A charge ‘Q’ is given to a conducting sphere of radius R. The total energy stored is Choose answer:

To solve for the total energy stored in a conducting sphere with a charge $Q$ and radius $R$, we can follow these steps:

1. Break Down the Problem

We need to find the total electrostatic energy stored in the electric field around a charged conducting sphere. We will use the formula for the energy stored in the electric field of a charged conductor.

2. Relevant Concepts

The electric potential $V$ of a charged conducting sphere of radius $R$ with charge $Q$ is given by the formula: $V = \frac{1}{4\pi \epsilon_0} \cdot \frac{Q}{R}$ where $\epsilon_0$ is the permittivity of free space.

The energy $U$ stored in the electric field can be calculated using the formula: $U = \frac{1}{2} Q V$

3. Analysis and Detail

Substituting for $V$ from the potential equation into the energy equation: $U = \frac{1}{2} Q \left( \frac{1}{4\pi \epsilon_0} \cdot \frac{Q}{R} \right)$ Simplifying this expression: $U = \frac{Q^2}{2 \cdot 4\pi \epsilon_0 R}$ $U = \frac{Q^2}{8\pi \epsilon_0 R}$

4. Verify and Summarize

The derived expression shows the total energy stored in terms of the charge $Q$ and radius $R$ of the sphere.

Final Answer

The total energy stored in the conducting sphere is given by: $U = \frac{Q^2}{8\pi \epsilon_0 R}$