What is Electromagnetism?

Electromagnetism is the branch of physics that studies the interactions between electrically charged particles and their associated fields. These interactions are described in terms of electric and magnetic fields, which together form the electromagnetic force — one of the four fundamental forces of nature. 

In engineering electromagnetics, engineers are primarily concerned with the electromagnetic properties of components and how they relate to electromagnetic fields. In essence, engineers are concerned with:

• Studying the physics behind electrical systems and devices
• Establishing engineering analysis tools to reliably characterize these phenomena

Consequently, electromagnetics informs critical design considerations in such applications as electric circuits, magnetic circuits, integrated circuits, and semiconductor devices.

Maxwell’s publication of the Treatise on Electricity and Magnetism in 1873 showed that interactions between electrically charged particles were mediated by a single force, namely the electromagnetic force.

At the macroscopic scale, the following effects of this force can be observed:

• Like electric charges (positive or negative) repel each other while unlike electric charges attract, the magnitude of the electromagnetic force in each situation is inversely proportional to the square of the distance between the charges.
• Similarly, magnetic poles (north or south) attract or repel each other and always exist in pairs.
• An electric current propagating through a wire generates a circular magnetic field around the wire. The direction of the electric current determines the direction of the magnetic field, as seen in the image above.
• A conducting wire moving through a magnetic field generates an electric current that propagates through the wire. The direction of movement through the magnetic field determines the direction of travel of this current.

Characterizing Electromagnetic Interactions

The electromagnetic force constitutes the second strongest of the four fundamental forces of nature. It is largely responsible for interactions between atoms, molecules, and macroscopic objects. 

The electromagnetic force exerts its influence through the propagation of electric and magnetic waves that travel at right angles to each other, oscillating at specific frequencies. In a vacuum, these waves propagate at a constant speed, the speed of light in a vacuum — which is roughly equal to 3 x 108 m/s.

The speed of light in a vacuum c relates to the frequency v meters and wavelength λ Hz through a simple relationship as:

$$c = v\lambda $$

For many applications, electrical engineers do not need to delve into the study of electromagnetism. In many cases, electrostatics (the study of stationary electric charges) is sufficient. Equally, in other cases, magnetostatics (dealing with permanent magnets) is also sufficient.

Consequently, in pure electric or magnetic networks, even Maxwell’s equations may be dispensed with, yielding simpler treatments of networks. However, with the increasing electrification of devices at high frequencies and tighter packaging of devices that generate electromagnetic fields, electrodynamic considerations are increasingly important in product design.

Building on the work of physicists like Ampère, Coulomb, and Ørsted, Maxwell formulated a set of four equations, thereby expounding a unified theory of electromagnetics — something many scientists have called the "second great unification in physics,” in reference to Isaac Newton’s “great unification” of gravity.

The solution to Maxwell’s equations in free space (devoid of electric charges) results in wave equations describing electromagnetic waves that travel at the speed of light. This led Maxwell to suggest that light is, in fact, electromagnetic radiation, and that there exists a range of electromagnetic radiation differing only in their frequencies (or wavelengths).

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from low-frequency (radio waves) to high-frequency (gamma rays). Each type of radiation is characterized by its frequency and wavelength, which are inversely related. The spectrum includes:

Maxwell’s equations were verified when German physicist Heinrich Hertz proved the existence of electromagnetic radiation with his discovery of radio waves in the late 1880s.

Description of Electric and Magnetic Fields

In physics, fields describe interactions between energy and matter at specific points in space and time. Specifically, a vector field assigns an amplitude and direction to each of these points. An electric field surrounding a static electric charge is described by a vector field.

At each point, the vector’s amplitude describes the electric field’s strength, while its direction describes the direction of the field. By convention, the field points in the same direction as the force on positive charges, and in the opposite direction on negative charges.

Therefore, electric fields always flow away from positive charges and towards negative charges. The relationship between the force F exerted by a source charge (in newtons), a test charge q (in coulombs), and the electric field strength E (in volts per meter) is given by:

$$\overrightarrow{F} = q\overrightarrow{E}$$

A magnetic field surrounds a moving electric charge. This field affects other charges and magnets. The direction of the force on a moving charge in a magnetic field is perpendicular to both its direction of motion and the magnetic field lines.

In combination, electric and magnetic forces acting on a charged particle result in a Lorentz force — a force proportional to charge and electric field magnitude in the direction of the electric field E plus a force proportional to magnetic field magnitude, charge, and velocity in the direction at right angles to the particle velocity v and magnetic field B. Together with the Lorentz force law, Maxwell’s equations provide a complete classical description of electromagnetic interactions.

Maxwell's equations form the foundation of classical electromagnetism. These four equations, expressed in differential form, describe the behavior of electric and magnetic fields and their interactions with charges and currents:

Maxwell’s First Equation: Gauss’s Law

Gauss’s law (also known as Gauss’ flux theorem) relates the distribution of electric charges to the electric field. It states that the net electric flux through any closed surface (a Gaussian surface) is proportional to the net electric charge enclosed within that surface.

Therefore, where a surface does not enclose an electric charge, an electric flux does not exist. Consequently, where an electric charge is placed close to such a surface, electric fluxes into and away from the surface must cancel. 

Maxwell’s Second Equation: Gauss’s Law for Magnetism

Similarly to the first equation, Gauss’ law for magnetism describes the behavior of a magnetic flux through a closed surface. It states that this flux must always total zero. Therefore, if there is a magnetic field nearby, the magnetic flux into the surface must cancel the flux out of the surface.

Stated otherwise, magnetic monopoles cannot exist in the same way that electric monopoles (charges) exist. Therefore, positive and negative magnetic poles must always exist as dipoles (north and south).

Maxwell’s Third Equation: The Ampere-Maxwell Law

Ampère's law states that an electric current flowing through a wire generates a magnetic field. In a straight wire, the magnetic field curls around the wire, with the direction of flow indicated by the four fingers in the right-hand rule. In a coiled wire, the magnetic field points in a straight line indicated by the thumb in the right-hand rule.

Maxwell's extension to Ampère's law states that a time-varying electric field can also generate a varying magnetic field.

Maxwell’s Fourth Equation: The Maxwell-Faraday Equation

The Maxwell-Faraday equation describes how a time-varying magnetic field produces an electric field. It can also be derived from Faraday’s law and the Lorentz force law.

Under the influence of electric forces, static charged particles attract or repel each other. While moving, these particles also experience magnetic forces. Electromagnetic forces arise from the sum of these electric and magnetic interactions, exerting their influence through electromagnetic fields.

As it happens, the electromagnetic force regulates a range of interactions; for example, keeping negatively charged electrons bound to positively charged nuclei in atoms, also allowing the formation of molecules.

Relation to Electric Circuit Theory

In electric circuit theory, circuit designers abstract the behaviors of devices and systems such that they need not consider the underlying principles. For example, a resistor is simply a device that responds to a voltage V and a current I such that the resistance R is given by Ohm’s law:

$$R = \frac{V}{I}$$

In this “lumped-element” representation, there is no requirement to understand the nature of either the current (a conduction current) or voltage (an electrical potential). Many applications in electrical engineering lend themselves well to this lumped-element model.

But, equally, there are many instances when electromagnetic effects must be understood — for example, for signal integrity and electromagnetic compatibility. Therefore, in the case of the resistor, questions like the following may need to be answered:

• How can the resistor be designed to meet specific power-handling capabilities?
• How can practical resistors, which also exhibit reactance, be designed?
• How can capacitors, inductors, transformers, and other circuit components, which also exhibit resistance, be designed?

At low frequencies, electromagnetic wavelengths are large enough so as to have a negligible effect on circuits being designed, reducing these circuits to near-perfect DC circuits.

Once frequencies reach a few hundred megahertz and above, however, electromagnetic interactions become an important consideration. Antennas, for example, are, in effect, electromagnetic wave detectors.

Consequently, electromagnetic principles govern the designs of an array of modern devices, including motors, generators, antennas, waveguides, transformers, magnetic data storage devices, magnetic resonance imaging devices, and printed circuit boards, as well as technologies such as radar, fiber optics, photonics, and remote sensors.

Since ancient times, civilizations have attempted to explain natural phenomena — from the attraction they observed between pieces of iron ore and the static produced by rubbing materials to lightning.

However, it wasn’t until the 18th and 19th centuries that scientists such as Carl Friedrich Gauss, Michael Faraday, and Charles-Augustin de Coulomb began to formulate mathematical expressions to describe these phenomena.

Electricity and magnetism were long thought to be separate phenomena. However, in April 1820, the Danish physicist Hans Christian Ørsted observed that an electrical current running through a wire induced a deflection in a compass needle that was placed in the vicinity. He published his findings later that same year, showing that an electric current produces a circular magnetic field as it flows through a wire.

Ørsted’s discovery spurred intense investigation into the nature of electromagnetics, inspiring, for example, the work of André-Marie Ampère. This early step towards a unified electromagnetic theory was further extended when Faraday discovered, in 1831, that a magnetic field could induce an electric current — a process known as electromagnetic induction. He also established the concept of the electromagnetic field.

This unification process culminated in the 1860s with the Scottish physicist James Clerk Maxwell, who formulated his famous set of four partial differential equations, thereby providing a complete mathematical description of electromagnetic waves.

Maxwell further postulated the existence of self-sustaining electromagnetic waves, also suggesting that light represents one such wave.

In the modern era, Albert Einstein demonstrated with the Special Theory of Relativity (1905) how magnetism arises from electricity when charged particles are in motion. With the later advent of quantum mechanics, further modifications were applied to Maxwell’s equations to account for the quantized nature of matter. Thus, in quantum electrodynamics (QED), electromagnetic fields arise from discrete excitations of photons, which are quantized particles of light.

Basic electric circuit theory abstracts the behavior of devices and systems in such a way that engineers do not need to consider the underlying electromagnetic theory. In many instances, however, electrical engineers need to close the gap that exists between electric circuit theory and more general engineering applications.

Accordingly, the study of electromagnetics informs the design of devices such as conductors, capacitors, inductors, and semiconductors, as well as more complex integrated circuits, which enables the construction of electric vehicles, remote sensing devices, general instrumentation, electronics components, power equipment, and more.

Conductors

Conducting materials are materials that allow the free flow of electrons. Metals such as gold, silver, copper, and aluminum are effective conductors because they facilitate the decoupling of electrons from atomic nuclei.

In some materials, electrons remain bound to the nucleus but only require a small amount of energy to decouple. These materials are referred to as semiconductors, and this behavior is the underlying physics behind transistors that enable modern electronics.

Superconductors are materials that, when cooled below a critical temperature, exhibit zero electrical resistance and expel magnetic fields (Meissner effect). High-temperature superconductors, such as yttrium barium copper oxide (YBCO) compounds, can achieve superconductivity at temperatures above -140 °C, making them more practical for applications like MRI machines and maglev trains.

Insulators

Conversely, insulators are materials that inhibit the free flow of electrons. In insulating materials, electrons are tightly bound to atomic nuclei and do not easily decouple when an electric field is applied. As a result, insulators make perfect covers for conducting wires, enhancing safety.

Notably, some insulators may become polarized under the application of an electric field. As the field is applied, tiny displacements occur between charges to form positive and negative dipoles. These types of materials (known as dielectrics) are used in capacitors to increase their energy storage capacity.

Capacitors

Capacitors are electronic devices that store electrical energy in an electric field generated between two plates. Capacitance C measures a capacitor’s ability to store energy. It is proportional to the electrical permittivity   of free space, such that, for a plate area A:

$$C = \frac{\varepsilon_0A}{d}$$

A dielectric material multiplies permittivity, resulting in increased capacitance.

Inductors

Similarly, inductors are electronic devices that store energy within magnetic fields generated inside coiled wires. Following Ampère's law, a current flowing through a coiled wire generates a linear magnetic field. The energy stored is directly proportional to the current I, which is inversely proportional to the inductance L. The inductance measures a circuit’s resistance to change. Therefore, high inductance devices can be used to dampen alternating current circuits.

Semiconductors

Semiconductors are materials with electrical conductivity between that of conductors and insulators. Their conductivity can be controlled by introducing impurities (doping) or by applying external fields. This behavior forms the basis for transistors and other electronic components.

Semiconductor engineers can alter the conductivity of semiconductors by applying an electric or magnetic field, by varying exposure to heat or light, or by deforming a doped monocrystalline silicon grid.

Semiconductor devices are produced as standalone devices or integrated into circuits containing from two to hundreds of millions of devices, interconnected on a single wafer.

The two main types of semiconductors devices are:

• Diodes: Diodes are two-terminal devices that behave as one-directional switches for current, allowing current to flow easily in one direction only, in which case they are forward-biased. When reverse-biased, they behave as insulators. In photodiodes, exposure to light increases the number of free electrons, thereby increasing conductivity. Two-terminal devices include light-emitting diodes (LEDs), Gunn diodes, IMPATT diodes, laser diodes, tunnel diodes, photocells, and solar cells.
• Transistors: Transistors are three-terminal devices that amplify or switch electrical power. They constitute the building blocks of logic gates, acting as on-off switches in digital circuits. In contrast, in analog circuits (such as amplifiers and oscillators) they respond to continuous inputs, also supplying continuous outputs. In power integrated circuits (high current and voltage applications) they regulate the distribution of power. Metal-oxide-semiconductor field-effect transistors (MOSFETs) are, overwhelmingly, the most common type of transistor in existence. They rely on the application of an electric field to increase conductivity. Other transistor types include bipolar junction transistors (BJTs), junction field-effect transistors (JFETs), and insulated-gate bipolar transistors (IGBTs).

Wireless Power Transfer

Wireless power transfer (WPT) traces its origins to the late the 19th century, when Nikola Tesla showed that electric power could be transferred through air by generating a magnetic field between two coils — each termed a “transmitter” and “receiver”, respectively — in a phenomenon called magnetic resonant coupling.

The transmitter, when connected to a power source, generates a magnetic field, which in turn generates an electric current in the receiver.

WPT enables the wireless charging of personal, portable, and industrial devices, circumventing the need for cables, extending battery life, increasing convenience, and improving safety. The three common types of wireless charging are:

• Inductive charging: Working on the principle of electromagnetic induction, the device to be charged is placed near the charging station, but without the need for precise alignment.
• Resonant inductive coupling: More advanced than inductive charging, the transmitting and receiving coils are tuned to resonate at the same frequency, thereby improving the efficiency of power transfer.
• Radio frequency (RF) charging: In radio frequency charging, devices are fitted with receiving antennas that are tuned to pick up high frequency radio waves transmitting power. Although experimental, this technology enables the transfer of power over longer ranges.

Currently, consumer electronics represents the largest market for the adoption of wireless technology, driven by the proliferation of smartphones, tablets, and wearable devices. Consumer electronics are typically low power devices (<100 W). Consequently, inductive charging is the technology of choice.

A typical smartphone wireless charging setup operates as follows:

• A transmitter coil within a charging base (itself connected to an alternating power source) transmits a signal.
• Once this signal recognizes a receiver coil (fitted to a compatible smartphone), it triggers a flow of electrons within the transmitter, generating a time-varying electric current.
• This time-varying current generates a time-varying magnetic field, causing electrons to flow in the receiver coil (creating an induced alternating current).
• Within the smartphone device, a rectifier converts the alternating current to a direct current for storage in the battery.

Thus, power transfer is facilitated by a time-varying electromagnetic field between a transmitter and receiver coil. Inductive charging typically occurs at frequencies in the 110-205 KHz range.

As technology continues to advance, the study and application of electromagnetics remain crucial. From the development of quantum computing to the design of next-generation wireless networks, electromagnetic principles continue to shape our technological landscape. Understanding these principles is essential for engineers and scientists working at the forefront of innovation in fields such as telecommunications, energy systems, and medical technology.

Ansys SimAI software is a state-of-the-art multiphysics simulation software leveraging these advancements for electromagnetic field training and prediction. Together with Ansys Maxwell software and Ansys HFSS software, it transforms the design and analysis of electromagnetic components by reducing the field prediction time by tens to hundreds of times.

To learn more about SimAI software, watch the presentation “SimAI for Electromagnetics: Accelerating Electronics Components Design.”

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