❓How is the surface force on the field calculated in electrostatics?

The surface force $\mathbf{F}$ exerted by the field in one region ($x_3 > 0$) on the field in another region ($x_3 < 0$) across a boundary surface ($x_3 = 0$) is calculated by integrating the surface force element ($\mathbf{dF}$) over the entire boundary surface $S$. $\mathbf{F} = \int_{S} \mathbf{dF} = \int_{S} \mathbf{\sigma} \cdot \mathbf{n} dA$ In this problem, the normal vector $\mathbf{n}$ is $\mathbf{e}_3$, and the surface element is $$\mathbf{dF} = \sigma{i3} \mathbf{e}_i dA$$.

Here is the complete explanation:

🧮 Calculating Surface Force in Electrostatics

The calculation of the surface force on the electromagnetic field is a direct application of the Maxwell Stress Tensor ($\mathbf{\sigma}$) in its integral form. This method views the electromagnetic field itself as a medium under stress, which transmits forces across any imaginary boundary surface.

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