# Induced Magnetic H-field

Hello,
I have been trying to create a simulation where a current carrying loop is used to induce a current and corresponding H-field in and around a volumetric metal conductor. I have been using the Unstructured Magneto Quasi-Static solver to do this. The problem I'm having is that even though a current can be measured in the conducting ring, there is no H-field created by this. This has been tested by looking at the imaginary H-field (the induced current is imaginary, so the H-field should also be imaginary).

I have also tried comparing the calculated H fields between two simulations, one with and one without the volumetric conducting ring. The created H-fields have been identical when measured on the same unstructured mesh. This seems like a simple problem to be able to solve, so I hope that someone is able to provide me with some advice. I have probably forgotten to turn on some setting or change a parameter.

Any ideas are much appreciated.

What you are observing is a direct consequence of what the Quasi-Static solvers actually solves: they "only" solve for the quasi-static field equations when imposing a current (for magneto-solvers) or voltage (for the electro-solvers) source.

In the case of a current source, the solvers give you the magnetic field induced by the current and, in the case of the MQS solver, also the electric field induced by the magnetic field. Let's call these fields the "primary" induced fields.
The solver does not compute what we could call the "secondary" induced fields, that are induced by the primary fields (for example the magnetic field created by the current induced in a conducting loop).

Thanks to the linearity of the governing equations, however, this is not a problem and we can make use of the superposition principle to get the results we want. Indeed, if we could find out the current (let's call it I2) that is induced by the initial current source (with current I1), we could run a second simulation where we excite both loops with currents I1 and I2, respectively, and we would have the total induced H and E fields.
To find I2, I would suggest to find the self-inductance of each coil, as well as the mutual inductance between the two coils. This can be done by noting down the total magnetic energy (available e.g. when you select both B and H from a field sensor) when a single coil is excited (for the self-inductance) and when both coils are excited (to derive the mutual inductance). Let me know in case you need more details...

I hope this points you in the right direction!

Dear Sylvain,