# Problem on electromagnetic induction and Newtonian physics

Please imagine a solenoidal toroid (i.e. a donut shaped inductor) powered by an AC voltage source. It creates a changing magnetic field which is confined to the interior of the toroid (i.e. within the coils). Because of the laws of electromagnetic induction, this changing magnetic field must in turn create a changing electric field in the space surrounding the inductor. The electric field lines surrounding the inductor will be of course somewhat similar to the magnetic field lines surrounding a current carrying ring, in that they are closed upon themselves (i.e. sourceless).

Now if we place a charged object (such as a sphere) in the "donut hole" region of the inductor, this object will be accelerated back and forth through the "donut hole" by the changing electric field created by induction.

So, the electric field created by induction acts on the charged sphere ($F = Eq$) but the electric field of the charged sphere has nothing to act on in return. I.E. It cannot act on the source of the inductively created electric field, because there is none.

My question is this: What prevents this situation from being a violation of Newton's 3rd law?

For example, what if we clamp the charged sphere to the inductor. It seems that the whole apparatus would oscillate back and forth. More importantly, what if we connect the charged sphere to an AC voltage source which causes the magnitude of the charge on the sphere to vary in phase with the strength of the inductively created electric field? Then it seems we have a reactionless propulsion situation. Since EM induction is such a well known area of electromagnetism, my assumption is that this must not be the case.

Can you help explain the reasons why?

if we place a charged object (such as a sphere) in the "donut hole" region of the inductor, this object will be accelerated back and forth through the "donut hole" by the changing electric field created by induction.

is completely incorrect. There is never any magnetic field outside the solenoid, which means that there is never any induced electric field in the 'donut hole' region.

If you place the particle inside the inductor, then of course it will be accelerated by the EM field. In that case, it will produce magnetic forces in the solenoid, but more importantly, it will exchange energy and momentum with the EM field itself, in ways which have been thoroughly explored in other questions on this site.

• Wrong. An electric field appears from Fradays's law, just as the op says. However the chaging electric field induces a magetic field from Maxwell's equation for ${\rm curl\,} {\bf H}={\bf J}+ \dot {\bf D}$ and this produces a force on the current in the solenoid. Commented Dec 30, 2016 at 20:01
• @mikestone No. There is no induction outside the solenoid because there is no magnetic field outside the solenoid. Commented Dec 30, 2016 at 20:36
• Induction can produce electric fields even in regions where there is no magnetic field. Faraday's law- the mathematical relation between ${\bf E}$ and $\dot {\bf B}$ is similar to that between ${\bf H}$ and the current. Just as you have a magnetic field outside a current-carrying wire, you have an ${\bf E}$ outside a solenoid enclosing a time varying ${\bf B}$ field. Commented Jan 21, 2017 at 23:06
• @mikestone That completely ignores the role of the currents. But if you have an actual calculation to back up what you're saying I can take a look. Commented Jan 21, 2017 at 23:26
• Consider an infinitely long solenoid of radius unity lying parallel to the $z$ axis. There is a magnetic field ${\bf B}= (\sin \omega t )\hat {\bf z}$ within the solenoid, nothing outside. The flux though the $x$, $y$ plane is $\pi \sin \omega t$ Apply Stokes theorem to ${\rm curl}{\bf E}= - \dot {\bf B}$ Then the line integral of the electric field around a circle of radius $r>1$ is $-\pi \omega \cos \omega t$ so the $\theta$ component of the electric field is $E_\theta(r)= -\omega\cos\omega t/2r$. This is not zer0 even though there is no magentic field in the region $r>1$. Commented Jan 23, 2017 at 15:30

I do not have access to this paper which is, I think, at least related to your question:
Micronewton electromagnetic thruster by Charrier at Applied Physics Letters (2012)
abstract:
A low cost and light electromagnetic thruster, consisting in a disc rigidly attached with a coaxial coil, shows steady recoil by losing its linear momentum. The signal applied in the device is a square electric potential. A continuous thrust is observed on the center-of-mass in one single direction under electromagnetic excitation for various voltages and nominal high frequencies. At 1 kHz with 20 V amplitude, the recoil force reaches 4 μN (micronewton). The recoil is numerically quantified with induced electromotive and Lorentz forces. The presented device directly converts electric energy into kinetic energy.

mentioned here WP-Abraham Minkowski controversy as "claims that unidirectional thrust is produced by electromagnetic fields in dielectric materials"

Explanations on micronewton electromagnetic thruster by Charrier on youtube

If he is correct or not is questionable by now, imo - see WP-Reactionless drive and NASA.
Is it noise due to interaction with the ambient or the EM of Earth ?