# Supercapacitor and an applied exterior magnetic field?

I'm curious of the effects of an exterior magnetic field to a Supercapacitor, in both states of charging & discharging.

If the Supercap. is placed inside an area where an exterior magnetic field $$\B_{ext}\$$ is applied, while the capacitor is charged, and connected to a load, would the +/- ions move quicker(since the electrostatic force would push like charges away + the Lorentz force) from the double layer towards the electrolyte?

Likewise, for the case of charging, would the ions feel a force(Lorentz) while moving towards the electrode to form the double layer from their initial positions from the electrolyte?

Finally, if I moved the Supercap. in any state(charged/discharged) would the ions feel a Lorentz force(depending on $$\v_{SC}\$$)?

The exterior magnetic field can be in any direction $$\B_{ext}\$$ = $$\B\hat{i}\$$ , $$\B\hat{j}\$$ , $$\B\hat{z}\$$

• Any movement of charged particles like ions, electrons etc in a magnetic field will generate some effect. At the ionic speeds involved, and low fields involved, and large other effects involved (chemical, electrical), the effect on the operation of the capacitor will so infinitesimally small as to be totally, completely, and utterly negligible, undetectable and not worth considering. Apr 24 '19 at 7:38
• @Neil_UK You should write that as an answer. Right now you simply claim they are insignificant - OP or anyone else has no way to counter that if it's not true, or expand on it with actual calculations.
– pipe
Apr 24 '19 at 7:41
• @pipe the lack of calculations is why it's a comment, not an answer. Please feel free to do the calcs, compare the Hall forces with the others, and write an answer. I figure my half a loaf is better to the OP than none. Apr 24 '19 at 8:22
• @Neil_UK , I appreciate the "half-loaf" response, it is better than nothing. I reached to the same conclusion before, but I kind-off doubt it now. If I were to have a 3000F Supercapacitor that's capable of outputting high power(specifically 10kA of pulse DC) placed in a magnetic field of 0.5T or 1T it's really hard for me to see the effects being "negligible". It concerns me, or even if the Supercap. was part of a dynamic system and was "moved" certain stresses could be problematic, and could be internal w.r.t the Supercap. Apr 24 '19 at 12:06
• @e.d.m-II forces on ions and electrons within a supercap, being negligible compared to chemical and electrical forces so not disrupting operation of the supercap is one thing, Lorentz forces on a 10kA conductor is another. In a 1T field, a wire carrying 10kA will have 10kN/m force acting on it, probably enough to rip it from its connection points if not well restrained. The plates and electrlyte will have much lower densities of current, and being embedded in a solid construction will not feel anything like the same effect as a single wire. Apr 24 '19 at 12:17

## 1 Answer

If the Supercap is placed inside an area where an exterior magnetic field Bext is applied, while the capacitor is charged, and connected to a load, would the +/- ions move quicker(since the electrostatic force would push like charges away + the Lorentz force) from the double layer towards the electrolyte?

Notice that the Lorentz force is perpendicular to both the magnetic field and the direction of the charges' movement. So, will charges travelling through the magnetic field experience Lorentz force? - Yes, but only one perpendicular to their own motion, so charging/discharging rate is not increased by a static magnetic field (otherwise, you'd be violating §1 of thermodynamics). It might even decrease a little because the electrons may have to travel further because they are deflected from the shortest path.

Many capacitors (from electrolyte to "Ultra-Caps") are made by spooling sheets of electrode materials around a center rod, which means that the Lorentz forces in most directions will cancel each other out almost completely. (The electrons travel along the spool on almost circular paths experiencing a Lorentz force in one direction on one half of a circle and a force in the opposite direction on the other half.)

• I would agree that the charged ions would experience a Lorentz force, but wouldn't it be also negated? Since the Lorentz force has to overcome the electrostatic force between the like-charged ions? Also, can you clarify more on the spooling sheets? I couldn't imagine as to why the Lorentz force would sum to zero due to symmetry. May 5 '19 at 12:19
• @e.d.m-II "the Lorentz force has to overcome the electrostatic force" - Sorry, I don't understand what you mean. Why would the Lorentz force have to overcome any other force? May 13 '19 at 9:32
• As to the symmetry: A 'spooled' capacitor viewed from 'above' looks like a spiral of conductive material. The electrons, travelling along the spooled electrode, follow that spiral shape of the electrode and thus travel on (almost) circular paths, which means a net Lorentz force of 0 for every completed round. May 13 '19 at 9:44