I have a question about magnetic fields.?

Question

After looking at the Biot-Savart Law, a question came to my mind. Do magnetic fields decrease at a rate of 2πr? The Law stated the magnetic field at a distance away from a long, straight, current carrier is given uI / 2πr. I've noticed that gravitational and electric fields decrease at a rate of one over the distance squared, but I don't know about magnetic fields.

Answer 1

well, i would say you're sorta right there.

but i think i would clarify on a couple things.

it's not really a rate. i think the word you're looking for is an 'inverse relationship.'

and while gravitational and electrostatic forces (and fields) bear an inverse square relationship to distance, magnetic fields and different, and with reason.

remember that magnetic fields need not only charge, but moving moving charge.

what im really trying to say, is that all anyone can say about magnetic fields is that the magnetic field induced by a current-carrying wire is inversely proportional to the distance from that wire. that's really it. because you can have a magnetic field induced by a moving point charge or even a change in magnetic flux. but the point is, i dont think we can generalize so easily. thats all. ;)

Answer 2

Keep in mind here the fact that you're comparing apples and oranges - the electric field from a point charge and the magnetic field from a long wire. The geometries are different, so you can't expect the same results.

It turns out that the electric field from a long charged wire also drops off at a rate of 1/r (not 1/r^2 like a point charge).

The two laws you should look at to explain this are Gauss's law and Ampere's law, but the explanation requires an understanding of surface, line and volume integrals.

A rough explanation is as follows:

Gauss's law dictates that the total electric flux (electric field times the surface area) through a sphere surrounding a point charge is constant - double the distance, you have a sphere twice as large, with four times the surface area, and the same flux, so the electric field drops off by a factor of four.

Ampere's law pretty much states what you said about the 1/r dependence, instead of a sphere surrounding a point charge, it deals with a closed circle with a current flowing through the middle of it - the factor here is the circumference of the circle, not the surface area of a sphere.