MAGNETIC FIELD: INTENSITY, CHARACTERISTICS, SOURCES, EXAMPLES - PHYSICAL - 2024

The magnetic field is the influence that moving electric charges have on the space that surrounds them. Charges always have an electric field, but only those that are in motion can generate magnetic effects.

The existence of magnetism has been known for a long time. The ancient Greeks described a mineral capable of attracting small pieces of iron: it was the lodestone or magnetite.

Figure 1. Magnetite sample. Source: Wikimedia Commons. Rojinegro81.

The sages Thales of Miletus and Plato were busy recording magnetic effects in their writings; by the way, they also knew static electricity.

But magnetism did not become associated with electricity until the 19th century, when Hans Christian Oersted observed that the compass deviated in the vicinity of a current-carrying conductive wire.

Today we know that electricity and magnetism are, so to speak, two sides of the same coin.

Magnetic field in physics

In physics, the term magnetic field is a vector quantity, with modulus (its numerical value), direction in space and sense. It also has two meanings. The first is a vector sometimes called magnetic induction and is denoted by B.

The unit of B in the International System of Units is the tesla, abbreviated T. The other quantity also called the magnetic field is H, also known as the magnetic field intensity and whose unit is ampere / meter.

Both quantities are proportional, but they are defined in this way to take into account the effects that magnetic materials have on the fields that pass through them.

If a material is placed in the middle of an external magnetic field, the resulting field will depend on this and also on the material's own magnetic response. That is why B and H are related by:

B = μ _m H

Here μ _m is a constant that depends on the material and has suitable units so that when multiplying by H the result is tesla.

C

-The magnetic field is a vector magnitude, therefore it has magnitude, direction and sense.

-The unit of the magnetic field B in the International System is the tesla, abbreviated as T, while H is ampere / meter. Other units that appear frequently in the literature are the gauss (G) and the oersted.

-Magnetic field lines are always closed loops, leaving a north pole and entering a south pole. The field is always tangent to the lines.

-The magnetic poles are always presented in a North-South pair. It is not possible to have an isolated magnetic pole.

-It always originates from the movement of electrical charges.

-Its intensity is proportional to the magnitude of the load or the current that produces it.

-The magnitude of the magnetic field decreases with the inverse of the square of the distance.

-Magnetic fields can be constant or variable, both in time and in space.

-A magnetic field is capable of exerting a magnetic force on a moving charge or on a wire that carries current.

Poles of a magnet

A bar magnet always has two magnetic poles: the north pole and the south pole. It is very easy to verify that poles of the same sign repel, while those of different types attract.

This is quite similar to what happens with electrical charges. It can also be observed that the closer they are, the greater the force with which they attract or repel each other.

Bar magnets have a distinctive pattern of field lines. They are sharp curves, leaving the north pole and entering the south pole.

Figure 2. Magnetic field lines of a bar magnet. Source: Wikimedia Commons.

A simple experiment to look at these lines is to spread iron filings on top of a sheet of paper and place a bar magnet underneath.

The intensity of the magnetic field is given as a function of the density of field lines. These are always densest near the poles, and they spread as we move away from the magnet.

The magnet is also known as a magnetic dipole, in which the two poles are precisely the north and south magnetic poles.

But they can never be separated. If you cut the magnet in half, you get two magnets, each with its respective north and south poles. Isolated poles are called magnetic monopoles, but to date none have been isolated.

Sources

One can speak of various sources of magnetic field. They range from magnetic minerals, through the Earth itself, which behaves like a large magnet, to electromagnets.

But the truth is that every magnetic field has its origin in the movement of charged particles.

Later we will see that the primordial source of all magnetism resides in the tiny currents inside the atom, mainly those that are produced due to the movements of the electrons around the nucleus and to the quantum effects present in the atom.

However, regarding its macroscopic origin, one can think of natural sources and artificial sources.

Natural sources in principle do not "turn off", they are permanent magnets, however it must be taken into account that heat destroys the magnetism of the substances.

As for artificial sources, the magnetic effect can be suppressed and controlled. Therefore we have:

-Magnets of natural origin, made of magnetic minerals such as magnetite and maghemite, both iron oxides, for example.

-Electric currents and electromagnets.

Magnetic minerals and electromagnets

In nature there are various compounds that exhibit remarkable magnetic properties. They are capable of attracting pieces of iron and nickel, for example, as well as other magnets.

The iron oxides mentioned, such as magnetite and maghemite, are examples of this class of substances.

Magnetic susceptibility is the parameter that is used to quantify the magnetic properties of rocks. Basic igneous rocks are those with the highest susceptibility, due to their high content of magnetite.

On the other hand, as long as you have a wire that carries current, there will be an associated magnetic field. Here we have another way of generating a field, which in this case, takes the form of concentric circles with the wire.

The direction of movement of the field is given by the rule of the right thumb. When the thumb of the right hand points in the direction of the current, the four remaining fingers will indicate the direction in which the field lines are bent.

Figure 3. Right thumb rule to obtain the direction and sense of the magnetic field. Source: Wikimedia Commons.

An electromagnet is a device that produces magnetism from electrical currents. It has the advantage of being able to turn on and off at will. When the current ceases, the magnetic field disappears. In addition the field intensity can also be controlled.

Electromagnets are part of various devices, including speakers, hard drives, motors, and relays, among others.

Magnetic force on a moving charge

The existence of a magnetic field B can be verified by means of a test electric charge -called q- and that moves with speed v. For this, the presence of electric and gravitational fields is ruled out, at least for the moment.

In such a case, the force experienced by the charge q, which is denoted as F _B, is entirely due to the influence of the field. Qualitatively, the following is observed:

-The magnitude of F _B is proportional to q and a speed v.

-If v is parallel to the magnetic field vector, the magnitude of F _B is zero.

-The magnetic force is perpendicular to both v and B.

-Finally, the magnitude of the magnetic force is proportional to sin θ, where θ is the angle between the velocity vector and the magnetic field vector.

All of the above is valid for both positive and negative charges. The only difference is that the direction of the magnetic force is reversed.

These observations agree with the vector product between two vectors, so that the magnetic force experienced by a point charge q, moving with velocity v in the middle of a magnetic field is:

F _B = q v x B

Whose module is:

Figure 4. Right-hand rule for the magnetic force on a positive point charge. Source: Wikimedia Commons.

How is a magnetic field generated?

There are several ways, for example:

-By magnetizing an appropriate substance.

- Passing an electric current through a conductive wire.

But the origin of magnetism in matter is explained by remembering that it must be associated with the movement of charges.

An electron orbiting the nucleus is essentially a tiny closed current circuit, but one capable of contributing substantially to the magnetism of the atom. There are very many electrons in a piece of magnetic material.

This contribution to the magnetism of the atom is called the orbital magnetic moment. But there is more, because the translation is not the only movement of the electron. It also has a magnetic spin moment, a quantum effect whose analogy is that of a rotation of the electron on its axis.

In fact, the magnetic moment of spin is the main cause of the magnetism of an atom.

Types

The magnetic field is capable of taking many forms, depending on the distribution of currents that originate it. In turn, it can vary not only in space, but also in time, or both at the same time.

-In the vicinity of the poles of an electromagnet there is an approximately constant field.

-Also inside a solenoid a high intensity and uniform field is obtained, with the field lines directed along the axial axis.

-The magnetic field of the Earth approximates quite well the field of a bar magnet, especially in the vicinity of the surface. Further afield, the solar wind modifies the electric currents and noticeably deforms it.

-A wire that carries current has a field in the form of concentric circles with the wire.

Regarding whether or not the field can vary over time, we have:

-Static magnetic fields, when neither their magnitude nor their direction change over time. The field of a bar magnet is a good example of this type of field. Also those that originate from wires that carry stationary currents.

-Variable fields over time, if any of their characteristics varies over time. One way to obtain them is from alternating current generators, which make use of the phenomenon of magnetic induction. They are found in many commonly used devices, for example cell phones.

Biot-Savart's law

When it is required to calculate the shape of the magnetic field produced by a distribution of currents, use can be made of the Biot-Savart law, discovered in 1820 by the French physicists Jean Marie Biot (1774-1862) and Felix Savart (1791-1841).).

For some current distributions with simple geometries, a mathematical expression for the magnetic field vector can be obtained directly.

Suppose we have a wire segment of differential length dl that carries an electric current I. The wire will also be assumed to be in a vacuum. The magnetic field that produces this distribution:

-Decreases with the inverse of the square of the distance to the wire.

-It is proportional to the intensity of the current I that passes through the wire.

-Its direction is tangential to the circumference of radius r centered on the wire and its direction is given by the rule of the right thumb.

- μ _o = 4π. 10 ^-7 Tm / A

- d B is a magnetic field differential.

- I is the intensity of the current flowing through the wire.

- r is the distance between the center of the wire and the point where you want to find the field.

-r is the vector that goes from the wire to the point where you want to calculate the field.

Examples

Below are two examples of magnetic field and their analytical expressions.

Magnetic field produced by a very long rectilinear wire

By means of the Biot-Savart law it is possible to obtain the field produced by a thin finite conductor wire that carries a current I. By integrating along the conductor and taking the limiting case in which it is very long, the magnitude of the field result:

Field created by the Helmholtz coil

The Helmholtz coil is made up of two identical and concentric circular coils, to which the same current is passed. They serve to create an approximately uniform magnetic field within it.

Figure 5. Schematic of the Helmholtz coils. Source: Wikimedia Commons.

Its magnitude at the center of the coil is:

Y is directed along the axial axis. The factors of the equation are:

- N represents the number of turns of the coils

- I is the magnitude of the current

- μ _o is the magnetic permeability of the vacuum

- R is the radius of the coils.

References

1. Figueroa, D. (2005). Series: Physics for Science and Engineering. Volume 1. Kinematics. Edited by Douglas Figueroa (USB).
2. Magnetic field strength H. Recovered from: 230nsc1.phy-astr.gsu.edu.
3. Kirkpatrick, L. 2007. Physics: A Look at the World. 6th abridged edition. Cengage Learning.
4. Magnetic Field and Magnetic Forces. Recovered from: physics.ucf.edu.
5. Rex, A. 2011. Fundamentals of Physics. Pearson.
6. Serway, R., Jewett, J. (2008). Physics for Science and Engineering. Volume 2. 7th. Ed. Cengage Learning.
7. University of Vigo. Examples of magnetism. Recovered from: quintans.webs.uvigo.es