Magnetic field produced by two side by side wires - when do they cancel?

Greywolfe1982

I know that the magnetic field coming off the wire will be directed in a circle counterclockwise around the wire. So, from what I understand, it would work something like this:



Meaning that, at each magnetic field strength B of radius r from one wire there is an equal and opposite value for that coming from the other wire, meaning that they cancel along the radius and the answer is 4.

Is this right or wrong? Am I way off the mark, or somewhat close?

Yitzach

Your thread is in jeopardy of being deleted for not using the template.
You are way off. [tex]\vec{B_1}+\vec{B_2}=\vec{B}[/tex] Add only what is at a point, not what is on a circle of radius r when they only share a common point

berkeman

Not at all. He has included the things that we ask for in the template, for the most part.

Greywolfe1982 -- Remember to do the vector addition. draw the vector addition at several points along that mid-line SS'. You get the direction for each B vector component from the counter-clockwise rotation direction, and the magnitude falls off as what?

Greywolfe1982

Sorry about the template thing if it is an issue, I ordinarily use it but didn't think it fit this question.

And what do you mean "along that mid-line SS'" Wouldn't doing vector addition (assuming you use vectors from the same point on the circle, say both on the middle-right or middle-left) give a vector going in one direction that is twice the magnitude of B₁ or B₂?

berkeman

I guess I'm just trying to help you get some intuition about how the vector B fields add in this geometry. Pick a point along the midline SS', say a distance d down from the exact midpoint. Now draw the two contributing B vectors, and show the result of adding them.

Then think about all the other points in that 2-D plane of the paper, and what the magnitudes and directions of the two contributing B field vectors will look like, and hence what the result of adding them will be. Does that help you to see the answer to the question?

Greywolfe1982

I apologize for being so braindead tonight, I feel as if I should know this but I'm lost right now.

So I think that adding two vectors would look like this:



The filled dot being the middle, and the other being a distance d from the middle. The vectors added produce a triangle, but I don't see anything notable about it.

berkeman

Almost, but not quite. Just draw a nice circle around the left point that has a big enough radius to go through that bottom point. And then draw the same type of circle for the right wire, getting the radius right to go through that bottom point. Now more carefully draw the vectors, and show their addition....

Greywolfe1982

I take it this is what you meant? The vertical components cancel, but you're left with a horizontal component. At any point, wouldn't the addition of vectors leave you with either a horizontal or vertical component (or both)?

berkeman

Good! And yes, there are very, very few places in that plane where they cancel. Think of all the sets of circles around the two wires, and what the resultant vectors will add up to.

Now are you ready to answer the original question?

Greywolfe1982

I'm thinking of two answers right now, but the one that makes the most sense to me is 1. - at all points along the line connecting the wires. The magnetic fields would be two vertical components of the same magnitude and opposite direction, canceling each other out.

berkeman

But you just showed with your post #8 that it's not quite true...