Electromagnetism Notes
Electromagnetism
Electromagnetism is the science of charge and the forces and fields associated with charge.
Electricity and magnetism are two aspects of electromagnetism, initially thought to be separate forces.
The interrelated nature of electricity and magnetism was established in the 19th century.
Albert Einstein's special theory of relativity (1905) confirmed they are aspects of a common phenomenon.
Electric and magnetic forces behave differently and are described by different equations.
Electric forces are produced by electric charges, whether at rest or in motion.
Magnetic forces are produced only by moving charges and act solely on charges in motion.
Electric phenomena occur even in neutral matter due to forces acting on charged constituents.
The electric force is responsible for most physical and chemical properties of atoms and molecules.
It is an enormously strong force compared to gravity.
Example: The absence of one electron per billion molecules in two 70-kg people 2 meters apart would create a repulsive force of 30,000 tons.
Electric phenomena include lightning and thunder.
Electric and magnetic forces are detected in electric and magnetic fields.
These fields are fundamental and can exist in space, independent of the charge or current that generated them.
Electric fields can produce magnetic fields and vice versa, without external charge.
Michael Faraday discovered that a changing magnetic field produces an electric field, forming the basis of electric power generation.
James Clerk Maxwell deduced that a changing electric field produces a magnetic field.
Maxwell's equations incorporated light and wave phenomena into electromagnetism.
Electric and magnetic fields travel together as electromagnetic radiation waves, mutually sustaining each other.
Examples of electromagnetic waves: radio waves, television waves, microwaves, infrared rays, visible light, ultraviolet light, X-rays, and gamma rays.
All electromagnetic waves travel at the speed of light (approximately 300,000 kilometers or 186,000 miles per second).
They differ only in the frequency of oscillation of their electric and magnetic fields.
Maxwell’s equations provide a complete description of electromagnetism, except at the subatomic scale.
Einstein's special relativity merged electric and magnetic fields into a single field and limited the velocity of matter to the speed of electromagnetic radiation.
Physicists discovered other forces (strong and weak) have fields with a similar mathematical structure to the electromagnetic field.
The weak and electromagnetic forces have been combined into the electroweak force.
A grand unified theory aims to unite all fundamental forces, including gravity.
Electricity studies the behavior of aggregates of charge, including charge distribution and motion within matter.
Materials are classified as conductors or insulators based on the ability of charges to move freely.
Electric current is the measure of the flow of charges.
Laws governing currents are important in technology, especially for energy production, distribution, and control.
Voltage measures the propensity of charge to flow from one place to another.
Positive charges tend to move from high to low voltage.
A common problem in electricity involves determining the relationship between voltage and current or charge.
Fundamentals of Electromagnetism
Electromagnetic phenomena pervade modern life.
Examples include lightbulbs, electric clocks, radio, television, and automobile starters.
These devices derive from fundamental laws of electromagnetism.
Coulomb's Law
Coulomb’s law describes the electric force between charged objects.
It is analogous to Newton’s law for gravitational force.
Both forces decrease with the square of the distance and act along a line between the objects.
In Coulomb’s law, the magnitude and sign of the electric force are determined by the charge of an object.
Charge determines how electromagnetism influences the motion of charged objects.
Every constituent of matter has an electric charge with a value that can be positive, negative, or zero.
Electrons are negatively charged, and atomic nuclei are positively charged.
Most bulk matter has an equal amount of positive and negative charge and thus has zero net charge.
The electric force for charges at rest:
Like charges repel each other, and unlike charges attract.
The attraction or repulsion acts along the line between the two charges.
The size of the force is inversely proportional to the square of the distance between the charges.
The size of the force is proportional to the value of each charge.
The unit of charge is the coulomb (C).
Example: Two positive charges, 0.1 C and 0.2 C, repel each other with a force proportional to 0.2
eq 0.1.If each charge is halved, the repulsion is reduced to one-quarter.
Static cling is a practical example of the Coulomb force.
Objects collect charge, especially in dry winter air.
Insulators hold charge; charge cannot easily move from one part to another.
Office copy machines use electric force to attract ink particles to paper.
Principle of Charge Conservation
The principle of charge conservation is a fundamental law of nature: the charge of an isolated system cannot change.
For every additional positively charged particle that appears within a system, a particle with a negative charge of the same magnitude will be created at the same time.
Pair production: a pair of oppositely charged particles is created when high-energy radiation interacts with matter (electron and positron).
The smallest subdivision of charge has a magnitude equal to the charge of one proton, which is +1.602
eq 10^{-19} coulomb.The electron has a charge of the same magnitude but opposite sign, which is -1.602
eq 10^{-19} coulomb.An ordinary flashlight battery delivers approximately 5,000 coulombs, which corresponds to more than 10^{22} electrons, before it is exhausted.
Electric current is a measure of the flow of charge.
The size of the current is measured in amperes (i).
One ampere represents the passage of one coulomb of charge per second, or 6.2
eq 10^{18} electrons per second.A current is positive in the direction of positive charge flow and opposite to the flow of negative charges.
Electric Fields and Forces
Electric and magnetic forces are caused by electromagnetic fields.
A field denotes a property of space with a numerical value at each point, varying with time.
The electric or magnetic field is a vector quantity (magnitude and direction).
The electric field at a point in space equals the force on a unit charge at that position.
Every charged object creates an electric field in the surrounding space.
A second charge feels the presence of this field and is attracted or repelled, depending on the signs of the charges.
The second charge also has an electric field, so the first charge feels its presence too.
The electric field from a charge is directed away from the charge when the charge is positive and toward the charge when it is negative.
In calculations, it is often more convenient to deal directly with the electric field than with the charges.
The distribution of charges in conductors is generally unknown because the charges move freely within the conductor.
In static situations, the electric field in a conductor in equilibrium is zero.
The unit of electric field is newtons per coulomb, or volts per meter.
The electric potential is an alternative to the electric field in electrostatics problems and is easier to use because it is a scalar.
The difference in potential between two places measures the degree to which charges are influenced to move from one place to another.
If the potential is the same at two places, charges will not be influenced to move.
Potential is measured in volts, equaling the electrostatic energy a unit charge would have at that position.
In a 12-volt car battery, the + terminal is at a potential 12 volts greater than the − terminal.
When a wire is connected between the + and − terminals, charges move through the wire as an electric current and heat the filament, which radiates light.
Magnetic Fields and Forces
The magnetic force influences only charges in motion.
It is transmitted by the magnetic field.
Magnetic fields and forces are more complicated than electric ones.
The magnetic field points in a perpendicular direction to the source.
The magnetic force acts perpendicular to the direction of the field.
The electric force and field point directly toward or away from the charge.
For a long straight wire, the magnetic field encircles the wire on a plane perpendicular to it.
The strength of the magnetic field decreases with distance from the wire.
Electric fields begin on positive charges and end on negative charges, while magnetic fields do not have beginnings or ends and close on themselves.
Complex magnetic fields can be generated by the proper choice of conductors to carry electric currents.
Thermonuclear fusion reactors confine plasmas with magnetic fields (“magnetic bottles”).
Charged particles are confined by magnetic fields in nature, like the Van Allen radiation belts around Earth.
Disturbance of Earth’s magnetic field produces the northern lights.
If a charge is at rest, there is no interaction with a magnetic field.
Interaction of a Magnetic Field with a Charge
If the charge moves, it is subjected to a force.
The size of the force is directly proportional to the velocity of the charge.
The force is perpendicular to the direction of motion and the direction of the magnetic field.
There are two possible opposite directions for the force, determined by the charge's polarity.
Positive and negative charges moving in the same magnetic field experience forces in opposite directions.
Depending on the initial orientation, charges in a uniform magnetic field will follow a circular or helical path.
Electric currents in wires are not the only source of magnetic fields.
Naturally occurring minerals exhibit magnetic properties due to electron motion and the magnetic dipole moment.
In most materials, fields are not observed due to the random orientation of atoms.
In some materials, atoms align in one direction, creating a magnet.
Magnets have numerous applications, including toys, paper holders, and components in electric generators.
Ferromagnetic materials amplify magnetic fields.
Electric and magnetic effects are closely coupled when there are rapid time fluctuations.
Faraday’s law of induction states that a time-varying magnetic field produces an electric field.
Practical applications include the electric generator and transformer.
In a generator, physical motion of a magnetic field produces electricity.
In a transformer, electric power is converted from one voltage level to another.
Electromagnetic waves depend on the interaction between electric and magnetic fields.
Maxwell postulated that a time-varying electric field produces a magnetic field.
Radio waves are generated by oscillating currents in antennas.
Many electromagnetic devices can be described by circuits.
Circuits may operate with a steady or time-varying current.
Elements in circuits include electromotive forces, resistors, capacitors, and inductors.
Circuits can be described with algebra.
Two mathematical quantities associated with vector fields are the flux of a field through a surface and the line integral of the field along a path.
The flux of a field measures how much of the field penetrates through the surface.
The line integral of a field measures the degree to which the field is aligned with the path.
The fluxes of E (electric field) and B (magnetic field) and the line integrals of these fields play an important role in electromagnetic theory.
Examples
The flux of E through a closed surface measures the amount of charge contained within the surface.
The flux of B through a closed surface is always zero because there are no magnetic monopoles.
Effects of Varying Magnetic Fields
The merger of electricity and magnetism into electromagnetism is tied to three events:
(1) Ørsted’s discovery that electric currents produce magnetic fields
(2) Faraday’s proof that a changing magnetic field can induce a current
(3) Maxwell’s prediction that a changing electric field has an associated magnetic field.
These landmarks led to advances in electric power and radio communications.
Faraday’s discovery of magnetic induction is a milestone.
(1) A changing magnetic field in a circuit induces an electromotive force in the circuit.
(2) The magnitude of the electromotive force equals the rate at which the flux of the magnetic field through the circuit changes.
The electromotive force is measured in volts and is represented by the equation:
E = -\frac{d\Phi}{dt}
Where Φ is the flux of the vector field B through the circuit.
Analogy for flux: imagine water from rain passing through a ring of area A.
The flux of the magnetic field through a small area dA is given by B \cdot dA.
For a circuit consisting of a single turn of wire, adding the contributions from the entire surface surrounded by the wire gives the magnetic flux Φ.
The rate of change of this flux is the induced electromotive force.
The units of magnetic flux are webers, with one weber equaling one tesla per square metre.
The minus sign indicates the direction of the induced electromotive force.
Lenz’s law: “what happens is that which opposes any change in the system.”
Faraday’s law is valid regardless of the process that causes the magnetic flux to change.
A magnet may be moved closer to a circuit, or vice versa.
The circuit may change in size in a fixed external magnetic field, or the circuit may be a coil rotating in a magnetic field.
The magnetic flux Φ through a circuit has to be considered carefully in the application of Faraday’s law.
If a circuit consists of a coil with five closely spaced turns and if ϕ is the magnetic flux through a single turn, then the value of Φ for the five-turn circuit that must be used in Faraday’s law is Φ=5ϕ.
If the five turns are not the same size and closely spaced, determining Φ can be quite complex.
Self-Inductance and Mutual Inductance
The self-inductance of a circuit describes the reaction of the circuit to a changing current, while the mutual inductance describes the reaction to a changing current in a second circuit.
When a current i1 flows in circuit 1, i1 produces a magnetic field B1; the magnetic flux through circuit 1 due to current i1 is Φ11.
The self-inductance L1 of the circuit is defined by the equation:
L1 = \frac{\Phi{11}}{i_1}
The units of inductance are henrys.
If a second circuit is present, some of the field B1 will pass through circuit 2, and there will be a magnetic flux Φ21 in circuit 2 due to the current i1.
The mutual inductance M21 is given by:
M{21} = \frac{\Phi{21}}{i_1}
The magnetic flux in circuit 1 due to a current in circuit 2 is given by Φ{12} = M{12}i_2.
An important property of the mutual inductance is that M{21} = M{12}.
Therefore, it is sufficient to use the label M without subscripts for the mutual inductance of two circuits.
The value of the mutual inductance of two circuits can range from \sqrt{L1L2} to −\sqrt{L1L2}, depending on the flux linkage between the circuits.
If the two circuits are very far apart, the mutual inductance is zero.
If the rate of change with respect to time is taken for the terms on both sides of the equation L1 = \frac{\Phi{11}}{i1}, the result is \frac{d\Phi{11}}{dt} = L1\frac{di1}{dt}.
According to Faraday’s law, \frac{d\Phi_{11}}{dt} is the negative of the induced electromotive force.
The result is the equation frequently used for a single inductor in an AC circuit—i.e.,
E = -L1\frac{di1}{dt}
The phenomenon of self-induction was first recognized by Joseph Henry.
While a steady current is flowing in a coil, the energy in the magnetic field is given by \frac{1}{2}Li^2.
If the current is interrupted, a large potential difference is developed.
Due to advances in superconducting wires, it is possible to store electric energy as energy in the magnetic field.
Eddy currents are induced in the object to be heated by surrounding a relatively nonconducting vacuum enclosure with a coil carrying a high-frequency alternating current.
AC Transformer
A transformer is an example of a device that uses circuits with maximum mutual induction.
Coils of insulated conducting wire are wound around a ring of iron constructed of thin isolated laminations or sheets.
The laminations minimize eddy currents in the iron.
Eddy currents are oscillatory currents induced in the metal by the changing magnetic field.
Energy loss in a transformer can be reduced by using thinner laminations, very “soft” (low-carbon) iron and wire with a larger cross section, or by winding the primary and secondary circuits with conductors that have very low resistance.
Transformers used to transmit and distribute power are commonly 98 to 99 percent efficient.
In a transformer, the iron ensures that nearly all the lines of B passing through one circuit also pass through the second circuit and that, essentially all the magnetic flux is confined to the iron.
Each turn of the conducting coils has the same magnetic flux; thus, the total flux for each coil is proportional to the number of turns in the coil.
As a result, if a source of sinusoidally varying electromotive force is connected to one coil, the electromotive force in the second coil is given by:
V2 = \frac{N2}{N1}V1
Thus, depending on the ratio of N2 to N1 (where N1 and N2 are the number of turns in the first and second coils, respectively), the transformer can be either a step-up or a step-down device for alternating voltages.
Step-up transformers are used to obtain high voltages before electric power is transmitted to minimize energy lost by resistive heating of the conductors.
Faraday’s law constitutes the basis for the power industry and for the transformation of mechanical energy into electric energy.
Faraday’s earlier work, in which a wire carrying a current rotated around a magnetized needle and a magnetic needle was made to rotate around a wire carrying an electric current, provided the groundwork for the development of the electric motor.
Effects of Varying Electric Fields
Maxwell’s prediction that a changing electric field generates a magnetic field was a masterstroke of pure theory.
The Maxwell equations for the electromagnetic field unified all that was hitherto known about electricity and magnetism; the existence of an electromagnetic phenomenon can travel as waves with the velocity of \frac{1}{\sqrt{\epsilon0\mu0}} in a vacuum, which corresponds to the speed of light.
Einstein’s special relativity theory postulated that the value of the speed of light is independent of the motion of the source of the light., the speed of light serves as the new standard for length.
In 1983 it was defined to be exactly 299,792,458 metres per second.
Together with the cesium clock, which has been used to define the second, the speed of light serves as the new standard for length.
The circuit in is an example of a magnetic field generated by a changing electric field.
A capacitor with parallel plates is charged at a constant rate by a steady current flowing through the leads.
The objective is to apply Ampère’s circuital law for magnetic fields to the path P, which goes around the wire.
Ampère’s law states that the integral \oint B \cdot dl along a closed path surrounding the current i is equal to μ_0i.
(An integral is essentially a sum, and, in this case,\oint B \cdot dl the integral ∮B⋅dl is the sum of B cos θdl taken for a small length of the path until the complete loop is included. At each segment of the path dl, θ is the angle between the field B and dl. )
The current i in Ampère’s law is the total flux of the current density J through any surface surrounded by the closed path.
Maxwell’s resolution of this dilemma was his conclusion that there must be some other kind of current density, called the displacement current Jd, for which the total flux through the surface S2 would be the same as the current i through the surface S1.
The dilemma is that the value of the integral \oint B \cdot dl for the path P cannot be both μ_0i and zero.
Maxwell’s resolution of this dilemma was his conclusion that there must be some other kind of current density, called the displacement current J_d, for which the total flux through the surface S2 would be the same as the current i through the surface S1.
Maxwell decided that the new type of current density was associated with the changing of the electric field; Maxwell found that Jd is as follows:
J_d = \frac{dD}{dt}
Where D = \epsilon_0 E , and E is the electric field between the plates.
In situations where matter is present, the field D in equation (6) is modified to include polarization effects; the result is D = \epsilon_0 E + P.
The field D is measured in coulombs per square metre.
Adding the displacement current to Ampère’s law represented Maxwell’s prediction that a changing electric field also could be a source of the magnetic field B.
Heinrich Hertz initiated the era of radio communications in 1887 by generating and detecting electromagnetic waves.
Maxwell’s Equations
Using vector calculus notation, the four equations of Maxwell’s theory of electromagnetism are:
Gauss’s law for electricity:
\nabla \cdot D = \rho
Gauss’s law for magnetism:
\nabla \cdot B = 0
Faraday’s law of induction:
\nabla \times E = -\frac{\partial B}{\partial t}
Ampère-Maxwell’s law:
\nabla \times H = J + \frac{\partial D}{\partial t}
Where D = \epsilon0 E + P , and H = B/μ0 − M.
The first equation is based on Coulomb’s inverse square law for the force between two charges;
It is a form of Gauss’s law, which relates the flux of the electric field through a closed surface to the total charge enclosed by the surface.
The second equation is based on the fact that apparently no magnetic monopoles exist in nature;
If they did, they would be point sources of magnetic field.
The third is a statement of Faraday’s law of magnetic induction, which reveals that a changing magnetic field generates an electric field.
The fourth is Ampère’s law as extended by Maxwell to include the displacement current discussed above;
It associates a magnetic field to a changing electric field as well as to an electric current.
Maxwell’s formulas provide a full description of the classical theory of electromagnetism.
His revelation that light is an electromagnetic wave meant that optics could be understood as part of electromagnetism.
It is only in microscopic situations that it is necessary to modify Maxwell’s formulas to include quantum effects.
That modification, known as quantum electrodynamics (QED), accounts for certain atomic properties to a degree of precision exceeding one part in 100 million.
Sometimes it is necessary to shield apparatus from external electromagnetic fields.
For a static electric field, this is a simple matter; the apparatus is surrounded by a shield made of a good conductor (e.g., copper).
Shielding apparatus from a steady magnetic field is more difficult because materials with infinite magnetic permeability μ do not exist; for example, a hollow shield made of soft iron will reduce the magnetic field inside to a considerable extent but not completely.
It is sometimes possible to superpose a field in the opposite direction to produce a very low field region and then to use additional material with a high μ for shielding.
In the case of electromagnetic waves, the penetration of the waves in matter varies, depending on the frequency of the radiation and the electric conductivity of the medium.
The skin depth δ (which is the distance in the conducting medium traversed for an amplitude decrease of 1/e, about 1/3) is given by:
\delta = \sqrt{\frac{2}{\omega \mu \sigma }}
At high frequency, the skin depth is small.
A metal shield can have some holes in it and still be effective.
For instance, a typical microwave oven has a frequency of 2.5 gigahertz, which corresponds to a wavelength of about 12 centimetres for the electromagnetic wave inside the oven.
The metal shield on the door has small holes about two millimetres in diameter; the shield works because the wavelength of the microwave radiation is much greater than the size of the holes.
Historical Survey
Electric and magnetic forces have been known since antiquity, but they were regarded as separate phenomena for centuries.
Magnetism was studied experimentally at least as early as the 13th century; the properties of the magnetic compass undoubtedly aroused interest in the phenomenon.
Systematic investigations of electricity were delayed until the invention of practical devices for producing electric charge and currents.
As soon as inexpensive, easy-to-use sources of electricity became available, scientists produced a wealth of experimental data and theoretical insights.
As technology advanced, they studied, in turn, magnetism and electrostatics, electric currents and conduction, electrochemistry, magnetic and electric induction, the interrelationship between electricity and magnetism, and finally the fundamental nature of electric charge.
Early Observations and Applications
The ancient Greeks knew about the attractive force of both magnetite and rubbed amber.
Magnetite, a magnetic oxide of iron mentioned in Greek texts as early as 800 bce, was mined in the province of Magnesia in Thessaly.
Thales of Miletus, who lived nearby, may have been the first Greek to study magnetic forces. He apparently knew that magnetite attracts iron and that rubbing amber (a fossil tree resin that the Greeks called ēlektron) would make it attract such lightweight objects as feathers.
The oldest practical application of magnetism was the magnetic compass, but its origin remains unknown.
Some historians believe it was used in China as far back as the 26th century bce; others contend that it was invented by the Italians or Arabs and introduced to the Chinese during the 13th century ce.
The earliest extant European reference is by Alexander Neckam (died 1217) of England.
The first experiments with magnetism are attributed to Peter Peregrinus of Maricourt, a French Crusader and engineer.
Emergence of the Modern Sciences of Electricity and Magnetism
The founder of the modern sciences of electricity and magnetism was William Gilbert, physician to both Elizabeth I and James I of England.
Gilbert spent 17 years experimenting with magnetism and, to a lesser extent, electricity.
He assembled the results of his experiments and all of the available knowledge on magnetism in the treatise De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (“On the Magnet, Magnetic Bodies, and the Great Magnet of the Earth”), published in 1600.
As suggested by the title, Gilbert described Earth as a huge magnet.
He introduced the term electric for the force between two objects charged by friction and showed that frictional electricity occurs in many common materials.
He also noted one of the primary distinctions between magnetism and electricity: the force between magnetic objects tends to align the objects relative to each other and is affected only slightly by most intervening objects, while the force between electrified objects is primarily a force of attraction or repulsion between the objects and is grossly affected by intervening matter.
Gilbert attributed the electrification of a body by friction to the removal of a fluid, or “humour,” which then left an “effluvium,” or atmosphere, around the body.
Pioneering Efforts
During the 17th and early 18th centuries, as better sources of charge were developed, the study of electric effects became increasingly popular.
The first machine to generate an electric spark was built in 1663 by Otto von Guericke, a German physicist and engineer.
Guericke’s electric generator consisted of a sulfur globe mounted on an iron shaft. The globe could be turned with one hand and rubbed with the other. Electrified by friction, the sphere alternately attracted and repulsed light objects from the floor.
Stephen Gray, a British chemist, is credited with discovering that electricity can flow (1729).
He found that corks stuck in the ends of glass tubes become electrified when the tubes are rubbed.
He also transmitted electricity approximately 150 metres through a hemp thread supported by silk cords and, in another demonstration, sent electricity even farther through metal wire.
Gray concluded that electricity flowed everywhere.
From the mid-18th through the early 19th centuries, scientists believed that electricity was composed of fluid.
In 1733 Charles François de Cisternay DuFay, a French chemist, announced that electricity consisted of two fluids: “vitreous” (from the Latin for “glass”), or positive, electricity; and “resinous,” or negative, electricity.
In 1745 a cheap and convenient source of electric sparks was invented by Pieter van Musschenbroek, a physicist and mathematician in Leiden, Netherlands.
Later called the Leyden jar, it was the first device that could store large amounts of electric charge.
(E. Georg von Kleist, a German cleric, independently developed the idea for such a device but did not investigate it as thoroughly as Musschenbroek did.)
Revolutionized the Study of Electrostatics
Soon “electricians” were earning their living all over Europe demonstrating electricity with Leyden jars.
Typically, they killed birds and animals with electric shock or sent charges through wires over rivers and lakes.
In 1746 the abbé Jean-Antoine Nollet, a physicist who popularized science in France, discharged a Leyden jar in front of King Louis XV by sending current through a chain of 180 Royal Guards.
In another demonstration, Nollet used wire made of iron to connect a row of Carthusian monks more than a kilometre long; when a Leyden jar was discharged, the white-robed monks reportedly leapt simultaneously into the air.
In America, Benjamin Franklin sold his printing house, newspaper, and almanac to spend his time conducting electricity experiments.
In 1752 Franklin proved that lightning was an example of electric conduction by flying a silk kite during a thunderstorm.
He collected electric charge from a cloud by means of wet twine attached to a key and thence to a Leyden jar.
He then used the accumulated charge from the lightning to perform electric experiments.
Franklin enunciated the law now known as the conservation of charge (the net sum of the charges within an isolated region is always constant).
He argued that electricity consisted of two states of one fluid, which is present in everything.
A substance containing an unusually large amount of the fluid would be “plus,” or positively charged.
Matter with less than a normal amount of fluid would be “minus,” or negatively charged.
Franklin’s one-fluid theory, which dominated the study of electricity for 100 years, is essentially correct because most currents are the result of moving electrons.
Apparatus Design
Joseph Priestley, an English physicist, summarized all available data on electricity in his book History and Present State of Electricity (1767).
He repeated one of Franklin’s experiments, in which the latter had dropped small corks into a highly electrified metal container and found that they were neither attracted nor repelled.
The lack of any charge on the inside of the container caused Priestley to recall Newton’s law that there is no gravitational force on the inside of a hollow sphere.
From this, Priestley inferred that the law of force between electric charges must be the same as the law for gravitational force—i.e., that the force between masses diminishes with the inverse square of the distance between the masses.
Their mathematics was clarified and developed extensively between 1767 and the mid-19th century as electricity and magnetism became precise, quantitative sciences.
Charles-Augustin de Coulomb established electricity as a mathematical science during the latter half of the 18th century.
He transformed Priestley’s descriptive observations into the basic quantitative laws of electrostatics and magnetostatics.
He also developed the mathematical theory of electric force and invented the torsion balance that was to be used in electricity experiments for the next 100 years.
Coulomb used the balance to measure the force between magnetic poles and between electric charges at varying distances.
Mathematicians like Siméon-Denis Poisson of France and Carl Friedrich Gauss of Germany extended Coulomb’s work during the 18th and early 19th centuries.
Poisson’s equation (published in 1813) and the law of charge conservation contain in two lines virtually all the laws of electrostatics.
The theory of magnetostatics, which is the study of steady-state magnetic fields, also was developed from Coulomb’s law.
Michael Faraday
Faraday built upon Priestley’s work and conducted an experiment that verified quite accurately the inverse square law.
Faraday’s experiment involving the use of a metal ice pail and a gold-leaf electroscope was the first precise quantitative experiment on electric charge.
Foundations of Electrochemistry and electrodynamics
The invention of the battery in 1800 made possible for the first time major advances in the theories of electric current and electrochemistry.
Both science and technology developed rapidly as a direct result, leading some to call the 19th century the age of electricity.
The development of the battery was the accidental result of biological experiments conducted by Luigi Galvani.
Galvani, a professor of anatomy at the Bologna Academy of Science, was interested in electricity in fish and other animals.
Galvani´s observations, published in 1791, aroused considerable controversy and speculation.
Alessandro Volta, a physicist at the nearby University of Pavia, had been studying how electricity stimulates the senses of touch, taste, and sight.
Within six weeks of Volta’s report, two English scientists, William Nicholson and Anthony Carlisle, used a chemical battery to discover electrolysis (the process in which an electric current produces a chemical reaction) and initiate the science of electrochemistry.
Experimental and theoretical studies of electromagnetic phenomena
A French physicist, François Arago, observed in 1820 that an electric current will orient unmagnetized iron filings in a circle around the wire.
That same year, another French physicist, André-Marie Ampère, developed Ørsted’s observations in quantitative terms.
By the end of the
Electromagnetism studies charge, forces, and fields, uniting electricity and magnetism (confirmed by Einstein). Electric forces act on all charges; magnetic forces act only on moving charges.
Electric forces dictate atom/molecule properties and vastly outweigh gravity. Electric/magnetic fields can exist independently and interconvert; changing magnetic fields produce electric fields (Faraday), and vice versa (Maxwell).
Electromagnetic waves (radio, light, etc.) travel at light speed, differing in frequency. Maxwell’s equations describe electromagnetism (except subatomically).
Special relativity merges electric/magnetic fields and limits matter velocity to light speed. Other forces have similar field structures; electroweak and grand unified theories aim to unite them.
Electricity studies charge behavior, classifying materials as conductors/insulators. Electric current measures charge flow related to voltage, which indicates charge flow propensity.
Fundamentals of Electromagnetism
Electromagnetic devices pervade modern life, based on electromagnetism's fundamental laws.
Coulomb's Law
Coulomb’s law: electric force between charged objects, similar to Newton’s gravity law, depends on charge magnitude/sign.
Matter's constituents have positive, negative, or zero charge. Like charges repel; opposites attract, force size is proportional to charge and inversely proportional to distance squared. Charge unit: coulomb (C).
Static cling and copiers exemplify Coulomb force.
Principle of Charge Conservation
Charge of an isolated system remains constant. Pair production creates oppositely charged particles. Smallest charge subdivision equals one proton's charge (+1.602 \times 10^{-19} C).
Electric current measures charge flow in amperes (C/s), positive with positive charge flow.
Electric Fields and Forces
Electromagnetic fields cause electric/magnetic forces. Electric field: force on unit charge. Charges create electric fields, attracting or repelling other charges.
Electric field direction: away from positive charges, toward negative. Conductors in equilibrium have zero electric field in static situations. Electric field unit: N/C or V/m.
Electric potential (in volts) influences charge movement between places.
Magnetic Fields and Forces
Magnetic force acts only on moving charges, transmitted by magnetic field perpendicular to source/force direction.
Magnetic fields encircle long straight wires, decreasing in strength with distance. They don't have beginnings/ends and close on themselves.
Magnetic fields confine plasmas (thermonuclear fusion reactors, Van Allen belts). Disturbances cause northern lights. No interaction if charge is at rest.
Interaction of a Magnetic Field with a Charge
Moving charge experiences force proportional to velocity, perpendicular to motion/field. Force direction depends on charge polarity. Charges follow circular/helical paths in uniform magnetic fields.
Minerals exhibit magnetic properties. Ferromagnetic materials amplify magnetic fields. Time-varying magnetic fields produce electric fields (Faraday’s law); applications include generators/transformers.
Time-varying electric fields produce magnetic fields (Maxwell). Radio waves are generated by oscillating currents. Circuits describe many electromagnetic devices.
Flux and line integrals play a key role in electromagnetic theory.
Examples
Electric field flux measures charge within a surface; magnetic field flux is always zero.
Effects of Varying Magnetic Fields
Electromagnetism merges electricity/magnetism via Ørsted,Faraday, and Maxwell's discoveries, leading to electric power/radio communications.
Faraday’s law: changing magnetic field induces electromotive force (E) in circuit, quantified by E = -\frac{d\Phi}{dt}, where Φ is magnetic flux.
Lenz’s law: induced effect opposes change. Faraday’s law applies regardless of magnetic flux change process. For coils, Φ=nϕ (n = number of turns).
Self-Inductance and Mutual Inductance
Self-inductance reacts to changing current in a circuit; mutual inductance reacts to changing current in a second circuit.
Self-inductance L1 = \frac{\Phi{11}}{i1}. Mutual inductance M{21} = \frac{\Phi{21}}{i1}. Units are henrys.
M{21} = M{12} = M. Induced electromotive force: E = -L1\frac{di1}{dt}. Magnetic field energy: \frac{1}{2}Li^2. Eddy currents are induced for heating.
AC Transformer
Transformers use maximum mutual induction. Thin laminations minimize eddy currents. Efficiency: 98-99%.
V2 = \frac{N2}{N1}V1. Transformers step-up/step-down voltages. Step-up transformers minimize transmission energy loss. Faraday’s law powers industry and electric motor development.
Effects of Varying Electric Fields
Maxwell predicted changing electric fields generate magnetic fields. Maxwell's equations unify electromagnetism; electromagnetic waves travel at light speed (\frac{1}{\sqrt{\epsilon0\mu0}}).
Speed of light (exactly 299,792,458 m/s) is the standard for length. Displacement current Jd = \frac{dD}{dt}, where D = \epsilon0 E . Adding displacement current to Ampère’s law shows changing electric fields also create magnetic fields. Heinrich Hertz initiated radio communications in 1887.
Maxwell’s Equations
Maxwell’s equations:
Gauss’s law for electricity: \nabla \cdot D = \rho
Gauss’s law for magnetism: \nabla \cdot B = 0
Faraday’s law of induction: \nabla \times E = -\frac{\partial B}{\partial t}
Ampère-Maxwell’s law: \nabla \times H = J + \frac{\partial D}{\partial t}
Where D = \epsilon0 E + P and H = B/\mu0 − M.
They describe classical electromagnetism, unifying optics. Quantum electrodynamics (QED) modifies them microscopically. Shielding requires conductors for electric fields. Magnetic field shielding is harder. Skin depth: \delta = \sqrt{\frac{2}{\omega \mu \sigma }}. Metal shields with small holes work if wavelength >> hole size.
Historical Survey
Electric/magnetic forces were long considered separate until the 19th century.
Early Observations and Applications
Greeks knew about magnetite/rubbed amber attraction. Magnetic compass origin is debated (China, Italy, Arabs?). Peter Peregrinus did early magnetism experiments.
Emergence of the Modern Sciences of Electricity and Magnetism
William Gilbert founded modern electricity/magnetism science, described Earth as a magnet, and introduced 'electric' force.
Pioneering Efforts
Otto von Guericke built the first electric spark generator (1663). Stephen Gray discovered electricity flow (1729).
Electricity was thought to be fluid. Charles François de Cisternay DuFay identified two fluids: vitreous (+) and resinous (-).
Pieter van Musschenbroek invented the Leyden jar (1745) for charge storage.
Revolutionized the Study of Electrostatics
Electricians demonstrated with Leyden jars. Benjamin Franklin proved lightning was electric, advanced conservation of charge, and proposed one-fluid theory.
Apparatus Design
Joseph Priestley inferred inverse square law for electric charges. Coulomb established electricity as a mathematical science, inventing the torsion balance.
Poisson/Gauss extended Coulomb’s work. Faraday verified inverse square law precisely.
Foundations of Electrochemistry and Electrodynamics
Battery invention (1800) advanced electric current/electrochemistry theories. Luigi Galvani's biological experiments led
Electromagnetism is the study of charge, forces, and fields associated with charge. Electricity and magnetism, initially considered separate, are now understood as interrelated aspects of electromagnetism, a concept solidified by Einstein's special theory of relativity. Electric forces are produced by all electric charges, regardless of motion, while magnetic forces are produced only by moving charges, acting solely on other moving charges. Electric phenomena, significantly stronger than gravity, influence the physical and chemical properties of atoms and molecules. These forces are detected via electric and magnetic fields, which can exist independently and can induce each other; a changing magnetic field produces an electric field (Faraday's discovery), and a changing electric field produces a magnetic field (Maxwell's deduction). These fields travel together as electromagnetic waves at the speed of light, differing only in frequency. Maxwell’s equations comprehensively describe electromagnetism, except at the subatomic level. Special relativity combines electric and magnetic fields and limits the velocity of matter to the speed of light. Physicists have discovered other forces with similar field structures, leading to electroweak and grand unified theories.
Fundamentals of Electromagnetism: Electromagnetic phenomena are integral to modern life and are based on electromagnetism's fundamental laws. For example, devices such as electric clocks, radio, and television derive from these fundamental laws.
Coulomb's Law: Coulomb’s law describes the electric force between charged objects, analogous to Newton’s law for gravitational force. In Coulomb’s law, the magnitude and sign of the electric force are determined by the charge of an object. Every constituent of matter has an electric charge with a value that can be positive, negative, or zero. Like charges repel each other, and unlike charges attract. The attraction or repulsion acts along the line between the two charges. The size of the force is inversely proportional to the square of the distance between the charges. The size of the force is proportional to the value of each charge. Static cling and office copy machines are practical examples.
Principle of Charge Conservation: The principle of charge conservation is a fundamental law of nature, stating that the charge of an isolated system cannot change. Pair production involves the creation of oppositely charged particles. Electric current measures charge flow in amperes.
Electric Fields and Forces: Electric and magnetic forces are caused by electromagnetic fields. The electric field at a point in space equals the force on a unit charge at that position. Charges create electric fields, attracting or repelling other charges. In static situations, the electric field in a conductor in equilibrium is zero. The electric potential influences charge movement between places.
Magnetic Fields and Forces: Magnetic force acts only on moving charges, transmitted by magnetic field perpendicular to source/force direction. Charged particles are confined by magnetic fields in nature, like the Van Allen radiation belts around Earth. No interaction if charge is at rest.
Interaction of a Magnetic Field with a Charge: Moving charge experiences force proportional to velocity, perpendicular to motion and field. Electric and magnetic effects are closely coupled when there are rapid time fluctuations. Faraday’s law of induction states that a time-varying magnetic field produces an electric field; applications include generators/transformers. Maxwell postulated that a time-varying electric field produces a magnetic field.Circuits describe many electromagnetic devices. Flux and line integrals play a key role in electromagnetic theory.
Effects of Varying Magnetic Fields: Electromagnetism merges electricity/magnetism via Ørsted, Faraday, and Maxwell's discoveries, leading to electric power/radio communications. changing magnetic field induces electromotive force quantified by E = -\frac{d\Phi}{dt}, where Φ is magnetic flux. The units of magnetic flux are webers, with one weber equaling one tesla per square metre. Lenz’s law states that the induced effect opposes change. Faraday’s law applies regardless of the magnetic flux change process.. For coils, Φ=nϕ (n = number of turns).
Self-Inductance and Mutual Inductance: Self-inductance reacts to changing current in a circuit; mutual inductance reacts to changing current in a second circuit. Units are henrys. where M{21} = M{12} = M. Induced electromotive force: .Eddy currents are induced for heating.
AC Transformer: Transformers use maximum mutual induction. Transformers step-up/step-down voltages. Step-up transformers minimize transmission energy loss. Faraday’s law powers industry and electric motor development.
Effects of Varying Electric Fields: Maxwell predicted changing electric fields generate magnetic fields.Maxwell's equations unify electromagnetism; electromagnetic waves travel at light speed ($\frac{1}{\sqrt{\epsilon0\mu0}}$). Displacement current Jd = \frac{dD}{dt}, where D = \epsilon0 E . Heinrich Hertz initiated radio communications in 1887.
Maxwell’s Equations: Maxwell's equations describe classical electromagnetism, unifying optics. Shielding requires conductors for electric fields. Magnetic field shielding is harder. Skin depth: \delta = \sqrt{\frac{2}{\omega \mu \sigma }}.
Historical Survey: Electric/magnetic forces were long considered separate until the 19th century.
Early Observations and Applications: Greeks knew about magnetite/rubbed amber attraction. Peter Peregrinus did early magnetism experiments.
Emergence of the Modern Sciences of Electricity and Magnetism: William Gilbert founded modern electricity/magnetism science, described Earth as a magnet, and introduced 'electric' force.
Pioneering Efforts: Otto von Guericke built the first electric spark generator (1663). Stephen Gray discovered electricity flow (1729). Pieter van Musschenbroek invented the Leyden jar (1745).
Revolutionized the Study of Electrostatics: Electricians demonstrated with Leyden jars. Benjamin Franklin proved lightning was electric and advanced conservation of charge.
Apparatus Design: Coulomb established electricity as a mathematical science, inventing the torsion balance. Poisson/Gauss extended Coulomb’s work. Faraday verified inverse square law precisely.