnetic-field energy density is 9.1 × 10¹⁰. Determine the value of a.

1. 7
2. 9
3. 8
4. 6

Correct answer: 9

Solution

On axis, E/B = x*c^2/(2*pi*f*R^2), so E/(cB) = x*c/(2*pi*f*R^2) = (0.2*3e8)/(2*pi*1e4*0.01) = 9.55e4. Then u_E/u_B = (E/(cB))^2 = 9.1e9, giving a = 9.

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