How Electricity and Magnetism Are Related
Electricity and magnetism are joined at the hip. When an electric current flows, a magnetic field is produced. When a magnetic field changes, electricity is generated. Everyday things are made from atoms consisting of a cloud of electrons surrounding protons and neutrons. Electrons carry a property called negative charge. When electrons skip from atom to atom in a wire, an electric current is said to flow. In the drawing to the right, a vertical wire is shown carrying an electric current flowing in the direction of the blue arrow. The magnetic field produced by the current circles around the wire, becoming weaker as you move away from the center. Note the compass in the drawing. The compass aligns with the green magnetic force lines, always tangent to the circles and never pointing towards the wire. If you double the current in a wire, the strength of the magnetic field is also doubled. For long wires, if you move twice as far away, the magnetic field is only half as strong. However, if the wire is short or the distance is great, the field strength falls off faster.
If a wire is wrapped around a nail, you get an electromagnet that behaves very much like a bar magnet. Since the magnetic field circles around a wire, each turn of a coil produces a field down the middle of the coil. Then the forces from adjacent turns add to the effect creating a stronger magnetic field. Such a coil of wire is called a solenoid which is drawn below with blue wires. If you are well inside the coil, the strength of the field does not change as you move around. Note how similar the green field lines look compared to those of a permanent bar magnet. If an iron bar is placed in the middle of the coil, ferromagnetic enhancement occurs to make a stronger magnet.
Many modern marvels depend on electromagnets and coils. The speaker in your favorite stereo is a coil sitting inside a permanent magnet. When electricity flows through the coil, the electromagnetic field reacts with the permanent field and moves the coil. The coil is attached to a cone which pushes air around to make music. And we can't forget motors. Almost all electric motors are nothing but coils and magnets. The fields are turned on and off at appropriate times to push the rotor of the motor causing it to spin. The faster the motor turns, the faster the magnetics have to be pulsed to keep up with the rotor. To get personal, the hard drive in your very own computer is another example. Not only does it need a motor to spin the memory disk, but the data is actually recorded and read by a coil of wire interacting with tiny magnetic spots on the disk. Without electromagnetic technology, say goodbye to radios, televisions, computers, clothes washers and dryers, automobiles, air conditioners ... heck, say goodbye to the twentieth century.
So far we have assumed that the electric wires and magnetic fields are not in motion or changing in time. Things become much richer if they do. That's a nice way of saying things get darn complicated. When a wire moves through a magnetic field or when a magnetic field changes, an electric field and associated currents are generated. Consider a coil of wire like the solenoid pictured above with a switch to connect it to a battery. When the switch closes, the battery tries to push electrons through the wire. As the electrons start to move, a magnetic field begins to build. But the changing magnetic field reacts with the coil producing a new current that opposes the original current. This prevents things from happening too rapidly much like a train that must slowly accelerate a heavy load of freight cars. Both the current and the magnetic field rise as an exponential function of time. That means they rise slowly to a maximum determined by the capability of the battery and the resistance of the coil wires. So, an electromagnet is similar to a permanent magnet that can be turned on, but with a rise time that limits how fast things change.
Let's imagine that you hold a permanent magnet in one hand and an electromagnet in the other. What's the difference? First, let's consider a practical electromagnet that is 3 inches in diameter. Assuming it is a simple coil of wire, it might generate a 100 gauss field in 1 millisecond (which is 1/1000 second). When the electromagnet is switched on, the magnetic field passing through your hand rises from zero to full force in the risetime of the coil. And what happens to your hand? Assuming you are mostly made of salty fluid, the changing magnetic field will produce a circulating electric field which will cause a small electric current to flow. This won't have much of a counter effect on the magnetics but it may have an effect on your body chemistry. After all, you are an electrochemical machine of sorts. The effect would be proportional to the rate of change of the magnetic field, in this case 100 gauss per millisecond.
What about the permanent magnet? Let's assume it is 1 inch in diameter and has a field strength of 1000 gauss near the pole face. If it is held steady, no rate effects occur. However if the magnet were rolled in your hand, the field might swing by 1000 gauss in a second. That's a rate of change of 1000 gauss per second. But in a millisecond, the change is only 1 gauss which is 1% of the rate of the electromagnet described above. So, the currents induced by the strong permanent magnet would be one hundred times smaller than those of the electromagnet. If the permanent magnet were belted to your hand or another body part, movement would be restricted and the potential for induced currents would be even smaller. Many people feel that belting magnets to painful joints or sleeping on magnetic mattress pads helps reduce pain and improve healing. It would follow that any benefit from a permanent magnet must be due to the steady field and not rate of change effects. On the other hand, electromagnets seem better suited to induce tiny electrical currents via a rate of change effect.
The circulating currents produced by electromagnets are driven by induced electric fields. Electric field strength is usually expressed in units of volts per meter (volts/meter). A flashlight battery is a 1.5 volt source of electricity and your arm is about one meter long. If you press one end of a flashlight battery to your nose and touch the other end with a finger tip, you will produce a 1.5 volts/meter electric field down the length of your arm. This electric field will cause a small current to flow, mostly on the surface of your skin. If you get nervous and sweat, the current will increase. The fields produced by electromagnets can penetrate much deeper than the skin and we can estimate these fields using Faraday's Law. Since we are talking about coils, imagine a circle inside your hand a little bit smaller than the coil itself. A magnetic field passing through this circle will produce an electric field that will drive a circulating current. By Faraday's Law, the electric field around the edge will be proportional to rate of change of the magnetic field averaged over the area of the circle. For a 3 inch coil with a uniform magnetic field that is changing at 100 gauss per millisecond, the induced electric field is 0.15 volts/meter.
How does all of this compare to the electrochemistry within the human body? The long axons of nerve fibers fire at an electric field gradient of about 13 volts/meter. The coil above operates at about 1% of this level. It won't make your hand twitch but it may have a gentle effect on the electrochemistry. Nerve pulses typically operate in the millisecond range and then require a rest period of tens of milliseconds before they can retrigger. This suggests that electromagnets should fire millisecond pulses at a repetition rate of several pulses per second to influence the nervous system. Imagine that a tense muscle is locked in a biological feedback loop whereby the muscle pinches nerves that cause the muscle to contract which further pinches the nerves and so on. If the pinched nerves are being stimulated at near their firing threshold, a pulsing magnetic field may provide just enough energy to drop the stimulation below the threshold. This would inhibit some muscle contraction and further reduce the stimulation. In a few minutes, enough muscle fibers might relax to break the feedback loop and stop the pain. In such a situation, the magnetic field doesn't have to operate at 100% of the nerve energy threshold. All it has to do is play the spoiler at a few percent.