Calculating Magnetic Field from Parallel Wires

[DMac]

Homework Statement

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.

Homework Equations

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.

 

[alphysicist]

Hi DMac,

You don't need to use Ampere's law at this point in the problem; Ampere's law would be used to derive the formula that you are using.

What I think you have not calculated yet is the directions of the fields from each wire. (If the are in the same direction, the total field is found by just adding the numbers together; if they are in opposite direction, you subtract the numbers to find the total field.)

So for part a, if the currents are going in opposite directions, what direction is the field from A and the field from B? It probably will help to draw a diagram, and then use the right hand rule for fields from a long wire.

 

[DMac]

Ah, I think I get it. Using the right hand rule, I found that for part a my fingers wrapped around in the same direction for both wires. And, consequently, I found that they were wrapped in opposite directions in part b. Thanks.