Note 35 — ON THE FUNDAMENTAL CONCEPTS OF ELECTROSTATICS.[26]

The energy of a sphere of radius r charged with the quantity q is 1/2(q2/r). If the radius increase by the space dr a loss of energy occurs, and the work done is 1/2(q2/r2)dr. Letting p denote the uniform electrical pressure on unit of surface of the sphere, the work done is also 4r2πpdr. Hence p = (1/8r2π)(q2/r2). Subjected to the same superficial pressure on all sides, say in a fluid, our half sphere would be an equilibrium. Hence we must make the pressure p act on the surface of the great circle to obtain the effect on the balance, which is r2πp = 1/8(q2/r2) = 1/8V2.