Question

Derive an expression for the capacitance of two concentric hollow spherical conductors of radii R1 and R2. What value do you get for the capacitance when R1 = ? and R2 = ?

Answer 1

To derive the capacitance of two concentric hollow spherical conductors, one can use Gauss's Law and the definition of capacitance involving the charge and the potential difference between the conductors.

Step-by-step explanation:

The capacitance of two concentric hollow spherical conductors can be derived using Gauss's Law and the definition of capacitance. First, we assume the two spheres have charges +Q and -Q. By applying Gauss's Law to a spherical surface between the conductors, we find that the electric field E at a radius r is given by E = Q / (4πε₀r²). The potential difference V between the two spheres is obtained by integrating the electric field over the radial distance from R1 to R2. The capacitance C is then given by C = Q / V.