A spherical capacitor is formed from two concentric,...

A spherical capacitor is formed from two concentric, spherical, conducting shells separated by vacuum. The inner sphere has radius 15.0 $\mathrm{cm}$ and the capacitance is 116 $\mathrm{pF}$ (a) What is the radius of the outer sphere? (b) If the potential difference between the two spheres is $220 \mathrm{V},$ what is the magnitude of charge on each sphere?

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Key Concepts

Capacitance Calculation in Spherical Geometry

The capacitance of a spherical capacitor is determined from the geometry of the system. It is expressed in terms of the radii of the two shells and the permittivity of the medium (vacuum in this case). This derivation demonstrates how the spatial configuration of conductors affects the device’s ability to store electric charge.

Charge-Voltage Relationship

The basic relation Q = C × V links the stored charge (Q) to the capacitance (C) and the potential difference (V) between the conductors. This concept is fundamental in electrostatics and allows one to compute the charge distribution on capacitors when the potential difference is known.

Spherical Capacitor

A spherical capacitor consists of two concentric spherical conductors separated by an insulating medium (often vacuum). The key aspect of this configuration is that its capacitance depends only on the radii of the inner and outer spheres, not on their absolute sizes, and it is derived using principles of symmetry and Gauss's law in electrostatics.

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