A metallic sphere of radius R1 and charge +Q is nested inside a metallic spherical shell that has radius R2 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 R2 while leaving R1 fixed.
III: Increase R1 while leaving R2 fixed.
IV: Increase both R1 and R2 while leaving the difference in radii, R2−R1, fixed.
A
I only
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B
II only
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C
III only
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D
III and IV only
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E
II, III, and IV only
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Solution
The correct option is D III and IV only Capacitance of spherical capacitor, C=4πϵo1R1−1R2=4πϵo(R1R2)R2−R1