ELECTROMAGNETISM

ELECTROMAGNETISM

Electromagnetism is one of the fundamental forces of nature. Early on, electricity and magnetism were studied separately and regarded as separate phenomena. Hans Christian Ørsted discovered that the two were related – electric currents give rise to magnetism. Michael Faraday discovered the converse, that magnetism could induce electric currents, and James Clerk Maxwell put the whole thing together in a unified theory of electromagnetism. Maxwell's equations further indicated that electromagnetic waves existed, and the experiments of Heinrich Hertz confirmed this, making radio possible. Maxwell also postulated, correctly, that light was a form of electromagnetic wave, thus making all of optics a branch of electromagnetism. Radio waves differ from light only in that the wavelength of the former is much longer than the latter. Albert Einstein showed that the magnetic field arises through the relativistic motion of the electric field and thus magnetism is merely a side effect of electricity. The modern theoretical treatment of electromagnetism is as a quantum field in quantum electrodynamics.

In many situations of interest to electrical engineering, it is not necessary to apply quantum theory to get correct results. Classical physics is still an accurate approximation in most situations involving macroscopic objects. With few exceptions, quantum theory is only necessary at the atomic scale and a simpler classical treatment can be applied. Further simplifications of treatment are possible in limited situations. Electrostatics deals only with stationary electric charges so magnetic fields do not arise and are not considered. Permanent magnets can be described without reference to electricity or electromagnetism. Circuit theory deals with electrical networks where the fields are largely confined around current carrying conductors. In such circuits, even Maxwell's equations can be dispensed with, and simpler formulations used. On the other hand, a quantum treatment of electromagnetism is important in chemistry. Chemical reactions and chemical bonding are the result of quantum mechanical interactions of electrons around atoms. Quantum considerations are also necessary to explain the behavior of many electronic devices, for instance the tunnel diode.

Electromagnetism is one of the fundamental forces of nature alongside gravity, the strong force and the weak force. Whereas gravity acts on all things that have mass, electromagnetism acts on all things that have electric charge. Furthermore, as there is the conservation of mass according to which mass cannot be created or destroyed, there is also the conservation of charge which means that the charge in a closed system (where no charges are leaving or entering) must remain constant. The fundamental law that describes the gravitational force on a massive object in classical physics is Newton's law of gravity. Analogously, Coulomb's law is the fundamental law that describes the force that charged objects exert on one another. It is given by the formula

${\displaystyle F=k_{e}{q_{1}q_{2} \over r^{2}}}$

where F is the force, K_e is the Coulomb constant, q₁ and q₂ are the magnitudes of the two charges, and r² is the square of the distance between them. It describes the fact that like charges repel one another whereas opposite charges attract one another and that the stronger the charges of the particles, the stronger the force they exert on one another. The law is also an inverse square law which means that as the distance between two particles is doubled, the force on them is reduced by a factor of four.

In physics, fields are entities that interact with matter and can be described mathematically by assigning a value to each point in space and time. Vector fields are fields which are assigned both a numerical value and a direction at each point in space and time. Electric charges produce a vector field called the electric field. The numerical value of the electric field, also called the electric field strength, determines the strength of the electric force that a charged particle will feel in the field and the direction of the field determines which direction the force will be in. By convention, the direction of the electric field is the same as the direction of the force on positive charges and opposite to the direction of the force on negative charges. Because positive charges are repelled by other positive charges and are attracted to negative charges, this means the electric fields point away from positive charges and towards negative charges. These properties of the electric field are encapsulated in the equation for the electric force on a charge written in terms of the electric field:

${\displaystyle F=qE}$

where F is the force on a charge q in an electric field E.

As well as producing an electric field, charged particles will produce a magnetic field when they are in a state of motion that will be felt by other charges that are in motion (as well as permanent magnets). The direction of the force on a moving charge from a magnetic field is perpendicular to both the direction of motion and the direction of the magnetic field lines and can be found using the right-hand rule. The strength of the force is given by the equation

${\displaystyle F=qvB\sin \theta }$

where F is the force on a charge q with speed v in a magnetic field B which is pointing in a direction of angle θ from the direction of motion of the charge.

The combination of the electric and magnetic forces on a charged particle is called the Lorentz force. Classical electromagnetism is fully described by the Lorentz force alongside a set of equations called Maxwell's equations. The first of these equations is known as Gauss's law. It describes the electric field produced by charged particles and by charge distributions. According to Gauss's law, the flux (or flow) of electric field through any closed surface is proportional to the amount of charge that is enclosed by that surface. This means that the greater the charge, the greater the electric field that is produced. It also has other important implications. For example, this law means that if there is no charge enclosed by the surface, then either there is no electric field at all or, if there is a charge near to but outside of the closed surface, the flow of electric field into the surface must exactly cancel with the flow out of the surface.^[11] The second of Maxwell's equations is known as Gauss's law for magnetism and, similarly to the first Gauss's law, it describes flux, but instead of electric flux, it describes magnetic flux. According to Gauss's law for magnetism, the flow of magnetic field through a closed surface is always zero. This means that if there is a magnetic field, the flow into the closed surface will always cancel out with the flow out of the closed surface. This law has also been called "no magnetic monopoles" because it means that any magnetic flux flowing out of a closed surface must flow back into it, meaning that positive and negative magnetic poles must come together as a magnetic dipole and can never be separated into magnetic monopoles. This is in contrast to electric charges which can exist as separate positive and negative charges.

The third of Maxwell's equations is called the Ampère–Maxwell law. It states that a magnetic field can be generated by an electric current. The direction of the magnetic field is given by Ampère's right-hand grip rule. If the wire is straight, then the magnetic field is curled around it like the gripped fingers in the right-hand rule. If the wire is wrapped into coils, then the magnetic field inside the coils points in a straight line like the outstretched thumb in the right-hand grip rule. When electric currents are used to produce a magnet in this way, it is called an electromagnet. Electromagnets often use a wire curled up into solenoid around an iron core which strengthens the magnetic field produced because the iron core becomes magnetized. Maxwell's extension to the law states that a time-varying electric field can also generate a magnetic field. Similarly, Faraday's law of induction states that a magnetic field can produce an electric current. For example, a magnet pushed in and out of a coil of wires can produce an electric current in the coils which is proportional to the strength of the magnet as well as the number of coils and the speed at which the magnet is inserted and extracted from the coils. This principle is essential for transformers which are used to transform currents from high voltage to low voltage, and vice versa. They are needed to convert high voltage mains electricity into low voltage electricity which can be safely used in homes. Maxwell's formulation of the law is given in the Maxwell–Faraday equation—the fourth and final of Maxwell's equations—which states that a time-varying magnetic field produces an electric field.

The electromagnetic spectrum

Together, Maxwell's equations provide a single uniform theory of the electric and magnetic fields and Maxwell's work in creating this theory has been called "the second great unification in physics" after the first great unification of Newton's law of universal gravitation. The solution to Maxwell's equations in free space (where there are no charges or currents) produces wave equations corresponding to electromagnetic waves (with both electric and magnetic components) travelling at the speed of light. The observation that these wave solutions had a wave speed exactly equal to the speed of light led Maxwell to hypothesize that light is a form of electromagnetic radiation and to posit that other electromagnetic radiation could exist with different wavelengths. The existence of electromagnetic radiation was proved by Heinrich Hertz in a series of experiments ranging from 1886 to 1889 in which he discovered the existence of radio waves. The full electromagnetic spectrum (in order of increasing frequency) consists of radio waves, microwaves, infrared radiation, visible light, ultraviolet light, X-rays and gamma rays.

The lab frame

The electron's rest frame

A further unification of electromagnetism came with Einstein's special theory of relativity. According to special relativity, observers moving at different speeds relative to one another occupy different observational frames of reference. If one observer is in motion relative to another observer, then they experience length contraction where unmoving objects appear closer together to the observer in motion than to the observer at rest. Therefore, if an electron is moving at the same speed as the current in a neutral wire, then they experience the flowing electrons in the wire as standing still relative to it and the positive charges as contracted together. In the lab frame, the electron is moving and so feels a magnetic force from the current in the wire but because the wire is neutral it feels no electric force. But in the electron's rest frame, the positive charges seem closer together compared to the flowing electrons and so the wire seems positively charged. Therefore, in the electron's rest frame it feels no magnetic force (because it is not moving in its own frame) but it does feel an electric force due to the positively charged wire. This result from relativity proves that magnetic fields are just electric fields in a different reference frame (and vice versa) and so the two are different manifestations of the same underlying electromagnetic field.

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