Calculate the magnitude of the magnetic field at a point midway between two long, parallel wires that are 1.0 m apart and have currents of 10.0 A and 20.0 A, respectively, if the currents are:
a) In opposite directions, and
b) In the same direction.
B = m(I/(2*pi*r)), where m is NOT mass, it's the permeability of free space, whose value is 1.25663706 × 10^-6 (with appropriate units).
The Attempt at a Solution
Since r = 0.5 (midway between the wires), I calculated B (using the formula) to be 4 x 10^-6 T (for just the 10.0 A wire), and 8 x 10^-6 T (for the 20.0 A wire).
The answers are: a) 1.2 x 10^-5 T
b) 4.0 x 10^-6 T
I'm not quite sure how to do this problem at all, because my textbook gives a very brief and confusing explanation about Ampere's Law, with one simple example (where they basically showed how to plug numbers into the formula).
Could someone please explain how to do this problem? (It would be greatly appreciated if they explained what Ampere's Law is in the first place, because I don't understand the whole thing about the closed loop path and whatnot.) Thanks in advance.