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A disc of radius R carries a surface charge density sigma(r) = sigma0*(1 - r/R), where sigma0 is constant and r is the distance from the centre. A large spherical surface that completely encloses the disc records electric flux phi0, while a concentric spherical surface of radius R/4 records flux phi. Find the ratio phi0/phi.

1. 6.4
2. 4.0
3. 8.0
4. 10.0

Correct answer: 6.4

Solution

Total charge q_total = sigma0*2*pi*(R²/2 - R²/3) = sigma0*2*pi*R²/6. Charge inside R/4 is q_small = sigma0*2*pi*((R/4)²/2 - (R/4)³/(3R)). The flux ratio equals the charge ratio, which works out to 6.4.

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