The two pages explain the Maxwell Stress Tensor ($\mathbf{T}$) and the simplifying effect of static and source-free conditions on the total electromagnetic force ($\mathbf{F}{\text{field}}$). The first defines the Maxwell Stress Tensor as a second-rank tensor representing the momentum flux (force per unit area) of the electromagnetic field, providing the general force equation $\mathbf{F}{\text{field}} = \int_V (\nabla \cdot \mathbf{T} - \frac{\partial \mathbf{g}}{\partial t}) d\tau$. The second then details how the static (\partial/\partial t=0) and source-free ($\rho=0, \mathbf{J}=0$) conditions simplify this total force expression to zero by two equivalent methods: the source-free condition directly eliminates the Lorentz force density ($\mathbf{f}{\text{matter}} = 0$), and the static condition eliminates the rate of change of momentum ($\partial \mathbf{g}/\partial t = 0$), leaving $\mathbf{F}{\text{field}} = \int_V (\nabla \cdot \mathbf{T}) d\tau$, where the source-free condition also ensures $\nabla \cdot \mathbf{T}=0$, ultimately confirming that the total electromagnetic force is zero in a static, source-free volume.

Cue Columns

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  1. What is the Maxwell stress tensor and how is it related to the total electromagnetic force?
  2. How do the static and source-free conditions simplify the expression for the total force on the electromagnetic field? </aside>