What Is a Magnetic Dipole?

Magnetic dipole is a physical model established by analogy with electric dipole. A system consisting of two points of magnetic charge with an equal sign is called a magnetic dipole ^[1] . But because no single magnetic monopole exists, the physical model of the magnetic dipole is not two magnetic monopoles, but a closed loop current. The magnetic dipole model can well describe the magnetic field distribution generated by small-scale closed circuit elements ^[2] .

Magnetic dipole is a physical model established by analogy with electric dipole. A system consisting of two points of magnetic charge with an equal sign is called a magnetic dipole ^[1] . But because no single magnetic monopole exists, the physical model of the magnetic dipole is not two magnetic monopoles, but a closed loop current. The magnetic dipole model can well describe the magnetic field distribution generated by small-scale closed circuit elements ^[2] .

Chinese name

Magnetic dipole

Types of

Physical model

Field

Electromagnetic physics

Solid

Loop current

Definition of magnetic dipole

Magnetic dipole is a physical model established by analogy with electric dipole. A system consisting of two points of magnetic charge with an equal sign is called a magnetic dipole ^[1] . For example, a small magnetic needle can be regarded as a magnetic dipole. The geomagnetic field can also be viewed as a field generated by a magnetic dipole. The magnetic dipole rotates under the action of torque. Only when the torque is zero will the magnetic dipole be in equilibrium. With this principle, magnetic field measurement can be performed. But because no single magnetic monopole exists, we use a circular circuit carrying a current as a model of the magnetic dipole.

Where I is the loop current and S is the loop area vector. The direction is determined by the current direction, which meets the right-hand rule. ^[3]

Magnetic dipole magnetic field characteristics

Analogous to the electric field strength and scalar potential of an electric dipole, magnetic dipoles also have almost uniform field strength and vector potential.

The relationship between the magnetic field strength B and the magnetic vector potential A is:

Note that the radial diameter of the vacuum magnetic dipole to a point in space is r , and its vector potential A is:

Is the vacuum permeability, the size is

.

The expression of the magnetic field strength of the magnetic dipole can be calculated by the above two formulas ^[4] . Since the vector potential of the magnetic dipole has a singularity at its position (origin O), it must be calculated with special care to get the correct answer. After careful derivation, the magnetic field can be obtained as:

among them,

Is the Dirac delta function. Since the Dirac delta function is in

The time scales are all 0, so the right term is omitted when the far field strength is sought. However, in quantum mechanics at the atomic scale, this item will make an important contribution. The Dirac delta function of the dipole magnetic field causes the atomic energy level to split, thereby forming a hyperfine structure. In astronomy, the ultrafine structure of the hydrogen atom gives a 21 cm spectral line. In the radio wave range of electromagnetic radiation, it is the most widespread electromagnetic radiation in the universe except for 3K background radiation. Astronomical research from the recombination to the reionization era can only rely on observing 21 cm spectral line radio waves. ^[5]

When several magnetic dipoles are given, according to the superposition principle, the total magnetic field is the total vector sum of the magnetic fields of each magnetic dipole.

Potential energy in the magnetic field of a magnetic dipole

Twisting the current-carrying cycle from angle arc ₁ to angle arc ₂ , the mechanical work W done by the magnetic field is

Note that the twist direction of the magnetic torque is counterclockwise, and is increasing clockwise, so a negative sign must be added. Set ₁ = / 2, then

Against the magnetic moment of this magnetic field, the current-carrying cycle is twisted from the angle arc / 2 to the angle arc _2. The mechanical work W _a is

The potential energy U defining the current-carrying cycle is equal to this mechanical work Wa, which is expressed by the equation as

Similar to the previous paragraph, the potential energy of a magnetic dipole can also be expressed by this equation. When the magnetic dipole moment is perpendicular to the magnetic field, the potential energy is equal to zero; when the magnetic dipole moment is in the same direction as the magnetic field, the potential energy is the minimum

; When the magnetic dipole moment is opposite to the magnetic field, the potential energy is the maximum

.

Comparison of magnetic dipole and electric dipole

A magnetic dipole is a small current loop, that is, a current-carrying coil, whose electromagnetic field and electric dipole are just dual. In contrast, the radiative resistance of magnetic dipoles is much smaller than that of electric dipoles. ^[3]