# What is divergence theorem in electrostatics?

1. Jul 30, 2011

### Lakshmi N

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 30, 2011

### Clever-Name

What do you mean :S

The divergence theorem just states:

$$\int_{\mathcal{V}}(\mathbf\nabla\cdot\mathbf{v})d{\tau} = \oint_{\mathcal{S}} \mathbf{v}\cdot d{\mathbf{a}}$$

This can be applied in electrostatics by:

$$\int_{\mathcal{V}} (\mathbf\nabla\cdot\mathbf{E})d{\tau} = \oint_{\mathcal{S}} \mathbf{E}\cdot d{\mathbf{a}} = \frac{1}{{\epsilon}_{0}}\int_{\mathcal{V}} {\rho} d\tau = \frac{1}{{\epsilon}_{0}} Q_{enc}$$