Hello Neophyte,
Neophyte said:
Anyways I always get the direction of b wrong I want both of them of them to point up, I know that they don't but I can't seem to figure out how to do this.
After adding the
B fields from each wire together (as vectors), the resulting vector will point up. But when taken individually, the
B field from each wire has an upward
component, but also a horizontal component too (either left or right, depending on the wire).
Once you find the magnitude of the
B vector at point P, for a given wire (just one of them), you need to break that vector into its respective x and y components.
I thought it was suppose to go in a concentric circle around the current and so it would be going counterclockwise
Yes, so far so good...
and at point p it would go up on both of them eventually,
Yes, but that won't be the case until after you add all the respective components together of both
Bs. When working with the
B vector associated with just one of the wires, you can expect an upward component; and then a left or right component depending on which wire. So an important step is to figure out how to break up these two
B vectors into their respective x and y components such that you can add them together.
but this method only seems to allow it to go up or down and idk anymore its becoming a problem. I mean I am missing something probably everything.
Don't get discouraged, you're doing okay.
Redraw the diagram on a piece of paper. This step is important because you're going to drawing a few angles and vectors and stuff on it.
Draw the line from one of the wires to point P. The length of this line is R (as in the 'R' in the relevant equation that you gave). Notice that
R,
d1 and
d2 form a right triangle, where
R is the hypotenuse. You can use the Pythagorean theorem to calculate the length of R.
This business of using right triangles is just getting started. Geometry/Trigonometry will mostly get your through the rest of this problem. I'll help out a little more and then leave the rest up to you.
Also note that you can calculate the angle θ between
R and
d2 at point P. The relationship
\mathrm{tan} \theta = \frac{\mathrm{opposite}}{\mathrm{adjacent}}
might help here.
From the right hand rule (or whichever rule you are using for the cross product), you know that the direction of
B is perpendicular to the direction of
R. So the direction of
B is the direction of
R, offset by 90
o.
Now, once you know the direction of
B, you can find its x and y components.
Next move on to the other wire (you can repeat the above again, or use symmetry to figure out the
B direction for the other wire).
