Physicopoeia

φυσικοποιΐα
THINGS I WISH I'D KNOWN WHEN I STARTED TEACHING PHYSICS

Permittivity and Permeability

Firstly, I get these the right way round by remembering that permeaBility applies to B-fields.

Secondly, if you've never asked a class who've come across both the permittivity of free space (ε = 8.85 x 10⁻¹²  Fm⁻¹) and the permeability of free space (μ = 4π x 10⁻⁷  Hm⁻¹) to calculate the value of

[1/sqrt(E0 x u0)]

and seen the look of amazement on their faces when they realise it's equal to the speed of light, then you really must. For an explanation, good pupils might spot that, since ε relates to how electric fields transmit their effects through a vacuum, and μ relates to how magnetic fields transmit their effects through a vacuum, it really shouldn't be surprising that some mathematical combination of the two will relate to how easily electromagnetic waves transmit their effects through a vacuum.

Thirdly, it can be really easy not to appreciate a fundamental difference between ε and μ, namely that one is a quantity like resistance but the other is more like conductance. Permittivity (ε) is like resistance - a higher value means that electric fields find it harder to propagate through a substance. Permeability (μ), on the other hand, is like conductance - a higher value means that magnetic fields find it easier to propagate through a substance. This explains why ε is on the denominator of the electric field equations studied in school, but  is in the numerator of many magnetic field equations.