The magnet for an MRI scanner makes up the large bulk of its price. The rest is actually pretty cheap. Little more than the patient handling gear (much the same as used on any X-Ray machine) some RF gear and compute. Years ago the compute was pretty expensive, you need to do a lot of FFTs, but by modern standards, trivial.
The big problem with the OP’s question is that it is a quite difficult problem to calculate. In principle all we need is the mass of the ball bearing, the distance from the magnet, the magnet’s strength, and its geometry. The equations for calculating the force on the ball bearing have been known for centuries. But they are not trivial. The main issue being that magnets are dipoles, and thus messy. If the question were “what is the force due to gravity on the ball bearing” it would be easy. Mass of ball, mass of MRI unit, distance, high school physics.
The point I have been laboring to make is that vibration of metallic objects in the oscillating field of the MRI machine is not the only concern; the video served to demonstrate that there is a large, non-oscillating force component that bears consideration. Whether the force on an ingested ball bearing is large enough to cause internal injury is still unknown, but I don’t think the question can be summarily dismissed.
“large amounts?” “all the time?” I’m curious for a cite that supports these assertions.
I hold in my hand a steel ball, 3/4" in diameter, which I would guess is about as large a someone would feel safe trying to swallow. It weighs 28.5 grams, or 1.01 oz.
Can someone take the next step in estimating what the force would be on a ball this size?
That’s why the suggestion to find one that’s about to be decommed. Causing a quench would just be a bonus to them.
As for the price of an MRI? Yeah, it’s huge. Not many hospitals own one around here. There’s a mobile 3T scanner that’s leased and shared among three local hospitals. AFAIK, it’s rotated among them - it’s driven from one to another for a week or so at a time, according to a friend who’s got ties to the board of directors for one of the hospitals.
OK, a few things. I was writing hastily (comes from posting at 2am). What you need are the dimensions of the ball and its permiability. So we have those, since it is a sphere, and made of steel. As I noted earlier, steel does not have a constant permiability. It rises with increasing flux density to a maximum that is considerably greater than the permiability at low fluxes, and then slowly diminishes to about 40% of the peak at the point where it saturates. Because we are using such huge field strengths from the main magnet, we need to take this into account. Indeed assuming the maximum value is probably not unreasonable.
That is the easy bit. The hard bit isn’t the ball, it is the main magnet. The force on the ball is dependant on the magnetic field gradient. If the ball was in a uniform field it would feel no force - you can regard the force as being the ball trying to find a place where the field is uniform. (It is uniform in the middle of the tunnel.) The actual gradient of the field around the magnet is dependant upon its geometry and design. Some MRI magnets are shielded, which significantly changes the gradient. You can’t actually shield the field, but you can direct it so that it stays closer to the physical magnet. This means that at a distance from the magnet the field is of much lower strength, but as you get within a critical distance the gradient is much higher than with an unshielded version. For the case where you had a ball bearing in your stomach the shielded version would be the more dangerous, with a much higher force exerted as you were trundled into the tunnel.
I don’t know how often MRI’s are decommed, but NMR’s aren’t decommed very often, and they are essentially the same thing. Old NMR’s get moved to lower level labs, then to the undergrad labs. I a tually ran one as an undergrad that didn’t require liquid nitrogen. Honest to god, the thing was analogue with a pen that I manually scanned across the frequencies. That thing rocked.
The point is, if an MRI is still functional enough go produce a massive field, there is no reason to decommission it. There are plenty of rural hospitals that would love to get their hands on even a peice of crap MRI.
The economics of MRI and NMR machines would preclude the use of any production unit for this experiment. However, there are probably magnets that could be used for this purpose, or with the coorperation of a manufacturer, a way to test this. But it would seem that the results could be predicted without conducting the experiment, at least to the extent that it could be determined if the ball bearing was either attracted with more than enough force, or nowhere enough force.
Nothing here is convincing me that it is for a magnetic ball bearing. The examples cited are about small light objects and cases where the object is free to accelerate. Of course what do I know? I can’t tell stainless steel from non-stainless.