1.4 Units and universal constants

The International System of Units (SI) is used throughout. Its base units relevant to us are the metre [m], the kilogram [kg], the second [s] and the ampere [A]. All other units are derived from them, for example

Checking that both sides of an equation have the same unit is the simplest and one of the most effective tests of a derivation, and it is used often in the solved problems.

Three universal constants characterise free space (vacuum):

• the speed of light in vacuum, $c=299792458$ m/s ($\approx 3\times 10^8$ m/s), exact by the definition of the metre,
• the permeability of free space, ${\mu }_0\approx 4\pi \times 10^{-7}$ H/m,
• and the permittivity of free space, ${\epsilon }_0$.

They are not independent: they are related by

In free space the flux densities are $D={\epsilon }_{0}E$ and $B={\mu }_{0}H$.

Solving Eq. (1.4.1) for ${\epsilon }_0$ with ${\mu }_0=4\pi \times 10^{-7}$ H/m and $c\approx 3\times 10^8$ m/s gives the value of ${\epsilon }_0$ used throughout these notes:

In electrostatic calculations the combination $1/(4\pi {\epsilon }_0)$ appears constantly, and with this choice it is simply $9\times 10^9$ m/F. All numerical examples in these notes use Eq. (1.4.2). With the exact speed of light $c=299792458$ m/s one would obtain ${\epsilon }_0\approx 8.854\times 10^{-12}$ F/m. The two values differ by only about 0.14 %, which is negligible in engineering work.