Magnetic field – sources and properties

A magnetic field is one of the most fundamental phenomena and terms in physics. It is generated by a moving electric charge and magnet. This text explains in brief what a magnetic field actually is, lists its sources and properties, and also its practical applications, in particular in stepper and induction motor designs.

• Magnetic field – basic information
• Gauss’s law and Ampère’s law in practice
• Magnetic field sources
• Magnetic field applications
  • Stepper motors
  • Induction motors
  • Other popular applications

Magnetic field – what is it and what are its properties?

Shortly speaking, a magnetic field is an area in space within which particles are affected by magnetic forces. A more accurate definition states that it is a specified condition of space within which magnetic forces affect moving electric charges and also bodies having the magnetic moment, regardless of their movement, and they affect them with a force referred to as the Lorentz force.

A magnetic field is closely related to an electric field, as both of them are a manifestation of an electromagnetic field. Therefore, depending on the reference system in which an observer is located, the same electromagnetic field phenomenon can be described as a manifestation of an electric field, a magnetic field or both at the same time.

A magnetic field is a vectorial field, which means that it has both a magnitude and a direction. The field direction is determined by the position of a magnetic needle or a circuit in which electric current flows. A magnetic field is described using two physical values, i.e. magnetic induction and current. The current flow inciting electric charge movement generates a constant magnetic field. On the other hand, charges moving alternately (decelerating or accelerating) create an alternating magnetic field propagated in a form of an electromagnetic wave. Generation of a magnetic field as a result of electric current flow and other electric charge movements is described by the Biot-Savart law and Ampère’s law, which, in their generalised form, are a part of the Maxwell’s equations.

A magnetic field can also be sourceless, which creates a situation totally different from the one in which it is generated within an electric field, where electrostatic field lines come out of positive charges and converge in negative charges. A sourceless magnetic field is described by the Gauss's law for magnetism, which states that magnetic field lines create closed curves, i.e. they do not start nor end in any specific point. See the following sections for more detail.

A magnetic field has several significant properties, two of which are key from the point of view of practical applications:

• magnetic forces affect the movement trajectories of charged particles, for example electrons in conductors;
• a magnetic field may induce electromotive force (SEM) in conductors. This phenomenon is referred to as electromagnetic induction and constitutes the basis for electric generator operation.

Gauss’s law and Ampère’s law – universal laws describing a magnetic field

The Gauss’s law, also known as Gauss’s law for an electric field or Gauss’s law for a magnetic field, is one of the fundamental electromagnetic laws which facilitate understanding and describing the behaviour of electric and magnetic fields in natural environments.

The Gauss’s law states that the flux of an electric or magnetic field “flowing” through an enclosed surface is directly proportional to the total enclosed electric charge or total electric current within this surface.

In the case of the Gauss’s law for an electric field, an electric field flux (indicated as ΦE) flowing through a closed surface is equal to the product of electric field intensity (E) and surface (A), i.e. ΦE = E * A, where electric field intensity is measured as the value of the strength of the electric field acting on a single charge.

In the case of the Gauss’s law for a magnetic field, a magnetic field flux (ΦB) flowing through a closed surface is equal to zero. It means that the total magnetic field flux flowing from a surface is equal to the total flux flowing to that surface. The mathematical notation is as follows: ΦB = 0. In principle, the analytically calculated Gauss’s law for the magnetic field itself is difficult to define, so it is more convenient to refer to the Ampère’s law mentioned below.

The Gauss’s law facilitates analysing electric and magnetic fields. It makes it possible to make simplified calculations for the determination of an electric or magnetic field. It facilitates the determination of the field intensity in points where an analysis performed using the Coulomb’s law or Biot-Savart law would be more complex.

Another law that is useful to describe a magnetic field was formulated by André-Marie Ampère. It expresses the following relationship between flowing current and a magnetic field induced by this current: a magnetic field inside an infinite rectilinear current-carrying conductor increases in proportion to the radius R as it passes from the conductor centre to its surface. In the form modified by Maxwell, it becomes one of the Maxwell’s equations, which are a fundamental pillar of electrodynamics.

Magnetic field sources

Generally, there can be two types of magnetic field sources: firstly, it is generated around magnets, and secondly – around moving electric charges. The former include, for example, such magnetic materials as ferromagnetic substances. In their case, the constant magnetic field is generated by superposition of orbital magnetic moments of electrons (by orbital movement of electrons with electric charges around a nucleus, in the quasi-classic Bohr’s model).

A magnetic field is also generated by an alternating electric field, the origin of which results from movement of electric charges, and it is an alternating magnetic field, but not a constant one. Interestingly, an alternating magnetic field generates an electric field, as mutual induction of fields in an electromagnetic wave occurs in this case. The above-mentioned constant magnetic field does not generate an electric field, which results directly from the Maxwell’s equations.

In principle, the most important magnetic field sources boil down to just a few elements.

1. Electric current: flowing electric current is one of the main sources of an electric field which forms around an electric conductor through which the current flows. The higher the current (intensity), the stronger the magnetic field generated. The direction of the magnetic field created around a conductor is determined by the right-hand rule, i.e. if the right hand embraces the conductor so that the thumb points in the current flow direction, the fingers align themselves along the direction of the actual magnetic field.
2. Permanent magnets (e.g. neodymium magnets with two poles (N and S). They generate a constant magnetic field. In such magnets, magnetic domains are ordered, which results in the generation of a strong magnetic field.
3. Alternating current flowing through conductors or coils generates an alternating magnetic field. It is used in transformers, alternating current generators and other electric devices.
4. Generally speaking, electromagnets expand on the previous point (alternating current), as they are components in which a magnetic field is generated by a coil through which electric current flows. Depending on the current magnitude, a coil can generate a weak or strong magnetic field, which can then be switched on and off, depending on the actual needs, which is a phenomenon used in various devices, e.g. motors or conductors.
5. Microwave and radio-frequency wave currents – we refer here to antennas supplied with high-frequency currents, which also generate magnetic fields. This property facilitates electromagnetic wave transmission and reception.

Magnetic field – practical applications

It is not a surprise that all the above-mentioned magnetic field sources are used in diverse applications. In practice, magnetic fields are widely applied in a variety of fields, e.g. in electronic engineering, electric engineering, medicine, transport, telecommunications, industry, etc.

Stepper motors

The main advantage of stepper motors is the possibility to precisely control the angle of rotation. By supplying a correct sequence of electric pulses to coils, such a motor can take very precise steps, which makes it a perfect solution for such applications as, for example, robot-assisted systems. Stepper motors are also characterised by high reliability and relatively simple design, which makes them a popular choice in numerous industries.

Stepper motors use a magnetic field to operate with such precision. The field is generated by electromagnets located on the stator and permanent magnets on the rotor. Two most basic types of stepper motors can be distinguished, i.e. single-magnet or dual-magnet motors.

Single-magnet stepper motors consist of one electromagnet on the stator (which generates the magnetic field) and a rotor with permanent magnets. The rotor looks like a disc with equally spaced magnets. After an electric pulse is applied to the electromagnet, a magnetic field is created which attracts the magnets located on the rotor. This causes the rotor to rotate by a specific step. When the pulse ends, the magnetic field is deactivated and the rotor stops in its new position.

Two-magnet stepper motors come with two electromagnets located on a stator. These electromagnets (phases) are supplied in sequence to generate necessary magnetic fields. The rotor includes permanent magnets located similarly to single-magnet motors. After the first phase is supplied, the rotor rotates by a single step. Next, the second phase is supplied to rotate the rotor by another step. This process is repeated for the motor to continue the stepped movement. Stepper motors are used in various fields where movement precision is crucial, for example, in robot-assisted systems, 3D printers, CNC drives, industrial automation systems and medical instruments.

Induction motors

Induction, i.e. asynchronous, motors are most commonly used electric motors. They employ a magnetic field to generate the rotor movement. As their name suggests, the electromagnetic induction is the main principle of induction motor operation, and it results from electric field alterations in a stator.

The induction motor design includes two key components – a stator and rotor. The stator consists of an iron package with coils placed above it. These coils create electromagnets which, in turn, generate a magnetic field. The rotor is made of a conductive material (e.g. copper) and placed inside the stator. The induction motor operation process starts with connecting it to a power supply source in order to supply stator coils with current. The current flow through coils generates an alternating magnetic field which is transferred to the rotor. This magnetic field induces current in inductive rotor components.

The electromagnetic induction phenomenon creates a magnetic field in the rotor, whose direction is opposite to the magnetic field generated by the stator. This field is dynamic, which generates electromagnetic forces resulting in rotor movement. As a result of the interaction between the stator magnetic field and rotor magnetic field, the rotor starts rotating. This movement is reliable and synchronised with the stator magnetic field, which results in generating torque, which in turn translates into the rotor rotational movement. Note also that the induction motor rotational speed is slightly lower than the speed of the magnetic field in the stator. This difference in speeds is referred to as “slip”. Slip is necessary to generate torque and ensure correct induction motor operation.

Induction motors offer numerous advantages. They are reliable, robust and high-performance designs. Additionally, the lack of physical connection with the rotor results in the fact that induction motors are brushless, which makes them maintenance-free, reduces friction and largely improves their failure rates. Therefore they are commonly used in industrial applications, i.e. water pumps, fans, compressors, conveyors, and also in the automotive sector.

Other common magnetic field applications

Stepper and induction motors are not the only examples of practical applications of magnetic field and its property. See the list below for a few major examples:

1. Electric energy transformation: a magnetic field is a key component of transformers used to alter the alternating current voltage. Current flowing through transformer coils generates a magnetic field which induces current in the second coil to facilitate voltage alteration.
2. MRI ( Magnetic Resonance Imaging): in medical applications, a magnetic field is used in MRI scanners to obtain images of human organs. First, strong MRI-generated magnetic fields interact with atoms in a patient's body. Next, detectors record such interactions to obtain detailed organ and tissue images.
3. Magnetic card readers: a magnetic field is used in magnetic (credit or ID) card readers. Such cards come with magnetic strips storing certain information, and readers use a magnetic field to read out the stored data.
4. Audio equipment: an electromagnetic field is used in speakers and microphones to convert electric signals into sound, and vice versa. Speakers use a magnetic field to drive the membrane movement to induce sound waves, and microphones use this field to convert changes in pressure into electric signals.
5. Electromagnets are very useful in numerous applications, for example, metallurgical industry, waste segregation, conveyor systems, magnetic support systems, valves or brakes. In such devices, a magnetic field is generated by current flowing through coils, which facilitates generating a controlled magnetic effect.
6. Wireless communication: magnetic fields are also used in wireless communication technologies, such as NFC (Near Field Communication) and RFID (Radio Frequency Identification). These technologies employ magnetic fields to transmit data and facilitate identification, for example, in payment or office administration systems.

Note here that radio-frequency waves are, in fact, electromagnetic waves within a certain frequency range, so it can be stated that the entire radio communication (from classic AM radio stations to Internet connectivity over Wi-Fi or satellite networks) is a certain form of electromagnetism. However, we will discuss this issue in detail in another text.

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