# Is there any way of clearly defining pressure for non-contact forces?

A friendly note: If this is a duplicate then please guide me to that question. I searched for a similar question and ended up with nothing. Also, if anybody understands my point then please edit it into a better question. I tried my best.

It just struck me that when we define pressure as a force per unit area we take the area in contact. For example the classic situation of a thumbnail being pierced into a board the contact area is different at the tip and at the "handle?" and thus the pressure is a lot larger if the tip is in contact with the board's surface.

But let's say I have two magnets and I try to bring the similar poles near. They will repel each other by virtue of their magnetic forces (non-contact). I hold them together and I feel that they are trying to push my fingers away.

Questions-

1. Is this an example of pressure (acting between the magnets)?

2. Can we define a term similar to pressure (with units N/m^2) between the two objects using their magnetic fields and fluxes?

3. Is there any way in which a non-contact force can cause pressure (obviously I don't mean putting a wooden board between opposite magnetic poles)?

Why I'm asking this question is because at the fundamental level there is no true contact between two surfaces. In normal case the repulsion happens at a microscopic level between the charges and in case of these magnets it happens at a macroscopic level. So there should be a way to draw analogy... right?

• Keep in mind that pressure, just like temperature, is a concept that can only be defined at a macroscopic level. At microscopic level the only correct picture is interactions between particules which may affect their state and energy. – Ronan Tarik Drevon Apr 28 '17 at 12:03
• @RonanTarikDrevon The repulsion between magnetic poles is macroscopic right? I mean the origin of magnetism is microscopic but the phenomena is observed macroscopically. So according to your statement In that case there should be a pressure involved too... right? My question is- how do we define it correctly? – Sad_lab_rat Apr 29 '17 at 10:24
• Alright! I think that magnetic forces are volume forces (such as gravity) whereas pressure results from a force F applied on a surface S such that $P=F/S$. But even in the case of a magnetic force , I suppose you could determine the force $F=\nabla (\mathbf M\cdot\mathbf B)$ and then consider that force to be applied on the surface of the magnet $P=F/S$(sounds a bit weird though). A better exemple of non contact pressure forces would be the radiation pressure! – Ronan Tarik Drevon Apr 29 '17 at 18:17
• @RonanTarikDrevon Ah! yes.. radiation pressure. That's the clue I was looking for! Thanks for taking the time to address my question :D – Sad_lab_rat May 1 '17 at 4:37