We say this from personal experience. First, when using a right-hand rule, use big, easy-to-see gestures. A
right-hand rule is like a form of advertisement: it is a way that your hand tells your brain what the answer
to a problem is. You want that advertisement to be like a billboard—big, legible, and impossible to
misread. Tiny gestures will only lead to mistakes. Second, when using a right-hand rule, always use your
right hand. Never use your left hand! This will cost you points!
Exam tip from an AP Physics veteran:
Especially if you hold your pencil in your right hand, it’s easy accidentally to use your left hand. Be
careful!—Jessica, college sophomoreThe Biot-Savart Law and Ampére’s Law
So far we’ve only discussed two possible ways to create a magnetic field—use a bar magnet, or a long,
straight, current-carrying wire. And of these, we only have an equation to find the magnitude of the field
produced by the wire.
Biot-Savart Law
The Biot-Savart law provides a way, albeit a complicated way, to find the magnetic field produced by
pretty much any type of current. It’s not worth worrying about using the law because it’s got a
horrendously complicated integral with a cross product included. Just know the conceptual consequence:
a little element of wire carrying a current produces a magnetic field that (a) wraps around the current
element via the right-hand rule, and (b) decreases in magnitude as 1/r 2 , r being the distance from the
current element.
So why does the magnetic field caused by a long, straight, current-carrying wire drop off as 1/r rather
than 1/r 2 ? Because the 1/r 2 drop-off is for the magnetic field produced just by a teeny little bit of
current-carrying wire (in calculus terminology, by a differential element of current). When we include the
contributions of every teeny bit of a very long wire, the net field drops off as 1/r .
Ampére’s Law
Ampére’s law gives an alternative method for finding the magnetic field caused by a current. Although
Ampére’s law is valid everywhere that current is continuous, it is only useful in a few specialized
situations where symmetry is high. There are three important results of Ampére’s law:
The magnetic field produced by a very long, straight current is