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eep
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do we know why gravitational and electromagnetic forces inversely proportional to the square of the distance? is there any sort of underlying principle as to why they must be this way?
eep said:do we know why gravitational and electromagnetic forces inversely proportional to the square of the distance? is there any sort of underlying principle as to why they must be this way?
DaTario said:It is natural to indentify the chances of A hitting B as inversely proportional to the distance AB (consider solid angle in the anallysis). Also the chances of B hitting A is inversely proportional to the distance BA which is equal to AB (this, although aparently obvious, seems to me as fundamental to this issue).
DaTario said:So, if we intend to compute the chances of hearing an "ouch", no matter the author, A ou B, the expression for tis chance would involve the inverse square law in distance, as it seems to me up to now.
MalleusScientiarum said:I think it should be pointed out that the gravitational and electromagnetic forces are 1/r^2 forces in only certain special circumstances. Things get more complicated with GR and Electrodynamics.
DaTario said:What specific situations are you referring to ?
What specific situations are you referring to ?
Crosson said:Suppose you have a negative charge, and a small distance away you have a charge of equal but opposite magnitude. Then the electric field in the surrounding space will have a 1/r^3 dependence.
LeonhardEuler said:A simple real situation where Coulomb's law is violated is the following: a point is located 1 light year from a charge. The charge then moves at .5c for [itex]\frac{1}{2}[/itex] a year, so that at the end of this time it is .75 light years from the point in question. Coulomb's law would require that the [itex]\vec{E}[/itex] field at this point be stronger than it was [itex]\frac{1}{2}[/itex] a year ago, but we know that this is impossible because it would reqiure information (in the form of the [itex]\vec{E}[/itex] field) to travel faster than the speed of light. Gauss's law still holds in this case, though, because the [itex]\vec{E}[/tex] field has not changed at any point on the sphere centered at the charges original position with radius 1 light year, so [itex]\oint\vec{E}\cdot d\vec{A}[/itex] will still have the same value over this surface. Gauss's Law will actually hold over any surface, including those with part of the [itex]\vec{E}[/itex] field changed and the rest not.
edit:Something simmilar is true of gravity. Information in the form of an increased gravitational force can also not travel faster than c. Actually, it is my understanding that there is no gravitational "force" in general relativity, but certainly don't claim to know what I'm talking about when it comes to GR.
Crosson said:I think that the situation of two charges near each other occurs more frequently then "extra dimensions"
DaTario said:Ok I agree, some other laws of nature may (and in fact do) disturb the Coulomb's law. But the ontology of the inverse square law is still strong. Note that if you calm down the situation (force the situation to be electrostatic of gravitostatic, the 1/(r*r) comes out again after a finite time. In this sense, it seems to be an interesting procedure to attribute to the inverse square law the status of existing thing inside the domains of Newton's Force Based Physical Theories
arildno said:And why should Gauss' law be anything but an ad hoc fantasy?
Just because you start off with fancier maths doesn't resolve the issue.
The Inverse Square Law is a physical law that describes the relationship between the strength of a force and the distance between the objects exerting and experiencing that force. It states that the force is inversely proportional to the square of the distance between the objects.
The Inverse Square Law applies to gravitational forces because the strength of the gravitational force between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the gravitational force between them decreases.
The Inverse Square Law also applies to electromagnetic forces, such as the force between two electrically charged particles. This means that as the distance between the particles increases, the force between them decreases according to the Inverse Square Law.
The Inverse Square Law is important in physics because it helps us understand and predict the behavior of forces, such as gravity and electromagnetism, at different distances. It also allows us to calculate the strength of these forces and how they change with distance.
While the Inverse Square Law applies to many physical phenomena, there are some exceptions. For example, the force between two magnets does not follow the Inverse Square Law, as it depends on the orientation and size of the magnets in addition to the distance between them. Additionally, the Inverse Square Law does not apply to the strong and weak nuclear forces, which govern interactions between subatomic particles.