LOOPS AND LOOPHOLES

When a current flows through a conductor, the latter is surrounded by a magnetic field, which is something that acts on a compass needle in the direction of the field and with a strength proportional to the density of the lines of force (of the field). Magnetic field lines are always closed, forming a closed curve such as a circle, but also more complicated closed curves. The direction of the lines of force is found by the "screwdriver rule: "when the (conventional) current flows in the direction of the screwdriver, the magnetic field lines have the direction of tightening the screw. The figure shows the example of a current flowing out of the page (left) and into the page (right), but it is important to note that this would be so only if there were but one such current at a time, not the two currents together.

[What's a "conventional" current? In the 18^th century they knew that a current flows between the plus and minus electrodes, but they did not know which way. So with a 50-50 chance they guessed it flows from plus to minus, and Murphy's law, they guessed wrong. Today we know that an electric current is the flow of free electrons, which move from minus to plus. This is the (true) "electronic" current. But there are so many ingrained rules such as the screwdriver rule that we also keep up the fiction of the "conventional" current. For example, using the electronic current, we would have to tighten a screw with a left-handed thread to get the right result for the magnetic field.]

But the "screwdriver rule" figure, in which each of the currents should be considered by itself, is an abstraction. A current must form a closed loop and if it flows into the page, it must flow out of (a big enough) page again somewhere. What does the magnetic field of such a loop look like? This is shown in the next figure, using the screwdriver rule for each current and combining the two results, which will mean adding the field between the wires and partially canceling them outside of them. At a distance much greater than the distance between the wires, the field goes down with the inverse 3^rd power of the distance, i.e., very fast (at twice the previously considered distance one only gets 1/8 of the field). This is the usual case, for the wires feeding, e.g., an electric clock, are, say, ¼ of an inch apart, so that at distances much greater than ¼" from them you practically get nothing at all instead of cancer, leukemia and whatever else superstition monger Brodeur warns of.

But inside the loop and above or below it, where the fields add, the story is quite different. Even a worm like Brodeur is not small enough to crawl into the space between the wires or inside a clock. If he could, he would be application of the screwdriver rule and vector addition find what the next figure shows:

As you can see, the result is a strong field in, just above, and just below the loop. The "zero" field is true only for that direction far away from the loop (many times the separation of the currents flowing in opposite directions).