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In geometry point is a dimension less quantity as it doesn't have length, breath or height. But when we define columbs law in electrostatics, we define points holding charges or Newton's law of gravitation is primarily defined for point masses. So if a point doesn't have any dimension how can it have charge or mass at all?

Demietra95
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  • possible duplicate of How can a point-particle have properties? – John Rennie Jun 08 '15 at 07:08
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    To summarize Russel's answer: a physical "point" is merely the center of mass/charge/etc. of an extended object for which we ignore all physical effect that are caused by the object's extension. We never mean anything else by "point". – CuriousOne Jun 08 '15 at 08:46
  • @JohnRennie I looked at the possible duplicate you cite. The two questions started off somewhat different to each other but rapidly became more so with the answers and discussion. The other is dealing with elementary particles (and even his initial eg '... spin...' highlights this - and the answers follow. This one is more 'physical world approximations' related. – Russell McMahon Jun 08 '15 at 09:35

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A "point xxx" is almost invariably a theoretical concept intended either to simplify assumptions, or to allow you to ignore aspects which are more or less irrelevant to the aspects being considered.

Any physical attribute in a point object usually would led to an infinite value of some other attribute. A point charge has infinite charge density and so infinite ionic potential which may have an "interesting effect" on charged particles elsewhere. (Inverse square law will reduce the effect but as the ionic potential is infinite ...).

Also, many of the attributes of an object may act as if they were related to the object being at a point in space or time or in some other relevant field. For example, the centre of gravity of an object is the point in space at which all "gravitational" forces react on the object in the same manner as if its mass was concentrated at the c of g. Note that for the c of g it is an equivalent "all mass" point for gravitational forces but NOT for all mass related forces. When calculating inertial forces on a body the mass may not be assumed to lie at the c of g.

As an easily visualised example, imagine a balanced rotating flywheel which has say 90% of the mass distributed in the disk and 10% of the mass in an outer rim. The flywheel has a certain moment of inertia and the c of g is at the centre if the disk. If you progressively reduce the disk thickness and move mass into the riin tem the moment of inertia will progressively rise but the c of g ill remain at the centre.

So - a point-anything is a

theoretical
or mathematical
but essentially non-existant

construct used because it is useful.

Not really relevant asides, added to forestall pedantry :-)

  • I said "almost invariably" as arguably a few things do reduce to or exist as a point in reality - but its usually aspects of reality that are in themselves relatively inaccessible in reality. For example, anything moving at the speed of light in the reference frame of an observer usually has zero "size". [I added the usually after wondering about Photons in cold traps in Bose-Einstein condensates - label that a red-shifted-herring and proceed ... ]

  • And you can argue that point-xxx's cannot exist as the minimum 'meaningful' lengh is the Planck length - although at 1.6...E-35m that's getting rather pointy.

Russell McMahon
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