I am taking an introductory physics course, and the chapter we are on is about electrostatics.
One section of our textbook has talked about the electric field generated by a charged object that is infinite in one or more dimensions (such as a point in 0 dimensions, a line in 1 dimension, or a plane in 2 dimensions.)
We have used integrals to prove the following statements:
The electric field at a point that is a distance of r away from a point is proportional to r^-2.
For an infinite line the field is proportional to r^-1.
For an infinite plane, the field is constant (is proportional to r^0.)
I have heard of people generalising the laws of physics into higher dimensions, and curious to see if there is a way to generalize this pattern the same way.
I tried to do it myself but I have only just finished calculus A, and such a task is beyond my humble abilities.
When the thought first popped into my head, I speculated that the exponent in the equation for the electric field might be the number of dimensions of the object generating it minus 2; but it seemed extremely unlikely to me that the field some distance r away from an infinitely extending 3d object in a 4d world would INCREACE linearly with the distance.
Edit: As Puk pointed out in the comments, this could not happen, because the inverse square law would become an inverse cube law in 4 dimensions.
Could someone with a deeper understanding of physics shed some light on this idea of electric fields generated by infinitely extending objects in more than 3 dimensions? Thanks in advance.
