Two metallic spheres of radii a and b are placed faraway from each other and are connected for a thin conducting wire. A charge Q is given to one of the spheres . Calculate the charge on each sphere at electrostatic equilibrium.

Explanation

To solve the problem of finding the charge on each metallic sphere at electrostatic equilibrium, we can follow these steps:

### Step 1: Understand the System
We have two metallic spheres with radii \( a \) and \( b \). Initially, one sphere has a charge \( Q \), and the other is neutral. When connected by a thin conducting wire, charges will redistribute until electrostatic equilibrium is reached.

### Step 2: Conservation of Charge
The total charge in the system must remain constant. If we denote the charge on sphere 1 (radius \( a \)) as \( Q_1 \) and the charge on sphere 2 (radius \( b \)) as \( Q_2 \), we can write:
\[
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