Two spherical conductors of radii R1 and R2 are separated by...

Two spherical conductors of radii $R_{1}$ and $R_{2}$ are separated by a distance much larger than the radius of the either sphere. The spheres are connected by a conducting wire as shown in Fig. 3.75. If the charges on the spheres in a. $R_{2} / R_{1}$ b. $R_{2}^{2} / R_{1}^{2}$ c. $R_{1} / R_{2}$ d. $R_{1}^{2} / R_{2}^{2}$

Two spherical conductors of radii $R_{1}$ and $R_{2}$ are separated by a distance much larger than the radius of the either sphere. The spheres are connected by a conducting wire as shown in Fig. 3.75. If the charges on the spheres in
a. $R_{2} / R_{1}$
b. $R_{2}^{2} / R_{1}^{2}$
c. $R_{1} / R_{2}$
d. $R_{1}^{2} / R_{2}^{2}$

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Key Concepts

Electrostatic Equilibrium

When conductors are connected by a conducting wire, they reach a state of electrostatic equilibrium where there is no net movement of charge between them. In this state, all points in the conductors are at the same electric potential, which dictates how charge is distributed across the connected objects.

Electric Potential of a Charged Sphere

For a spherical conductor, the electric potential on its surface is given by the equation V = Q/(4???R), where Q is the charge, R is the radius, and ?? is the permittivity of free space. This relationship shows that, for a given charge, a sphere with a larger radius will have a lower potential, and vice versa.

Charge Distribution

Since the connected spheres must have the same electric potential, their charges adjust so that Q1/(R1) = Q2/(R2). This means that the ratio of the charges on the spheres is directly proportional to the ratio of their radii, specifically Q1:Q2 = R1:R2. This concept explains how charge redistributes in conductors of different sizes to maintain equal potential.

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