Question

Two conducting sphere of radii a and b are placed at separation d. It is given that d≫a and d≫b so that charge distribution on both the sphere remains spherically symmetric. Assume that a charge +q is given to the sphere of radius a and −q is given to the sphere of radius b.

Write the electrostatic energy (U) of the system and calculate the capacitance of the system using the expression of U.

Answer 1

The electrostatic energy (U) of the system can be calculated using the potential energy equation. The capacitance of the system is calculated using the expression C = q / V. The charges on the spheres are +q and -q, resulting in a total charge of 0 and a capacitance of d / k.

Step-by-step explanation:

The electrostatic energy (U) of the system can be calculated by considering the potential energy between the two charged spheres. The potential energy between two point charges is given by the equation U = k(q1 imes q2) / r, where k is the electrostatic constant, q1 and q2 are the charges on the spheres, and r is the separation between the spheres. In this case, the charge on the sphere of radius a is +q and the charge on the sphere of radius b is -q, so the potential energy can be written as U = k(q^2) / d.

The capacitance of the system can be calculated using the expression C = q / V, where C is the capacitance, q is the charge on each sphere, and V is the potential difference between the spheres. Since the charges on the spheres are +q and -q, the total charge on the system is 0 and the potential difference can be written as V = U / q = kq / d. Substituting this into the equation for capacitance gives C = q / (kq / d) = d / k.