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Properties of Field Lines

A metallic sp...

Question

A metallic sphere of radius $R_{1}$ and charge $+ Q$ is nested inside a metallic spherical shell that has radius $R_{2}$ and charge $Q$ .
Which of the following changes will increase the capacitance of the system?
I: Increase the magnitude of the charge, $Q$ .
II: Increase $R_{2}$ while leaving $R_{1}$ fixed.
III: Increase $R_{1}$ while leaving $R_{2}$ fixed.
IV: Increase both R1 and R2 while leaving the difference in radii, $R_{2} - R_{1}$ , fixed.

I only

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II only

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III only

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III and IV only

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II, III, and IV only

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Solution

The correct option is D III and IV only
Capacitance of spherical capacitor, $C = \frac{4 π ϵ_{o}}{\frac{1}{R_{1}} - \frac{1}{R_{2}}} = \frac{4 π ϵ_{o} (R_{1} R_{2})}{R_{2} - R_{1}}$
Thus option D is correct.

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The correct option is D III and IV onlyCapacitance of spherical capacitor, C=4πϵo1R1−1R2=4πϵo(R1R2)R2−R1Thus option D is correct.

The correct option is D III and IV only
Capacitance of spherical capacitor, $C = \frac{4 π ϵ_{o}}{\frac{1}{R_{1}} - \frac{1}{R_{2}}} = \frac{4 π ϵ_{o} (R_{1} R_{2})}{R_{2} - R_{1}}$
Thus option D is correct.