Ampere's law vs. Biot-Savart law

kasse
What's the difference? Is Ampere's law a special case (when the conductor carrying the current is a straight wire?)

Mephisto
Biot-Savart law is the more important and fundamental one. Ampere's law can be derived from it but can only be used in some very specific situations, but not only in straight wire cases. It can be applied to sheets of current, solenoids, etc.

kasse
Biot-Savart law is the more important and fundamental one. Ampere's law can be derived from it but can only be used in some very specific situations, but not only in straight wire cases. It can be applied to sheets of current, solenoids, etc.

OK, thanks. Btw, isn't the last calculation wrong here: http://planetphysics.org/encyclopedia/QuarterLoopExampleOfBiotSavartLaw.html

There should be no "pi" in the answer if I'm right.

Nick89
Ampere's law is usually only applied to problems that have certain symmetry.

For example, a straight wire is symmetric about it's center axis, a sheet is symmetric, a solenoid is symmetric, etc...

Some arbitrary wire is not symmetric however and Ampere's law can generally not be used there.

Also if you only have a short solenoid or wire for example (a short length in relation to it's radius) then Ampere's law does not give a very accurate answer either, because it ignores the fact that the magnetic field lines curve away from the wire at the ends; it assumes the magnetic field is nearly constant.

About the link, if the calculation up until the integral is correct then yes, the pi should cancel indeed. I haven't checked what they did before that though, but I think it's correct (so the pi is wrong).