I was reading Introduction to Electrodynamics By D.J. Griffiths Chapter 8 Conservation Laws , Maxwell's Stress Tensor.The starting lines are the following
Let's calculate the total electromagnetic force on the charges in volume $\textit{V}$ :
$$\mathbf{F}=\int _\mathit{V} ( \mathbf{E} + \mathbf{v} \times \mathbf{B} )\rho d\tau $$
$$ =\int _\mathit{V} ( \rho \mathbf{E} + \mathbf{J} \times \mathbf{B} )d\tau . $$
My doubt is that '' Is $\mathbf{E} \ \mathit{and} \ \mathbf{B} $ are external fields or internal fields? If internal due to charge distribution of you are applying lorentz force? If external then How they are using the Maxwell's Equations where As I know $\mathbf{E} \ \mathit{and} \ \mathbf{B} $ are not the source terms but produced due to $\mathit{J} \ \textit{and} \ \rho$. Correct me if I am going in wrong direction.