# How might I measure the force produced by a fluctuating magnetic field?

I would like to apply a fluctuating AC current (not sinusoidal) through a solenoid, then measure the resulting magnetic field. As a non-expert I am not sure what this entails.

How can one measure a magnetic field through time with high temporal resolution, sampling say at 200Hz or so? Any advice is appreciated.

• Hall effect flux transducer (Hall sensor). Commented Aug 19, 2021 at 4:20
• Kevin, why exactly? There really isn't such a thing as a magnetic field, anyway. It's a high level classic concept. But not real. The reality is more that the effect is entirely relativistic with respect to the time it takes for electric field effects to transmit over distance. The fact is that positive and negative charges cancel out to far better than 1 part in 10^25 so that the relativistic effects of even very small velocities can show themselves -- as what are called "magnetic fields." But this is entirely a classical -- pre-relativistic view. So what exactly do you want to measure here?
– jonk
Commented Aug 19, 2021 at 4:28
• @jonk are you really saying magnetic fields don't really exist? That anyone who wants to measure one is in error? Commented Aug 19, 2021 at 4:31
• @kevinkayaks Okay. While I suspect, but don't know, that your question might be better placed in the physics stackexchange, perhaps someone will surprise me here. I've not sat down to struggle with a sphere and a solenoid. So I'd like to learn, as well. The free motions constrained within the sphere would need some kind of simplifying view, I suspect. And I'm thinking Stokes/Green's right now. Anyway, perhaps someone will help out.
– jonk
Commented Aug 19, 2021 at 5:07
• @mkeith I just went over to confirm my poor memory. See Volume II, Chapter 1, section 1-5. I not only remembered correctly, but I even got the power right from memory. I'm proud of myself! And the OP can do anything they want. If you define your concept exactly, you can measure it. It still doesn't mean it is reality. But it may look good! And no, I'm not saying the concept of magnetic fields are a useless concept. Quite the opposite. It's just that they aren't physical. So the goals matter. That's all.
– jonk
Commented Aug 19, 2021 at 5:29

You have an interesting problem.

You can calculate the solenoid force at a fixed position and DC current using finite element methods and make a table. The instantaneous magnetic force can then be inferred from the instantaneous current - but only at this one position and only for slowly changing fields. You would then have to repeat these calculations if different relative positions are necessary. You will find that the force increases dramatically in the nearer positions, so you will need more resolution if you are moving and operating near this position. Then you could refine further by knowing the mass of sphere and calculate the acceleration or deceleration of the mass to determine the contribution from the inertia. You would need to measure current directly, because a solenoid presents both inductance and a "back-emf" type of response from any relative motion of the sphere, so voltage cannot be used to infer current. Your sample rate would depend on how fast the position changes in operation.

For more rapidly changing fields, you would have to account for eddy currents, because you will induce currents both in your solenoid core (if it is conductive) and in your sphere. These losses will increase with the rate-of-change of the current, so you would have to have knowledge of previous samples and perform transient-style finite-element or finite-boundary analysis to predict the result. This approach seems somewhat problematic in real time, but would be possible for a static system as a post-processing step.

Good luck!

If you have a rough idea of what the maximum magnetic flux density is in your solenoid, AND you are able to design the solenoid core so that the field goes through a magnetic flux sensor in a controlled way, then you can potentially choose a linear hall effect sensor and use it to measure the field strength with a bandwidth much higher than 200 Hz.

For example TI part number DRV5055A4.

It can measure fields up to 169 mT. This is the highest field rating I could find. If you want to measure smaller fields there are many more choices. Maybe you can find higher fields, too. I did not look very hard. Signal bandwidth is 20 kHz. If you can design an air gap into your core and put the sensor in the gap, I think it should reliably measure the field strength (or at least be proportional to the actual field strength...)

I am sure that in some sense Jonk is correct that magnetic fields don't really exist. Honestly I don't understand what he is saying at all which reflects on me, not him. He is smart and usually correct. Nonetheless, linear Hall effect sensors are commonly used to measure "magnetic fields" in various types of controls and in brushless DC motors, etc. Current probes with DC bandwidth also rely on Hall effect sensors to measure "magnetic fields" in the gap of a gap core through which the current passes.

Maybe this is one of those things like the centrifugal force and corriolis force. Some people insist that these forces don't really exist. I totally understand the argument. Nevertheless, artillery shells have to compensate for corriolis force in order to hit their targets. And centrifuges are able to function despite the fact that the centrifugal force does not exist.