What is divergence theorem in electrostatics?

[Lakshmi N]

 

[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:

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