Solenoid Physics

I've always been wondering about how magnetism really works. This article is a concise summary of the physics of solenoids. It gives valuable guidelines about when the formulas hold true, and outlines your main design decisions.

Solenoids

"One of the most practical ways to create a controlled magnetic field is to construct a solenoid. A solenoid is a long cylinder upon which is wound a uniform coil of wire. When a current is sent through the wire, a magnetic field is created inside the cylinder.

The usual solenoid has a length several times its diameter. The wire is closely wound around the outside of a long cylinder in the form of a helix with a small pitch. The magnetic field created inside the cylinder is quite uniform, especially far from the ends of the solenoid. The larger the ratio of the length to the diameter, the more uniform the field near the middle.

The approximate value of the magnetic field is given by B = u₀nI, where B is the magnetic field, u₀ the permeability of free space, n is the number of turns of wire per unit length, and I the current through the wire. This relationship would hold exactly if the solenoid were infinitely long. A more precise calculation shows that the above relationship is within 2 percent of the correct value at the center of a solenoid if the ratio of the length to the diameter is five or greater.

This equation shows that one way to increase B is to increase I. But, because all wire has resistance, this procedure requires an increase in voltage across the solenoid and results in more heat being generated by the resistance of the wire. Another way to increase B is to increase n. But this increase can only be accomplished by decreasing the wire size (if the solenoid, as is usually the case, has turns wound as closely as possible), resulting in an increase in resistance and an increase in the voltage required for a given current, as well as an increase in heat generated by the resistance of the wire. An alternative way to increase n is to wind several layers of wire. This procedure increases the resistance of the wire, adds insulation problems, and decreases the length to diameter ratio. The selection of the appropriate trade-off is the principle problem that must be solved by the solenoid designer.

If a soft iron rod is placed partly inside a solenoid and the current turned on, the rod will be drawn into solenoid by the resulting magnetic field. This motion can be used to actuate a lever, unlock a door, or operate a relay. In this way the operation of a small electric switch can produce a large mechanical action at a remote location. It is worth noting that the iron core has to be placed at the end of the solenoid where the field is non-uniform for it to move. Furthermore, it is not necessary for the current to flow in one direction only. An alternating current will work also.

The magnetic field of a solenoid can also be used directly. It is used to deflect the beam of electrons in a television tube. Solenoids are also used to provide the magnetic field for magnetic resonance imaging.

Physics textbooks often use solenoids in problems about magnetic fields because the field produced by the solenoid is easily calculated and is easy to visualize. "

Source: "MacMillan Encyclopedia of Physics", p.1459, John S. Rigned, copyright 1996, ISBN 0-02-897359-3 (set).