Expert: Daniel Mazur - 5/13/2005

Question
I have study physics for some years now. Just a few days ago I read about Ampere's Law. I am not sure what it actually mean. Would you mind explaining to me the meaning behind this law. If not, could you please tell me a website that might be helpful.

Cheers.

Answer
In essence Ampere's Law tells us, where magnetic field comes from: it's caused by electrical currents, or more generally, by electrical charge in motion. That's the "philosophical" essence of it. This far it resembles Gauss' Law that says that electric field comes from charged bodies. At the simplest level you can also see it as a law of proportionality between the magnitude of the electrical currents and the magnitude of the resulting magnetic field.
"Magnetic induction is directly proportional to the current causing it. If there are more currents flowing in the system, one has to carry out the vector summation of the currents and the 'total' mag.induction is then proportional to the 'total' current - or you calculate magnetic inductions caused by each current separately and do a vector summation of the resulting mag.inductions. Both aproaches give the same result."
The second step to take still at high school is to familiarize with the relations between the directions of electrical currents and magnetic field. The right-hand rule can cause as much confusion as help.

At this point I would use a more spefific information on the level you are at, in physics. High school physics usually would not go beyond the outlined understanding niveau, as it is usually challenging enough to get students used to think of magnetic field and the basic vector algebra of its effects. Only in a college one gradually learns enough of advanced calculus to grasp Ampere's Law in all its forms.

I will gladly extend my answer at any level, if you specify precisely where you are at. At the basic (high school) level you might find it useful to look at

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html

It you are already familiar with integral and differential vector calculus, you are probably more concerned about an accessible interpretation of the general equations of Ampere's Law. If this is so, you will certainly find the text in quotation marks above unsatisfactory. A reading of the likes of

http://maxwell.byu.edu/~spencerr/websumm122/node67.html

might bring some answers and I will gladly discuss and try to clarify, what's left hazy.

Cheerio!
Daniel