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3 months ago in Electromagnetics By Anita Bhatia

What is vacuum permittivity in two dimensions?

We all know ε? ≈ 8.85×10?¹² F/m in our 3D world. If I'm working in a purely 2D electrostatic model, what value do I use?

DimensionalAnalysis

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By Sourabh Answered 3 months ago

You don't plug in the 3D value—you redefine the units. In 2D, the electric field from a point charge falls off as 1/r, not 1/r². The constant ε? gets absorbed into a rescaled charge unit. Conveniently, we often set the 2D "permittivity" to 1/(2π) so Gauss's law becomes ? E · dl = q / ε_2D. It's not the same physical constant; it's a model parameter.

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