electromagnetism - What is the relationship between the magnetic units oersted and tesla?

How are the units oersted and tesla related? For example, how would you express $20\:\mathrm{Oe}$ in tesla?

Answer

They are technically units for incommensurate quantities, but in practice this is often just a technicality. The magnetic field that makes sense ($B$) is measured in teslas (SI) or gauss (CGS), and the magnetic field that people spoke about 100 years ago ($H$) is measured in amps per meter (SI, also equivalent to a number of other things) or oersteds (CGS).

To go between the two unit systems, we have

$$\begin{align} 1\ \mathrm{G} & = 10^{-4}\ \mathrm{T}, \\ 1\ \mathrm{Oe} & = \frac{1000}{4\pi} \mathrm{A/m}. \end{align}$$ To go between the two magnetic fields, we have $$\begin{align} \frac{B}{1\ \mathrm{G}} & = \mu_r \frac{H}{1\ \mathrm{Oe}} & \text{(CGS)}, \\ B & = \mu_r \mu_0 H & \text{(SI)}, \end{align}$$ where $\mu_r$ is the dimensionless relative permeability of the medium ($1$ for vacuum and pretty much any material other than strong magnets) and $\mu_0 = 4\pi \times 10^{-7}\ \mathrm{H/m}$ (henries per meter) is the vacuum permeability.

Therefore a $1\ \mathrm{Oe}$ corresponds to $10^{-4}\ \mathrm{T}$ in non-magnetic materials.

---

One caveat is that there are cases where $B$ and $H$ are not so simply related. If you are interested in their directions and not just magnitudes, then in some materials $\mu_r$ is actually a tensor and can rotate one field relative to the other. In this case the relation is still linear. In worse cases (e.g. ferromagnets) the relationship is not linear and cannot be expressed in the forms presented above. At least the $\mathrm{G} \leftrightarrow \mathrm{T}$ and $\mathrm{Oe} \leftrightarrow \mathrm{A/m}$ relations always hold.