Modern Physics

# Magnetic field: intensity, characteristics, sources, examples

The magnetic field is the influence that electrical charges in motion have on surrounding space. Charges always have an electric field, but only those 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 magnet or the magnetite stone.

Figure 1. Sample of magnetite. Source: Wikimedia Commons. Rojinegro81 [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)].

The Thales sages of Miletus and Plato took care to record the magnetic effects in their writings; By the way, they also knew static electricity.

But magnetism was not associated with electricity until the 19th century, when Hans Christian Oersted observed that the compass deviated in the vicinity of a conducting wire that carried current.

We now 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 magnitude, with magnitude (its numerical value), direction in space, and direction. 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 magnitude also called the magnetic field is H , also known as the magnetic field strength and whose unit is ampere/meter.

Both magnitudes 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 it and also on the magnetic response of the material itself. That’s why B and H are related by:

B = µm H

Here mis a constant that depends on the material and is suitable for multiplying H units the result is tesla.

## C Characteristics of a Magnetic Field

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

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

-The magnetic field lines are always closed loops, which leave a north pole and enter the south pole. The field is always tangent to the lines.

-Magnetic poles always appear in North-South pairs. It is not possible to have an insulated magnetic pole.

– Always originates in the movement of electrical charges.

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

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

-Magnetic fields can be constant or variable, both in time and 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’s very easy to see if poles of the same signal repel each other while those of different types attract.

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

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Bar magnets have a distinct pattern of field lines. They are sharp curves that leave the north pole and enter the south pole.

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

The strength of the magnetic field is given as a function of the density of the field lines. They are always denser near the poles and extend 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 the magnet is cut in half, two magnets are obtained, each with its respective north and south poles. Isolated poles are called magnetic monopoles , but so far no one has been isolated.

## fountains

You can talk about various magnetic field sources. They range from magnetic minerals, through the Earth itself, which behaves like a large magnet, to reaching electromagnets.

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

Later we will see that the primary source of all magnetism resides in the small currents within the atom, mainly those that occur due to the movement of electrons around the nucleus and to the quantum effects present in the atom.

However, in terms of macroscopic origin, natural and artificial sources can be considered.

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

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

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

Electric currents and electromagnets.

### Magnetic minerals and electromagnets

In nature, there are several compounds that exhibit remarkable magnetic properties. They are able to attract pieces of iron and nickel, for example, in addition to other magnets.

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

The magnetic susceptibility is the parameter used to measure the magnetic properties of the rocks. Basic igneous rocks are those with the greatest susceptibility, due to their high magnetite content.

On the other hand, as long as there is a current carrying wire, there will be an associated magnetic field. Here we have another way to generate 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 right thumb rule. When the thumb of the right hand points in the direction of the current, the remaining four fingers indicate the direction in which the field lines are curved.

Figure 3. Right thumb rule for getting the direction and direction 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 it on and off at will. When the current ceases, the magnetic field disappears. Furthermore, the field strength can also be controlled.

Electromagnets are part of many 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 an electrical test charge – called q – and moved with velocity v . For this, the presence of electric and gravitational fields is ruled out, at least for the time being.

In this case, the force experienced by the charge q , which is designated as B , is entirely due to the influence of the field. Qualitatively, the following is observed:

-The magnitude of B is proportional to q and velocity v .

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

-O magnetic force is perpendicular to both v as B .

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

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

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

B = q v B

Which module is:

B = qvBsen θ

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

## How is a magnetic field generated?

There are several ways, for example:

-By magnetization of an appropriate substance.

– Passing an electrical current through a conducting 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 small closed-current circuit, but capable of substantially contributing to the atom’s magnetism. There are too many electrons in a piece of magnetic material.

This contribution to the magnetism of the atom is called orbital magnetic moment . But there’s more, because translation isn’t the only movement of the electron. It also has a magnetic rotational moment , a quantum effect whose analogy is that of an electron rotating on its axis.

In fact, the magnetic rotational moment is the main cause of an atom’s magnetism.

## Types

The magnetic field is capable of taking various 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 Earth’s magnetic field closely approximates the field of a bar magnet, especially near the surface. Furthermore, the solar wind modifies electrical currents and visibly deforms them.

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

As for the possibility or not of the field varying over time, they 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.

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-Changing fields over time, if any of their features change over time. One way to obtain them is through alternating current generators, which make use of the phenomenon of magnetic induction. They are found in a number of commonly used devices, for example, cell phones.

### Biot-Savart’s Law

When it is necessary to calculate the shape of the magnetic field produced by a current distribution, it is possible to make use 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 can be obtained directly for the magnetic field vector.

Suppose we have a length of the differential wire segment dl carrying an electrical current I . It will also be assumed that the yarn is in a vacuum. The magnetic field that produces this distribution:

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

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

-Its direction is tangential to the circumference of the radius r centered on the wire and its direction is given by the rule of the right thumb. – μ the = 4π. 10 -7 Tm / A

– 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.

-d l is the vector whose magnitude is the length of the differential segment dl.

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

## Examples

Below are two examples of the magnetic field and its analytical expressions.

### Magnetic field produced by a very long straight wire

Through the Biot-Savart law, it is possible to obtain the field produced by a thin finite conductor wire that carries a current I. Integrating along the conductor and considering the limit case in which it is very long, the magnitude of the field occurs: ### Field created by Helmholtz coil

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

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

Its magnitude at the center of the coil is: And it is directed along the axial axis. The factors in 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 vacuum

– R is the radius of the coils.