# Magnetic Fields

Are you curious about magnetic fields? Well, a magnetic field is a space where a force is applied at every point. This force comes from a source, which can be electrical or magnetic. It's pretty fascinating, right? These fields are all around us, from the magnets on your fridge to the Earth itself. So, next time you see a magnet, remember that it's creating its own magnetic field! And if you want to learn more about magnetic fields, keep reading and exploring the wonders of science.

## Magnetic Field Lines

Have you ever seen what happens when you put a magnet under a thin surface and throw metal shards on top? You might be surprised to see that the shards align themselves in a specific shape, just like the needle of a compass. That's because they are following the lines of the magnetic field that the magnet is generating. These lines represent the force vectors of the field, which means that the denser they are in a particular area, the stronger the magnetic field is in that area. Check out Figure 1 to see what we mean! Understanding how magnetic fields work can be a fascinating topic, and it's all around us, from the magnets on your fridge to the Earth itself. So keep learning and exploring the wonders of science.

## Lines created by a magnet applied to iron particles

Did you know that every line in a magnetic field is a closed loop that goes from one pole to the other? This is what makes a magnetic field solenoidal, which is different from the electric field. Unlike the electric field, the magnetic field doesn't have a magnetic monopole, which means it's closely connected to the electric field. How are they related, you ask? Well, they generate each other through the movement of charges. To understand this relationship better, we need to consider the Lorentz force. It's amazing how different fields can interact with each other, and studying them can help us understand the world around us.

## The Direction of Magnetic Field: The Lorentz force

It's fascinating to think about the relationship between electric and magnetic fields, and how a charged particle passing through them can be subject to a force that's dependent on both fields. This force is always perpendicular to the magnetic field and can be visualized using Fleming's rule of the left hand. By following this rule, we can determine the direction of the vector product between the velocity of the charged particle and the magnetic field. This rule is a powerful tool in understanding the Lorentz force, which is the force that acts on a charged particle moving through a magnetic field. By considering the ordered triplet of electric field, magnetic field, and charged particle, we can better understand the complex interactions of these fields and how they affect the behavior of particles.

The expression for the Lorentz force is F = q(E + v x B), where q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field. When we apply this expression to the Lorentz force, we can use the right-hand rule to determine the direction of the force. The right-hand rule states that if we point our right thumb in the direction of the velocity of the charged particle, our index finger in the direction of the magnetic field, then our middle finger will point in the direction of the resulting force. This visualization can help us understand the complex interactions between electric and magnetic fields and how they affect the behavior of charged particles. Additionally, there is a similar rule called the right-hand grip rule that can help us determine the direction of the magnetic field around a current-carrying wire. By pointing our thumb in the direction of the current, the direction of the magnetic field can be determined by the direction in which our fingers curl around the wire. These rules are powerful tools in understanding the behavior of electromagnetic fields and their interactions with charged particles.

## Magnetic Fields: What is the difference between H and B?

When we consider the vacuum as the area where the magnetic field is present, the magnetic field strength and magnetic field flux density are proportional to each other. However, when we consider materials, the two quantities can be different, as the magnetic field can be affected by the properties of the material. Specifically, magnetic field strength is defined as the force per unit current per unit length, while magnetic field flux density is defined as the magnetic flux per unit area perpendicular to the magnetic field. The magnetic flux is the portion of the magnetic field passing through a surface per unit time. In materials, the relationship between magnetic field strength and magnetic field flux density is governed by the material's permeability, which measures the degree to which a material can support the formation of magnetic fields. Understanding the difference between these two quantities is important in the study of electromagnetism and its applications, such as in the design of electrical machines and devices.

**Magnetic flux density**

The term "magnetic field" is used to describe two related but distinct quantities: magnetic field intensity, denoted by H, and magnetic flux density, denoted by B. In vacuum, H and B are proportional to each other due to the vacuum permeability, but in materials, the magnetization M must be taken into account when calculating B. Magnetization is a measure of the degree to which a material is magnetized in response to an external magnetic field, and it accounts for the effect of magnetic polarization within the material. The concept of magnetization is dual to that of electric polarization, which gives symmetry to the formulas describing the electromagnetic field. Understanding the relationship between H, B, and M is important in the study of electromagnetism and its applications, such as in the design of magnetic storage devices and magnetic sensors.

## What is electromagnetic induction?

Electric fields and magnetic fields generate each other, but how does that happen? The explanation is electromagnetic induction, which is the phenomenon causing a current to be generated into a conductor thanks to a magnetic field.

**Generating an electromotive force with a magnetic field (Faraday's law)**

Lenz's law states that the induced magnetic field generated by the induction current within a material by an external magnetic field opposes this last one. This makes perfect sense as, otherwise, the magnetic field within the material will increase exponentially. This law was deduced in 1834 by the Russian physicist Heinrich Friedrich Emil Lenz (1804–65). It is a manifestation of the conservation of energy. The induced emf produces a current that opposes the change in flux, because a change in flux means a change in energy. Energy can enter or leave, but not instantaneously. Lenz’s law is a consequence. As the change begins, the law says induction opposes and, thus, slows the change.

Faraday studied the effect of a magnetic field applied to an electric circuit and discovered that moving a magnet with the circuit immersed into its field, or moving a magnet into a loop formed by the circuit, causes a current to flow in the circuit itself[^5]. Moreover, this current is proportional to the speed of the movement that is represented by the time derivative d / dt of the magnetic field flux ΦB.

EMF here is the electromotive force measured in Volts.

**Magnetic Fields: Alternating current**

The induction motor is an invention that works on the principle of induction and uses the magnetic field to generate a current that produces AC. It consists of a magnetically charged armature called a stator, which contains a moving part called a rotor. The rotor is connected to the circuit through wirings that sense the magnetic field, which always faces the same direction but imposes a current that changes as the rotor moves. As the rotor turns, it generates an alternating current with a sinusoidal waveform, which is expressed in the form:

V(t) = Vmax sin(ωt)

where Vmax is the maximum voltage, ω is the angular frequency, and t is time.

It is important to note that by inverting the functions of the stator and the rotor in a magnetic field generating a current, one can obtain a circuit that generates mechanical movement. This is the basis for many other inventions, such as the electric generator, which converts mechanical energy into electrical energy.

The induction motor is widely used in various applications such,, and machines, due to its efficiency and reliability. Its simple design and low maintenance make it a popular choice for many industrial and commercial applications.

**Magnetic Fields: Inductance and flux linkage**

Loops in an electrical circuit interact with the magnetic field, which is the basis of the inductor, an element that inherits this quality. To study how it works, we can define the flux linkage as the total flux passing through a coil, which is obtained by multiplying the magnetic flux by the number of loops.duct identified by, defined as magnetic linkage of an object divided by the current that causes that flux. When the current causing the flux linkage is also the one linking the coil, it takes the name of self-inductance.

The magnetic field is strictly linked to the electrical field. The two generate each other and are the two faces of the same medal: the electromagnetic force. There is a difference between H and B when the field is applied to a material, while they have the same value in a vacuum. When an electromagnetic field is applied to a moving particle, the particle is subject to a perpendicular force called the Lorentz force. The phenomenon of induction causes a magnetic field to be generated by an electric field.

Remarkable inventions based on induction are the AC motor or induction motor and the transformer. The AC motor uses the principle of induction to generate a current that produces AC, while the transformer uses the principle of electromagnetic induction to transfer electrical energy from one circuit to another through a changing magnetic field. These inventions have revolutionized the way we use electricity and have led to many other innovations in the field of electrical engineering.

## Magnetic Fields

**What is a magnetic field?**

It is the area where the magnetic force acts on particles.

**Where is the magnetic field the strongest?**

The magnetic field is the strongest at the poles because of the concentration of field lines.

**Why does Earth have a magnetic field?**

Earth has a magnetic field because there are currents flowing in its core.

**Does Mars have a magnetic field?**

Mars doesn't have a magnetic field, even though it used to.

**What's the unit of the magnetic field H?**

The magnetic field is measured in [A] / [m]