Magnets always exist with two poles or in a form called magnetic dipoles; no one has ever been able to isolate a single magnetic monopole. Magnetic poles are defined in terms of whether they would point toward the north pole or the south pole of the Earth when the magnet is mounted on a frictionless support. For many purposes we can consider the Earth as having a large magnetic dipole in its core. Many materials that exist in nature are magnetic, and there are many man-made materials that also have magnetic properties. In a manner similar to the situation with electric charges, unlike magnetic poles attract one another, and like poles repel one another. These forces can be described in Coulomb's Law for Magnetism, which is quite similar to Coulomb's Law for Electric Charges that was studied in Chapter 12. The magnetic force depends upon the product of the pole strengths and is inversely proportional to the square of the distance between the poles. Therefore we have yet another inverse square law describing a physical phenomenon. We describe the "action at a distance" behavior of magnetic forces using field lines similar to the electric field lines studied earlier. We consider magnetic field lines to start on the north-seeking pole of a magnet and to end on a south-seeking pole.

Oersted discovered that a current carrying wire can also produce a magnetic field. For the case of a long, straight wire the magnetic field lines form concentric circles about the wire. The direction of the current is determined by grasping the wire with your right hand with your extended thumb pointing in the direction of the current. Your fingers will then curl around the wire in the direction of the magnetic field lines. This form of the right hand rule is shown in Figure 14.9 on page 281 in the text.

A magnetic field can produce a force on an electric charge, but it does so only when the charge is moving. In addition the velocity of the charge must be perpendicular to the direction of the magnetic field. In equation form the relationship is F = q v B where q is the magnitude of the charge, v is the velocity of the charge, and B is the magnetic field strength measured in Tesla. The direction of the resulting force is determined by using another right hand rule. An example of the application of this right hand rule is shown in the text in Figure 14.12 on page 282. To use the right hand rule, point the index finger of your right hand in the direction of the velocity of a positive charge. Then extend your second finger to be perpendicular to the palm of your hand, and point it in the direction of the magnetic field. Your thumb will point in the direction of the force on the positive charge. As a practice example consider the case where the velocity of a positive charge is toward the top of this page, and the magnetic field vector points to the left on the page. The force on the moving positively charged particle due to the magnetic field will be directed out of the page.

A magnetic field may also exert a force on a current carrying wire, because the current consists of moving charges. This force may be calculated as the product of the current in the wire, I, times the length of the segment of the wire in the magnetic field, L, times the strength of the magnetic field, B, or F = I L B.

Ampere discovered that a current carrying wire can exert a force on another current carrying wire. You may think of this as the magnetic field of one wire producing a force on the moving charges in the second wire.

A wire bent into a circular loop also produces a magnetic field as shown in Figure 14.13 on page 283 in the text. Near the center of the loop the magnetic field is quite similar to that of a magnetic dipole or bar magnet. Magnetic flux is defined as the product of magnetic field strength times the area through which the field lines pass. Faraday showed that a changing magnetic flux (represented by either a change in the magnetic field strength or a change in the area through which it passes or both) results in a voltage being induced in the circuit that experienced the changing magnetic flux. This phenomenon is responsible for the operation of generators, electric motors, and transformers. Lenz's Law tells us that the induced current that is produced by such a changing magnetic flux will be in a direction that opposes the change in the original magnetic flux.

Faraday investigated the effects produced with a change in the magnetic field passing through a coil. He concluded that a voltage was induced in a coil or circuit whenever the magnetic flux was changed. The magnetic flux, is defined as the product of the magnetic field strength and the area through which it passes, f = B A. The maximum flux is obtained when the field lines pass through the coil or circuit in a direction perpendicular to the plane of the coil or circuit. If the field lines are parallel to the plane of the coil or circuit there is no flux. Faraday found that the induced voltage, e, depends upon the rate of change of the magnetic flux, e = Df /t . The more rapid the change in the flux, the greater is the magnitude of the induced voltage.

Lenz's Law identifies the direction of the induced current in the coil or circuit and is really a result of the principle of conservation of energy. The direction of the induced current is such as to produce a magnetic field that opposes the change in the original magnetic flux, thereby preventing us from "getting something for nothing."

Transformers use Faraday's Law of Electromagnetic Induction to change an a.c. voltage to a different value. We have step-up transformers that increase the voltage and step-down transformers that decrease the voltage. Again because of conservation of energy, when the voltage is stepped-up in a transformer the result must be a decrease in the current, because power is the product of voltage times current, and a transformer does not have the ability to add power to the circuit. The ratio of the step up or down is given by the ratio of the number of turns on each side of the transformer, DV₂ / DV₁ = N₂ / N₁.