Is Venus' magnetosphere actually more powerful than the solar wind's magnetic field that induced it or vice versa?

Question

Is the Venusian magnetic field actually more powerful than the solar wind's magnetic field that induced it? I know that Venus' magnetic field is not due to Magnetohydrodynamic processes rather, it is induced via incoming solar wind which forms a bow shock and a magnetosphere, but is the magnetosphere stronger than the magnetic field of the solar wind particles

For example, in an transformer, analogy to Venus' magnetosphere, the transformer has a primary coil similar to solar wind, and a secondary one similar to the ionosphere. The solar wind is moving with a charge at ultra high speed which in turn creates a magnetic field, now this magnetic field comes close to the ionosphere and that due to Faraday's law of electromagnetic induction, then this current acts like an electromagnet and produces a magnetosphere via Ampere's law which fends off the solar wind, and prevents atmospheric escape. So is this a step up transformer or step down transformer (I'm not an mechanic, but the analogy to transformer was simple)

My second question is that, what are the tesla values of the magnetosphere vs solar wind? This will assist in deciding whether it is step up or step down, since different sources give different result

Answer 1

Is the Venus's magnetosphere actually more powerful than the solar wind's magnetic field that induced it or vice versa?

I think you are asking whether the magnitude of the magnetic field is larger at Venus than in the ambient solar wind near Venus, correct? If so, then yes, the induced magnetic field of Venus is several times larger than the local, ambient solar wind plasma. This is because the solar wind is supersonic, so its impact on the ionized Cytherian atmosphere results in a bow shock. Thus, the induced field can exceed the ambient field because of the work done by the change in the ram kinetic energy of the solar wind across the Cytherian bow shock (i.e., the plasma compresses the induced field and compressed fields are enhanced fields, e.g., see https://physics.stackexchange.com/a/490664/59023).

I know that Venus magnetic field is not due to Magnetohydrodynamic processes...

It's not? One can have magnetic induction in MHD. So I would not say that the induced field is not due to magnetohydrodynamic processes.

My second question is that, what is the tesla values of the magnetosphere vs solar wind?

Typical magnetic field values in the solar wind near Earth are ~3-14 nT (e.g., see https://ui.adsabs.harvard.edu/abs/2021RvGeo..5900714W/abstract). Venus is 70% of the distance from the Sun as Earth and the solar wind magnetic field changes roughly as $r^{-2}$ (e.g., see https://physics.stackexchange.com/a/527527/59023). So the ambient solar wind near Venus is typically in the ~6-20 nT range. The magnetic field downstream of the bow shock is upwards of four times larger than whatever was incident (you can guess this from the strong shock limit of the Rankine–Hugoniot relations).