Basic to magnetism are magnetic fields and their effects on matter, as, for instance, the deflection of moving charges and torques on other magnetic objects. Evidence for the presence of a magnetic field is the magnetic force on charges moving in that field; the force is at right angles to both the field and the velocity of the charge. This force deflects the particles without changing their speed. The deflection can be observed in the torque on a compass needle that acts to align the needle with the magnetic field of Earth. The needle is a thin piece of iron that has been magnetized—i.e., a small bar magnet. One end of the magnet is called a north pole and the other end a south pole. The force between a north and a south pole is attractive, whereas the force between like poles is repulsive. The magnetic field is sometimes referred to as magnetic induction or magnetic flux density; it is always symbolized by B. Magnetic fields are measured in units of tesla (T). (Another unit of measure commonly used for B is the gauss, though it is no longer considered a standard unit. One gauss equals 10−4 tesla.)

A fundamental property of a magnetic field is that its flux through any closed surface vanishes. (A closed surface is one that completely surrounds a volume.) This is expressed mathematically by div B = 0 and can be understood physically in terms of the field lines representing B. These lines always close on themselves, so that if they enter a certain volume at some point, they must also leave that volume. In this respect, a magnetic field is quite different from an electric field. Electric field lines can begin and end on a charge, but no equivalent magnetic charge has been found in spite of many searches for so-called magnetic monopoles.

magnetism, phenomenon associated with magnetic fields, which arise from the motion of electric charges. This motion can take many forms. It can be an electric current in a conductor or charged particles moving through space, or it can be the motion of an electron in an atomic orbital. Magnetism is also associated with elementary particles, such as the electron, that have a property called spin.

Basic to magnetism are magnetic fields and their effects on matter, as, for instance, the deflection of moving charges and torques on other magnetic objects. Evidence for the presence of a magnetic field is the magnetic force on charges moving in that field; the force is at right angles to both the field and the velocity of the charge. This force deflects the particles without changing their speed. The deflection can be observed in the torque on a compass needle that acts to align the needle with the magnetic field of Earth. The needle is a thin piece of iron that has been magnetized—i.e., a small bar magnet. One end of the magnet is called a north pole and the other end a south pole. The force between a north and a south pole is attractive, whereas the force between like poles is repulsive. The magnetic field is sometimes referred to as magnetic induction or magnetic flux density; it is always symbolized by B. Magnetic fields are measured in units of tesla (T). (Another unit of measure commonly used for B is the gauss, though it is no longer considered a standard unit. One gauss equals 10−4 tesla.)

A fundamental property of a magnetic field is that its flux through any closed surface vanishes. (A closed surface is one that completely surrounds a volume.) This is expressed mathematically by div B = 0 and can be understood physically in terms of the field lines representing B. These lines always close on themselves, so that if they enter a certain volume at some point, they must also leave that volume. In this respect, a magnetic field is quite different from an electric field. Electric field lines can begin and end on a charge, but no equivalent magnetic charge has been found in spite of many searches for so-called magnetic monopoles.

The most common source of magnetic fields is the electric current loop. It may be an electric current in a circular conductor or the motion of an orbiting electron in an atom. Associated with both these types of current loops is a magnetic dipole moment, the value of which is iA, the product of the current i and the area of the loop A. In addition, electrons, protons, and neutrons in atoms have a magnetic dipole moment associated with their intrinsic spin; such magnetic dipole moments represent another important source of magnetic fields. A particle with a magnetic dipole moment is often referred to as a magnetic dipole. (A magnetic dipole may be thought of as a tiny bar magnet. It has the same magnetic field as such a magnet and behaves the same way in external magnetic fields.) When placed in an external magnetic field, a magnetic dipole can be subjected to a torque that tends to align it with the field; if the external field is not uniform, the dipole also can be subjected to a force.

All matter exhibits magnetic properties to some degree. When placed in an inhomogeneous field, matter is either attracted or repelled in the direction of the gradient of the field. This property is described by the magnetic susceptibility of the matter and depends on the degree of magnetization of the matter in the field. Magnetization depends on the size of the dipole moments of the atoms in a substance and the degree to which the dipole moments are aligned with respect to each other. Certain materials, such as iron, exhibit very strong magnetic properties because of the alignment of the magnetic moments of their atoms within certain small regions called domains. Under normal conditions, the various domains have fields that cancel, but they can be aligned with each other to produce extremely large magnetic fields. Various alloys, like NdFeB (an alloy of neodymium, iron, and boron), keep their domains aligned and are used to make permanent magnets. The strong magnetic field produced by a typical three-millimetre-thick magnet of this material is comparable to an electromagnet made of a copper loop carrying a current of several thousand amperes. In comparison, the current in a typical light bulb is 0.5 ampere. Since aligning the domains of a material produces a magnet, disorganizing the orderly alignment destroys the magnetic properties of the material. Thermal agitation that results from heating a magnet to a high temperature destroys its magnetic properties.

Magnetic fields vary widely in strength. Some representative values are given in the Table.

Magnetic fields produced by electric currents can be calculated for any shape of circuit using the law of Biot and Savart, named for the early 19th-century French physicists Jean-Baptiste Biot and Félix Savart. A few magnetic field lines produced by a current in a loop are shown in Figure 1. These lines of B form loops around the current. The Biot–Savart law expresses the partial contribution dB from a small segment of conductor to the total B field of a current in the conductor. For a segment of length and orientation dl that carries a current i,

Electricity and Magnetism. Magnetism. Magnetic Field of Steady Currents. [Equation #1 online #34 print – Equation of magnetic field of a current going through a wire.]

In this equation, μ0 is the permeability of free space and has the value of 4π × 10−7 newton per square ampere. This equation is illustrated in Figure 2 for a small segment of a wire that carries a current so that, at the origin of the coordinate system, the small segment of length dl of the wire lies along the x axis.

Magnetic fields produced by electric currents can be calculated for any shape of circuit using the law of Biot and Savart, named for the early 19th-century French physicists Jean-Baptiste Biot and Félix Savart. A few magnetic field lines produced by a current in a loop are shown in Figure 1. These lines of B form loops around the current. The Biot–Savart law expresses the partial contribution dB from a small segment of conductor to the total B field of a current in the conductor. For a segment of length and orientation dl that carries a current i,

Electricity and Magnetism. Magnetism. Magnetic Field of Steady Currents. [Equation #1 online #34 print – Equation of magnetic field of a current going through a wire.]

In this equation, μ0 is the permeability of free space and has the value of 4π × 10−7 newton per square ampere. This equation is illustrated in Figure 2 for a small segment of a wire that carries a current so that, at the origin of the coordinate system, the small segment of length dl of the wire lies along the x axis.

Magnetic fields produced by electric currents can be calculated for any shape of circuit using the law of Biot and Savart, named for the early 19th-century French physicists Jean-Baptiste Biot and Félix Savart. A few magnetic field lines produced by a current in a loop are shown in Figure 1. These lines of B form loops around the current. The Biot–Savart law expresses the partial contribution dB from a small segment of conductor to the total B field of a current in the conductor. For a segment of length and orientation dl that carries a current i,

Electricity and Magnetism. Magnetism. Magnetic Field of Steady Currents. [Equation #1 online #34 print – Equation of magnetic field of a current going through a wire.]

In this equation, μ0 is the permeability of free space and has the value of 4π × 10−7 newton per square ampere. This equation is illustrated in Figure 2 for a small segment of a wire that carries a current so that, at the origin of the coordinate system, the small segment of length dl of the wire lies along the x axis.