After Class - Speaking of Magnetism
October 1958 Popular Electronics
For some reason, a lot of people seem to have a harder time grasping the concepts of magnetics than of electricity. Maybe it is because most of the machines and appliances we are familiar with run off of electricity. The fact that motors, transformers, and relays, which are present in one form or another in every household, office, and factory, are as reliant upon magnetic effects as much as they are electrical effects is lost on the multitudes. This article from the October 1958 edition of Popular Electronics helps bridge the gap of knowledge. Unfortunately, I do not have the edition with the first half of the article.
October 1958 Popular Electronics
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SPEAKING OF MAGNETISM - Part 2
What kind of force exists between two closely spaced, parallel, current-carrying wires? Are the wires attracted to one another or do they repulse each other? Before we attempt to answer these questions, let's refresh our memories on two simple "hand" rules concerning the direction of a magnetic field due to a current.
Rules of Thumb. The first is Oersted's famous rule: if the thumb of the left hand points in the direction of the electron current in a wire, the fingers then encircle the wire in the direction of the lines of force (Fig. 1). Small compasses distributed around the wire show - by the direction in which their little N-poles point - which way the field is going, and verify Oersted's rule. (If you have encountered this rule given for the right hand, It must have been in a book that still employs the old plus-to-minus current flow convention rather than the more modern electron current idea. See After Class, June, 1958.)
The second rule of thumb describes the direction of the magnetic field of a solenoid as related to the current flowing in the coil. If the fingers of the left hand encircle the coil in the direction of the electron current, then the extended thumb will point in the direction of the lines of force produced by the solenoid, as in Fig. 2. To distinguish this from Oersted's rule, it is commonly referred to as the "rule for coils."
Fig. 1. Oersted's left-hand rule specifies the direction of a magnetic field which surrounds a current-carrying conductor.
Fig. 2. The left-hand rule for coils is used in determining the direction of the magnetic field due to coil current.
Fig. 3. Two parallel conductors carrying currents in the same direction (A). and cross-section convention (B) for showing electron currents flowing in or out of the plane of the paper.
Fig. 4. Both currents flowing out of the paper produce two sets of clockwise fields (A); both currents flowing into the paper produce two sets of counterclockwise fields (B); and one current flowing into the paper and the other out of the paper produce oppositely circling fields (C).
Fig. 5. A primary magnetic field in the process of growing toward the right induces an electron current which causes a secondary field to grow to the left. The galvanometer needle indicates current flow in the secondary coil winding and the direction of the flow.
Fig. 6. With the primary and secondary coils end-to-end (A). polar approach predicts same induced current as field approach, but when primary is inside secondary coil (B). The polar approach gives incorrect induced current direction.
Obviously, an electron current traveling upward in the conductor of Fig. 1 would produce a clockwise rather than a counterclockwise field in the horizontal plane. If the electron current in the coil turns is reversed, the field direction will also reverse. Both these turnabouts are, of course, predicted by the applicable rule.
Using Field Theory. We now have everything we need to solve magnetic force problems of any type using field theory rather than magnetic poles. Suppose we have two parallel conductors in which current is flowing in the same direction. Looking at these conductors sidewise, they appear as shown in Fig. 3 (A).
From this perspective, it is difficult to visualize and draw the lines of force associated with the current. To make the job substantially easier, we will adopt a convention that is now universally accepted:
All wires pictured as little circles representing the cross section of the conductor passing through the plane of the paper at right angles.
If the current direction is out of the paper toward the reader, we imagine that he sees an arrow point; thus we designate an outward-flowing electron current by a dot in the center of the circle. For the opposite case, an electron current flowing into the paper away from the reader, we picture a receding arrow whose tail-feathers are visible. We show such a current as a cross (for the tail-feathers) in the center of the circle.
Force Directions.. Let us now visualize the two parallel wires of Fig. 3 (A) swung through 90° so that they present a cross-sectional view of two little circles. If the rotation occurs in one direction, the current will appear to be coming out of the paper toward the reader, as in Fig. 4 (A). In this case, Oersted's rule tells us that the magnetic field around each wire is clockwise; between the wires, adjacent lines of force have opposed directions, giving rise to an attractive force as required by the fourth characteristic of lines of force (see Part 1, August issue).
If you had pictured the two wires of Fig. 3 (A) swung around the other way, the electron currents would have had to be shown receding - crosses in the circles as in Fig. 4 (B)-and the circular fields would then have been counter-clockwise. Note, however, that this makes no difference in field theory application: the line directions are still opposite between the wires and the force is again attraction.
Fig. 4(C) illustrates the state of affairs when the current flows in opposite directions through two parallel wires. Adjacent lines between the two conductors have the same direction; so a force of repulsion appears between them as predicted by the second characteristic given for lines of force in Part 1. You can demonstrate these effects by stretching 8" lengths of #32 or #34 wire about 1 millimeter apart and connecting their ends to a 6-volt storage battery; the contact should be momentary to avoid overheating the wires.
These examples lend strength to our contention that polar reasoning must give way to the field approach merely because you cannot work with magnetic poles if you can't even find them! Our next example is really the clincher. We will show that with induced currents, the polar attack leads to two contradictory results.
Induced Currents. Two coils are positioned end-to-end as in Fig. 5. In series with one of them is a battery and a momentary push button or switch. A sensitive galvanometer with a center-zero scale is connected in the second coil circuit. When the key is momentarily pressed, the galvanometer needle swings one way, say to the right, and when the key is released, the needle swings to the left.
From the principles of electromagnetic induction, we know that while the magnetic field is building up and out of the first coil (the primary winding), it cuts through the secondary winding and induces a current. When the key is released, the primary field collapses, cutting back through the secondary coil and inducing a current whose direction is opposite from the first. The direction of the induced current is given by Lenz's law (which, by the way, is merely a restatement of the Law of Conservation of Energy in electrical terms): an induced current has such a direction that its magnetic action tends to oppose the motion by which it is produced.
Imagine that the key in Fig. 5 has just been closed so that a surge of electron current occurs in the direction shown. Using the rule for coils given previously, we can say that a magnetic field expands outward from the primary as a result of this current, cutting through the turns of the secondary, The current induced in the secondary coil, according to Lenz's law, must have such a direction that the field it produces opposes the initial, expanding field. This current direction - arrived at by again employing the rule for coils - is indicated by the arrows on the secondary turns.
When the primary circuit is then opened, the initial field collapses back into the first coil. This permits us to say that the actual motion of the field is now the reverse of what it was when the key was closed. To oppose this motion, the current in the secondary promptly and obligingly turns about and creates a magnetic field toward the right-in other words, it creates a field that opposes the collapse of the primary field.
This approach gives the right answer no matter what the relative positions of the coils may be. It works just as well if the primary coil is inside the secondary, outside the secondary, or end-to-end with it.
The Wrong Answer. Now let's see what happens if we try to use polar reasoning. Closing the key causes a growth of the primary field out of the right side of the coil when the windings are end-to-end; this necessitates labeling this side of the coil "N" and the left side "S." (Remember? The N-pole is the side from which the lines emerge.
To oppose the growth of an N-pole on the right side of the primary, an induced N-pole must form on the left side of the secondary; since like poles repel, opposition is being produced by repulsion in this instance. See Fig. 6 (A). So the answer we arrive at for the end-to-end arrangement coincides exactly with the solution obtained using field theory.
Here's the rub, however. If the primary coil is now inserted coaxially inside the secondary coil, the polar approach gives the wrong answer. With the expanding primary field producing an N-pole on its right end, the polar hypothesis demands that the secondary coil also form a budding N-pole on its right side to oppose the growth of an adjacent similar pole on the primary coil. Thus, this situation requires that the induced current in the secondary flow one way when the coils are end-to-end and in the opposite direction when one is inside the other as in Fig. 6 (B). This does not happen in practice!
As we showed earlier, field theory makes no distinction between relative positions of primary and secondary and therefore predicts the correct answer. The polar method, on the other hand, falls flat in this instance. Conclusion: abandon magnetic poles and think in terms of magnetic fields!