# Electromagnetism: An Introduction

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Electricity and magnetism were regarded as distinct phenomena for quite a while. However, as scientists started studying electrodynamics (the physics of moving charge), some interesting phenomena emerged.

They noticed that current-carrying wires could be affected by magnets, and also that magnetic fields could be generated with current. Somehow electricity and magnetism were linked.

## What Is Electromagnetism?

Formally, electromagnetism is the field of physics that pertains to phenomena in which electric fields and magnetic fields interact with each other.

This field of study looks at how magnetic fields can affect moving electric charges and how changing magnetic fields can induce electric current. It also looks at how magnetic fields can be generated by electric fields or electric current. It even explains the origins of electromagnetic radiation.

Ultimately, electromagnetism describes electricity and magnetism within one single framework as two manifestations of the same fundamental electromagnetic force.

## What Is a Field?

When learning about electricity and magnetism, you might hear the term “field” come up a lot. But what is an electric field or a magnetic field?

A field is a way to describe the effects or influence that a particular type of force has in a way that is independent of what that force might act upon. For example, the effect of the gravitational force that the Earth exerts on objects in its vicinity can be represented by a vector at each point in space around Earth.

Each such vector points toward the center of the Earth and has a magnitude that depends on Earth’s mass and the distance from Earth. Each vector gives you information about the relative size of the force that another mass would feel if placed at that location. The formula for the field vector is written in such a way that the force a mass ​m​ would feel at a particular location is equal to the product of ​m​ and the field vector at that location.

The notion of fields is useful because it allows scientists to describe the effects of an object independent of what it is acting upon. It also allows for an easier description of certain forces that seem to act at a distance without contact, such as gravity, the electric force and the magnetic force. Instead of treating objects as though they are exerting forces on each other from a distance, they can be treated as though a field is directly exerting a force on them at their given location.

Mathematically, the electric field at a distance ​r​ from charge ​Q​ is given by:

\vec{E} = \frac{kQ}{r^2}\hat{r}

Where the ​r​ with the hat on top is a unit vector pointing away from the charge.

You’ll note that this formula looks almost the same as the coulomb force equation (which gives the force between two point charges), except that it is missing the second charge. The units of the electric field are newtons per coulomb. In order to find the force felt by a charge ​q​ placed in the electric field, you need only multiply the field value by ​q​:

\vec{F_{elec}} = q\vec{E}

## How Electric Fields Can Create Magnetic Fields

If current is passed through a long, straight wire, it ends up generating a magnetic field in a direction that circles the wire. This can be observed by placing a compass near the wire and noting the deflection of the compass needle. (The compass will align itself with the magnetic field).

This observation can be used to create an electromagnet. This is done by coiling the wire. When the wire is coiled, and current is passed through, it creates a magnetic field that looks very similar to that of a bar magnet, with a north magnetic pole on one end and a south magnetic pole on the other end.

You can strengthen an electromagnet by placing a material such as iron in the center. You may have seen electromagnets made by wrapping wire around an iron nail and connecting it to a battery. The iron in the nail acts to amplify the magnetic field.

But what about bar magnets? They don’t seem to be generated by current, at least not in any obvious way. But the origins of the magnetic field of a bar magnet are actually from moving charge as well – just on a much smaller scale.

Each atom within the bar magnet has an electron cloud, which is essentially moving charge. Each atom, as a result, has a small magnetic field that looks very much like the field made by an electromagnet. In most materials, these tiny magnetic fields are lined up in different directions, and the net effect is cancellation.

But in certain materials, such as iron, the fields can all become aligned. This is what has happened in a bar magnet. The reason magnetic poles always come in pairs (a north pole and a south pole) is because of how magnetic fields are generated.

The origin of Earth's magnetic field is also a moving charge. In this case, it is the result of something called a dynamo effect, where the molten iron near the center of the Earth swirls around in a pattern that generates a dipole field.

Static electricity (charges that are not moving), however, can't create magnetic fields. In order to create a magnetic field, charge must move.

## How Magnetic Fields Can Create Electric Fields

Physicist Michael Faraday explored electromagnetism further by seeing if things could work the other way around – in other words, if electric fields can create magnetic fields, can magnetic fields create electric fields?

He set up a pair of circuits, the first of which had a coil and was connected to a battery and a switch. When turned on, a magnetic field would be generated within the coil. A second circuit had a similar coil lined up with the coil of the first circuit so that the magnetic field would extend into the second circuit’s coil.

The second circuit was not connected to a power supply, however; only to a galvanometer that would measure if any current flowed. What he discovered was that it was possible to generate current in the second circuit, but only as the switch was flipped on and off. In other words, a constant magnetic field wouldn’t do it, but a changing magnetic field did.

Later both Faraday’s law and Lenz’s law helped describe in more detail how this current was induced, and with what magnitude and direction. The phenomenon being described is called electromagnetic induction.

Another phenomenon demonstrating the interaction between electricity and magnetism occurs with the Lorentz force. If current is passed through a wire in the presence of an external magnetic field, that wire will feel a force due to the field and be pushed in one direction. The direction of this push depended on the direction of the field and the direction of charge flow.

## Maxwell's Equations

James Clerk Maxwell summarized all of the observations about the interactions between electric and magnetic forces in his famous Maxwell’s equations.

This is a set of four equations that essentially state the following:

• Point charges generate electric fields.
• There are no magnetic monopoles.
• Electric fields are generated by changing magnetic fields.
• Magnetic fields are generated by changing electric fields or current.

From this set of four equations, Maxwell was able to find a solution that described a self-propagating electromagnetic wave. Based on his calculations, such a wave necessarily traveled at the speed of light. This is how it was determined that the phenomenon of light was actually electromagnetic radiation.

## Electromagnetic Waves

Electromagnetic waves are the result of simultaneous and perpendicular oscillations in electric and magnetic fields. When it comes to electromagnetism, this is a prime example of how electricity and magnetism are intertwined.

While these waves all travel at the same speed, they can vary in wavelength and frequency and are classified based on the associated values of those quantities. Types of electromagnetic radiation include (from longest wavelength to shortest wavelength):

• Microwaves
• Visible light
• X-rays
• Gamma rays

## How the Units Fit Together

Charge is measured in coulombs, current in amperes, magnetic flux density in tesla and so on. But in the field of electromagnetism, these units must somehow relate to each other since electricity and magnetism are two sides of the same phenomenon.

The base units, from which all other units can be constructed are the kilogram (kg), second (s), kelvin (K), ampere (A), mole (mol), candela (cd) and meter (m). The following are how electromagnetism units relate to various combinations of these base units:

Electromagnetic Units
Quantity Unit Equivalent Base Units

Charge

coulomb

As

Current

ampere

A

Potential difference

volt

kgm2/(s3A)

Electrical resistance

ohm

kgm2(s3A2)

Electric flux

volt meter

kgm3/(s3A)

Electric field strength

newton per coulomb

kgm(As3)

Magnetic flux density

tesla

kg/(s2A)

Magnetic flux

weber

kgm2/(s2A)

Magnetic field strength

amperes per meter

A/m

## Applications of Electromagnetism

Electromagnetism has a multitude of applications, the largest set of which relate to the generation, distribution and application of electric energy.

Most electric power generators make use of electromagnetic induction. Since a changing magnetic field can induce an electric field (and cause current to flow through a wire), if you can physically rotate a large magnet within a wire coil, or rotate a wire coil in the presence of a magnetic field, this will induce a current.

In order to make the magnet or the coil rotate, some other form of energy must be used. In a wind generator, this is done by allowing wind to turn giant turbines. In hydroelectric, turbines are rotated by the flow of water. Coal plants burn coal to produce steam, which can turn turbines.

These electric power generators take mechanical energy and convert it into electrical energy. Because of how they function, the current they generate is alternating current. That is, current flows in one direction and then in the other direction in a continuous cycle.

Electric motors are another application of electromagnetism. These work in the reverse of generators. Instead of converting mechanical energy into electric energy, they convert electric energy into mechanical energy.