Question

What is the equivalent capacitance of the system consisting of two spherical conductors, A1 and A2, with radii r1 and r2, respectively, and carrying charges q1 and q2, connected in air by a copper wire?

Answer 1

The equivalent capacitance of the system is calculated using the formula 1/Ceq = 1/C1 + 1/C2, where C1 and C2 are the capacitances of the individual conductors. The capacitance of a spherical conductor can be calculated using the formula C = 4πε0(εr)R, where ε0 is the permittivity of free space, εr is the relative permittivity of the material, and R is the radius of the conductor.

Step-by-step explanation:

The equivalent capacitance of the system consisting of two spherical conductors, A1 and A2, connected by a copper wire in air can be calculated using the formula:

1/Ceq = 1/C1 + 1/C2

Where C1 and C2 are the capacitances of the individual spherical conductors A1 and A2, respectively.

The capacitance of a spherical conductor can be calculated using the formula:

C = 4πε0(εr)R

Where ε0 is the permittivity of free space (8.85 x 10^-12 F/m), εr is the relative permittivity of the material between the conductors (in this case, air), and R is the radius of the conductor.

Using these formulas, you can calculate the capacitance of each conductor and then use the first formula to find the equivalent capacitance of the system.