CAIE A-Level Physics A2 19.1.1 Capacitance As Applied to Both Isolated Spherical Conductors and to

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An isolated conducting sphere in a vacuum has radius r and is initially uncharged. It is then charged by friction so that it carries a final charge Q. This charge can be considered to be acting at the centre of the sphere.

By considering the electric potential at its surface, show that the capacitance C of the sphere is given by

C=4 \pi \varepsilon_{0} r

where $\varepsilon_{0}$ is the permittivity of free space.

C=Q / V
$V=Q /\left(4 \pi \varepsilon_{0} r\right)$ and so $C=Q /\left[Q /\left(4 \pi \varepsilon_{0} r\right)\right]=4 \pi \varepsilon_{0} r$

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CAIE A-Level Physics A2 19.1.1 Capacitance As Applied to Both Isolated Spherical Conductors and to Topic Practice

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