# 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?

• @ Ganesh, Oersted and Tesla dont talk to each other as each of them used to measure two physically different quantity.
– Mass
Jul 22, 2016 at 16:44

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.

• Worth noting there are still plenty of experimentalists who talk about $H$ because $H$ is directly related to current and therefore under your control, while $B$ includes the magnetic response of the medium and is usually more complicated.
– rob
Jul 22, 2016 at 19:37
• @rob any word on whether they use CGS or SI units? You'd how that all experiments now use SI, but with astronomy there to set the example, you never know. Jul 22, 2016 at 23:32
• @EmilioPisanty I can't think off the top of my head but I may have an opportunity to confirm soon. I expect "gauss" for both $B$ and $H$, which in free space isn't such a bad way to go.
– rob
Jul 23, 2016 at 0:15
• @rob gauss for $H$? That's the sort of stuff that makes cgs such a weird "almost" on being nice and consistent and stuff. What's with having independent but semi-commensurate units for quantities that ought to have the same dimensionality, anyway? Man, cgs is weird. Jul 23, 2016 at 2:03
• @chris white what does '1 Oe corresponds to 10^−4 T in non-magnetic materials' means.Does this indicates that 1Oe equals to 1G Jul 23, 2016 at 4:13

This is a relatively tricky one, because it involves the differences between the $\mathbf B$ field and the $\mathbf H$ field in the SI and CGS systems, and those relationships change in the different systems. In short:

• Oersteds are used to measure the $\mathbf H$ field in CGS units.

• Teslas are used to measure the $\mathbf B$ field in SI units.

• In the SI system, the two fields are related via $\mathbf B=\mu_0(\mathbf H+\mathbf M)$ where $\mu_0$ is the vacuum permeability and $\mathbf M$ is the magnetization (volumetric density of magnetic dipole moment).

• In a linear medium $\mathbf M=\chi_\mathrm m \mathbf H$, for $\chi_\mathrm m$ the material's dimensionless magnetic susceptibility, and the fields are related by $\mathbf B=\mu_0(1+\chi_\mathrm m)\mathbf H=\mu_0\mu_r\mathbf H=\mu\mathbf H$.

• In the SI system, the $\mathbf H$ field is measured in amperes per meter.

• In the CGS system (gaussian and EMU units) the two fields are related via $\mathbf B=\mathbf H+4\pi\mathbf M$.

• In a linear medium the magnetic polarization is also $\mathbf M=\chi_\mathrm m \mathbf H$ (but with a different susceptibility, $\chi_\mathrm m^\mathrm{(CGS)}=\frac{1}{4\pi}\chi_\mathrm m^\mathrm{(SI)}$), and $\mathbf B=(1+4\pi\chi_\mathrm m)\mathbf H=\mu\mathbf H$, where now the material's permeability and relative permeability coincide.

• Not all magnetic materials are linear. In particular, permanent magnets are best thought of as having a permanent, fixed magnetization $\mathbf M$. In these cases the magnetic susceptibility and permeability is undefined inside the material.

• As you might note, CGS has two distinct units, the oersted and the gauss, for two quantities of the same physical dimensionality. I'm not quite sure why people felt the need for two such units, but it's apparently one of the quirky reasons why using CGS units makes you "cool".

• To repeat the caveat that Chris mentions, even if a material is linear it might still be inhomogeneous (i.e. have a spatially dependent $\mu$), in which case the $\mathbf B\leftrightarrow\mathbf H$ relationship changes from place to place, and it might still be anisotropic, in which case $\mathbf B$ and $\mathbf H$ can point in different directions and you only have a linear relationship between their components, $B_j=\sum_k \mu_{jk}H_k$, and $\mu$ jumps from a scalar to a rank-two tensor (a.k.a. a matrix). In that case, you can still use the relationships below to relate the components and magnitudes of the fields, but you should doubly so heed the advice on sticking to a single system.

• Thankfully, the SI and CGS systems do agree at least on the relative permeability of linear materials.

The easy part of the answer is that in vacuum the two units can be uniquely identified. In this case a CGS $\mathbf H$ field strength of $1$ oersted coincides with a CGS $\mathbf B$ field strength of $1$ gauss, which is exactly $10^{-4}\:\mathrm T$.

On the other hand, in a magnetic material, i.e. anywhere where $\mathbf M≠0$, the conversion factor will depend on the material.

• If the material is not linear, then there is no way to relate the two, because you do not have enough information to relate the $\mathbf B$ and $\mathbf H$ fields.

• If you know the material is linear and has a relative permeability $\mu_r$ (equal to its CGS permeability), then a $\mathbf H$ field of $1$ oersted corresponds to a CGS $\mathbf B$ field of $\frac{1}{\mu_r}$ gauss and therefore an SI $\mathbf B$ field of $(10^{-4}/\mu_r)$ tesla.

If you want to interpret a CGS $\mathbf H$ field, a safer choice is to translate it into an SI $\mathbf H$ field, for which a CGS $\mathbf H$ field strength of $1$ oersted corresponds to an SI $\mathbf H$ field strength of $10^{-4}$ amperes per meter.

More generally, though, if you're looking to convert between teslas and oersteds, my advice is: don't. Choose one one EM unit+formula system, and stick to it. If you need data on a material's properties that's in another system, convert that to the one you're using first thing. If you're looking to compare $\mathbf B$ and $\mathbf H$ field values, you had better have a good idea of exactly what the deal is with your material - and still, you should stick to one system.

From a quick google search, it seems that Oersteds are used for defining magnetic field strength and Teslas are used for defining magnetic field strength in terms of flux density. They seem to not really be meant to be converted between, though you technically can (as evidenced by the other answers here).

This website and this website might be helpful to you.

Update:

The other answers here cover the conversion very well.