Magnetism is the key phenomenon behind:

MRIs – magnetic resonance imagers, useful in medicine.

Computer disk drives, audio cassettes, and floppy disks: magnetic storage of information.

Car alternators.

All electric motors rely on magnetism

Electricity is generated by devices using magnetism and electricity

Speakers, which convert electrical energy into sound waves

Maglev (magnetically levitating trains)
Electricity is the key phenomenon behind:

Refrigerators, dishwashers, dryers, washing machines, microwave ovens

Cell phones, tablets, computers, videogame consoles, chargers

Lamps, light bulbs, streetlights

Furnace and water heater

Electric cars, electric trains & trolleys, Maglev trains
We’ll learn that magnetism and electricity are not different things – but are really different aspects of the same thing! On Quora, Mark Eichenlaub writes:
…the history of electromagnetism is one of unification. Over and over, different ideas about how things work were subsumed into the same theoretical framework…. Electromagnetism is an example of a field theory, the central object of study in theoretical physics.
A “field” means that at any point in space and time, there’s an electric and magnetic vector there. These fields pervade all of space – they are in the room around you right now, and in outer space, even within you…
We don’t have a mechanical picture of what the field is, or why it is a certain way. It’s not like waves in the water or anything like that. It just exists, but we do have mathematical rules that describe how it works….
Michael Faraday investigated things like the way a wire carrying electric current deflects a compass needle. His crowning achievement was to discover that changing magnetic fields create electric fields, a phenomenon called induction.
James Clerk Maxwell looked at all that, sat down with pen and papers, and mathematically described Faraday’s results in a complicated set of differential equations, importantly including the idea that changing electric fields would create magnetic fields, completing the symmetry between the two.
When Maxwell finished his theory, he discovered that it allowed waves of electromagnetism to fly off at high speed – when he calculated the speed, it turned out to be the speed of light.
Experiments with radio waves soon verified that light was nothing more than a special form of electricity and magnetism.
You can think of it as if we had been studying the way hot air balloons and airplanes and things work, and so were thinking about the dynamics of air. In the process, we develop equations for air, and figure out that sound is just waves moving through the air. The theory of sound and the theory of airplanes are actually the same theory, even though they don’t seem very similar. That’s roughly what happened for light, except that unlike for sound, no one expected it. (Or at least it wasn’t obvious beforehand.)
Maxwell’s equations describe how electric and magnetic fields work, but those fields need to interact with matter – that happens via electric charge. Charge is an innate property of matter…
What exactly is the relationship between electricity, magnetism, and light?
We keep talking about the electromagnetic field. What exactly is a “field” anyways? How do understand what one is? See here: What are fields?
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The electromagnetic force is the force of nature behind electric fields, magnetic fields, and light.
It is one of the four fundamental forces in nature.
“Electromagnetism” is a compound form of two Greek terms:
ἤλεκτρον, ēlektron, “amber”, and μαγνῆτις λίθος magnētis lithos, which means “magnesian stone”, a type of iron ore.
The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of intermolecular forces between individual molecules in matter. Electrons are bound by electromagnetic wave mechanics into orbitals around atomic nuclei to form atoms, which are the building blocks of molecules.
This in turn governs chemistry, which arise from interactions between the electrons of neighboring atoms. This in turn is determined by the interaction between electromagnetic force and the momentum of the electrons.
The theoretical implications of electromagnetism, in particular the establishment of the speed of light based on properties of the “medium” of propagation, led to the development of special relativity by Albert Einstein in 1905.
Learning Standards
Massachusetts 2016 Science and Technology/Engineering (STE) Standards
HSPS24. Use mathematical representations of Newton’s law of gravitation and Coulomb’s law to both qualitatively and quantitatively describe and predict the effects of gravitational and electrostatic forces between objects.
HSPS25. Provide evidence that an electric current can produce a magnetic field and that a changing magnetic field can produce an electric current.
HSPS29(MA). Evaluate simple series and parallel circuits to predict changes to voltage, current, or resistance when simple changes are made to a circuit
HSPS31. Use algebraic expressions and the principle of energy conservation to calculate the change in energy of one component of a system… Identify any transformations from one form of energy to another, including thermal, kinetic, gravitational, magnetic, or electrical energy. {voltage drops shown as an analogy to water pressure drops.}
HSPS32. Develop and use a model to illustrate that energy at the macroscopic scale can be accounted for as either motions of particles and objects or energy stored in fields [e.g. electric fields.]
HSPS33. Design and evaluate a device that works within given constraints to convert one form of energy into another form of energy.{e.g. chemical energy in battery used to create KE of electrons flowing in a circuit, used to create light and heat from a bulb, or charging a capacitor.}
HSPS35. Develop and use a model of magnetic or electric fields to illustrate the forces and changes in energy between two magnetically or electrically charged objects changing relative position in a magnetic or electric field, respectively.
Learning Standards: Common Core Math
 CCSS.MATH.CONTENT.7.EE.B.4 Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
 CCSS.MATH.CONTENT.8.EE.C.7 Solve linear equations in one variable
 CCSS.MATH.CONTENT.HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (including isolating a variable)
 CCSS.MATH.CONTENT.HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
 http://www.corestandards.org/Math/
Common Core State Standards (Inversesquare law)
A FRAMEWORK FOR K12 SCIENCE EDUCATION
Practices, Crosscutting Concepts, and Core Ideas
Electric forces and magnetic forces are different aspects of a single electromagnetic interaction. Such forces can be attractive or repulsive, depending on the relative sign of the electric charges involved, the direction of current flow, and the orientation of magnets. The forces’ magnitudes depend on the magnitudes of the charges, currents, and magnetic strengths as well as on the distances between the interacting objects.
All objects with electrical charge or magnetization are sources of electric or magnetic fields and can be affected by the electric or magnetic fields of other such objects. Attraction and repulsion of electric charges at the atomic scale explain the structure, properties, and transformations of matter and the contact forces between material objects (link to PS1.A and PS1.B).
Coulomb’s law provides the mathematical model to describe and predict the effects of electrostatic forces (relating to stationary electric charges or fields) between distant objects.
At the macroscopic scale, energy manifests itself in multiple phenomena, such as motion, light, sound, electrical and magnetic fields, and thermal energy. Historically, different units were introduced for the energy present in these different phenomena, and it took some time before the relationships among them were recognized. Energy is best understood at the microscopic scale, at which it can be modeled as either motions of particles or as stored in force fields (electric, magnetic, gravitational) that mediate interactions between particles. This last concept includes electromagnetic radiation, a phenomenon in which energy stored in fields moves across space (light, radio waves) with no supporting matter medium.
Electric and magnetic fields also contain energy; any change in the relative positions of charged objects (or in the positions or orientations of magnets) changes the fields between them and thus the amount of energy stored in those fields. When a particle in a molecule of solid matter vibrates, energy is continually being transformed back and forth between the energy of motion and the energy stored in the electric and magnetic fields within the matter. Matter in a stable form minimizes the stored energy in the electric and magnetic fields within it; this defines the equilibrium positions and spacing of the atomic nuclei in a molecule or an extended solid and the form of their combined electron charge distributions (e.g., chemical bonds, metals).
Electromagnetic radiation (such as light and Xrays) can be modeled as a wave of changing electric and magnetic fields. At the subatomic scale (i. e., in quantum theory), many phenomena involving electromagnetic radiation (e.g., photoelectric effect) are best modeled as a stream of particles called photons. Electromagnetic radiation from the sun is a major source of energy for life on Earth.
The idea that there are different forms of energy, such as thermal energy, mechanical energy, and chemical energy, is misleading, as it implies that the nature of the energy in each of these manifestations is distinct when in fact they all are ultimately, at the atomic scale, some mixture of kinetic energy, stored energy, and radiation. It is likewise misleading to call sound or light a form of energy; they are phenomena that, among their other properties, transfer energy from place to place and between objects.