If a straight wire poked through the center of this paper, and carried a current

Question

If a straight wire poked through the center of this paper, and carried a current starting below the page and flowing above the page (generally toward you). What would be true of the magnetic field produced by this current in each of these places?

A.     it would point down at the middle of the top edge of the page

B.     it would point down at the middle of the left edge of the page

C.     it would point down at the middle of the bottom edge of the page

D.    it would point down at the middle of the right edge of the page

Please explain it.

Explanation / Answer

First we need to use hand rules to figure out where the magnetic field lines are pointint in this problem. Since this problem deals with the magnetic field of a current-carrying wire, we first point our right thumbs in the direction of the current (out of the page) and wrap our fingers around (pretend like you're grabbing a a microphone) and that will give us the direction. In this case, our hands end up in a thumbs-up position on the table surface and the magnetic field lines (our fingers) end up curled in a counter-clockwise direction.

Now the problem becomes a matter of figuring out which description of the magnetic field is correct, since we know now that it is counter-clockwise. The field lines around a current-carrying wire are set in concentric circles centered at the wire. Let's imagine that the page is actually a square sheet of paper. Let's now isolate our thinking to just one field line (one circle) that is tangent to all four sides of the piece of paper. Since it is a perfect circle in a perfect square, the tangential points are all the centers of the edges (the middles of the edges as described in the answer choices). We know from earlier that the direction of the field line is countre-clockwise. We can either draw arrows ttangent to each of the four points where the circle and the square touch. In that case, we will find that the only arrow that points downwards is the one on the left edge of the page. Therefore, the correct answer is B because the magnetic field points down at the middle of the left edge of the page.

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