Question

Based on its definition as electric flux per unit volume, what are the units of the divergence of electric field.

Short answer

The unit of divergence of electric field is $\left[\text{N}·\text{m}/\text{C}\right]$.

Step-by-step solution

Conceptual Explanation

The divergence of electric field at any point is the effect of the charge density in a medium

Formula of divergence of electric field

The electric flux of enclosed surface is given as:

$\varphi =\frac{Q}{{\epsilon }_0}......\left(1\right)$

Here, $Q$ is the enclosed charge and its units is Coulomb (C) and ${\epsilon }_0$is the permittivity of free space and its unit is ${\text{C}}^2/\text{N}·{\text{m}}^2$ so the unit of electric flux is $\text{N}·{\text{m}}^2/C$

The divergence of the electric field is given as:

$\nabla ·E=\frac{\varphi }{V}......\left(1\right)$

Determination of unit of divergence of electric field

Substitute units of electric flux and volume in the equation (1).

$$\begin{gathered} \nabla ·E=\frac{\text{N}·{\text{m}}^2/C}{{\text{m}}^3} \\ \nabla ·E=\left[\text{N}·\text{m}/\text{C}\right] \end{gathered}$$

Therefore, the unit of divergence of electric field on the basis of electric flux per unit volume is $\left[\text{N}·\text{m}/\text{C}\right]$.