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skyliner34
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Can anyone explain this to me?
Lojzek said:First you must think what are the possible vector fields caused by a single point source (charge).
All information you have is the location of 2 points: the source and the point where you want to evaluate the vector. The problem has cylindric symmetry around the axis connecting the two points, so vector MUST be directed parallel to this axis: either straigth away or towards the source.
The magnitude of the vector must be independent of the choise of coordinate system, so it can only depend on the distance between the two points..
Under this circumstances the integral of the electric field over a sphere is not difficult to evaluate.
Coulomb's law is a fundamental law of electrostatics that states the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Gauss' law is a fundamental law of electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface.
Coulomb's law can be derived from Gauss' law by using the divergence theorem, which states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of that field within the enclosed volume. By applying this theorem to Gauss' law, we can obtain Coulomb's law.
The mathematical equation for Coulomb's law is F = k(q1q2)/r^2, where F is the force between two point charges, k is the Coulomb's constant, q1 and q2 are the charges of the two point charges, and r is the distance between them.
Using Gauss' law, we can calculate the electric field by first choosing a closed surface that encloses the charge of interest. Then, we calculate the electric flux through that surface and equate it to the charge enclosed over the permittivity of free space. Finally, we can solve for the electric field at any point on the surface.
No, Coulomb's law can be applied to any two charges, regardless of their size or shape. However, it is most accurate for point charges or for charges that are significantly smaller than the distance between them. For larger and more complex charges, the law can still provide an approximation of the force between them.