Question

Two spheres have radii a and b and their centres are at a distance d apart. Show that the capacitance of this system is;

$C=\frac{4\pi {\epsilon }_o}{\frac{1}{a}+\frac{1}{b}\pm \frac{2}{d}}$

provided that d is large compared with a and b.

Answer 1

$V_1=\frac{KQ}{a}-\frac{KQ}{d}$

$V_2=-\frac{KQ}{b}+\frac{KQ}{d}$

$C=\frac{Q}{V_1-V_2}=\frac{4\pi {\epsilon }_0}{\frac{1}{a}+\frac{1}{b}-\frac{2}{d}}$