Question

Two charged metallic spheres with radii \(R_1\) and \(R_2\) are brought in contact and then separated. The ratio of final charges \(Q_1\) and \(Q_2\) on the two spheres respectively will be _____.
Fill in the blank with the correct answer from the options given below

• A. \(\frac{Q_2}{Q_1}=\frac{R_1}{R_2}\)
• B. \(\frac{Q_2}{Q_1}<\frac{R_1}{R_2}\)
• C. \(\frac{Q_2}{Q_1}>\frac{R_1}{R_2}\)
• D. \(\frac{Q_2}{Q_1}=\frac{R_2}{R_1}\)

Answer 1

The Correct Option is D

Upon contact and subsequent separation of two charged metallic spheres with radii \(R_1\) and \(R_2\), charge redistribution occurs, resulting in equal potentials on both spheres. The potential \(V\) for a sphere with charge \(Q\) and radius \(R\) is defined as:

\(V=\frac{Q}{R}\)

Let \(Q_1\) and \(Q_2\) denote the charges on spheres with radii \(R_1\) and \(R_2\), respectively, after contact. Equating their potentials yields:

\(\frac{Q_1}{R_1}=\frac{Q_2}{R_2}\)

Rearranging this equation provides the ratio of the charges:

\(\frac{Q_2}{Q_1}=\frac{R_2}{R_1}\)

The derived relationship is:

\(\frac{Q_2}{Q_1}=\frac{R_2}{R_1}\)