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Fields in Physics

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Fields in Physics

Quantum field theory is the most advanced scientific theory ever developed by humans. It is based on the quantum framework, but the main object of the theory are fields. Fields in physics are the most adequate entity physicists have found to describe reality. Two famous examples are the magnetic field and the electric field, thanks to which almost every device from mobile phones to particle accelerators works.

What are fields, and why are they important?

We are going to analyse how the concept of field evolved historically and what motivated its surge and evolution. Then, we will review some of the important consequences field theories have in physics.

Historical notions of field

Already in ancient Greece, philosophers and mathematicians developed an intuition regarding, mostly, non-contact forces of something that existed in space and caused things to move or behave in certain ways. A precise mathematical formulation of this idea was not achieved until Newton formulated his theory of gravitation. Since then, the basic characteristics of fields came understood to be:

  • Presence of a source responsible for the existence of the field. For instance, the usual source of the magnetic field is a magnet. In modern physics, advanced theories and measurements have led to the discovery of certain particles ‘carrying’ the interaction, such as photons in the case of the electromagnetic field.
  • Spacelike character: the field might behave as a scalar quantity throughout space, showing only magnitude, or it might have a direction or other more complicated features. For example, gravity has a direction towards the earth but temperature matters only as a number measuring its intensity.
  • Locality: this is the key characteristic of usual fields, which are functions of spacetime. That means that the most general field takes different values for different locations of space, and it evolves in time for each point. For instance, the temperature in a room changes over time and will be higher the closer we get to the heater.

Fields in Physics. Vector field. StudySmarterFigure 1. Example of a vector field. Source: AllenMcC, wikipedia.org (GNU FDL).

Although the spacelike character was quickly understood by scientists and philosophers, the nature of sources and of locality were widely questioned throughout history. Regarding the sources, it is true that, according to our understanding of fields, a proper source does not always exist, as, for instance, for temperature.

On the other hand, the issue of locality has posed a greater challenge when modelling and understanding fields. For example, it used to be believed that temperature was generated in ‘bubbles’ that floated around. Nowadays, although locality is a widely accepted principle, some non-local effects have led us to believe that it is approximately but not fully correct.


The importance of fields

Most physics problems in high school involve highly simplified forces acting in a very local way but only at a certain point in space. We find point-like particles to be the elemental objects that we work with. We have examples of these in the charges responsible for creating an electric field or in the majority of modern atomic models when considering the electron. Fields are a generalisation for the whole space of the local point-like forces we have mentioned. In the end, this is all thanks to the fact that interactions caused by fields occur in points smaller than any scale we consider.

What are the consequences of fields as physical objects?

We are going to review some of the implications of fields for physical theories. Specifically, we will briefly focus on a couple of mathematical aspects and then on some purely physical ones.

Mathematical implications

The basic implication of fields and their nature is the ability to use differential calculus to study how fields work. This is generally beneficial since we have a lot of notions of statistical manipulations, transformations of expressions, etc., which allow us to progress in many directions and to work with computers when systems are too complex. Nevertheless, field theories have had mathematical issues, which are being (and have been) addressed in order to get sensible results.

Physical implications

The physical implications, although not completely independent of the mathematical ones, are based on the fact that forces are now caused by an entity that permeates the whole space and evolves in time. The essence of a field is the abundance of information. Since, for each point, we have information about the strength of the field, its direction, its time evolution, etc., we can generalise the dynamics of any object subject to the influence of the field.

What are examples of physical fields?

We will, finally, list some examples of fields in physics and briefly explain their nature and role:

  • Gravitational field: probably the most famous and, still, widely investigated. It is generated by the presence of mass and has a direction. The first mathematical formulation is due to Newton, and it is the most relevant field at interplanetary scales.
  • Electromagnetic field: the runner-up in the contest of the fame of fields, it is generated by the presence of charge whose state of motion creates different kinds of electric fields, magnetic fields, or both. Modern theories of electromagnetism are based on particles, called photons, that are sourcing the field.
  • Stream current/wind: these are very similar in that they propagate on material mediums, air and water, and usually have a direction restricted to a plane (they do not go up or down). They do not have a proper physical source as in the previous examples but are caused by environmental phenomena.

Fields in Physics. Gravitational field. StudySmarterFigure 2. Gravitational field generated by the earth. Source: MikeRun, Wikimedia Commons (CC BY-SA 4.0).

Fields and their consequences - Key takeaways

  • Fields are the main basic objects of modern physics modelling interactions.

  • They usually feature a certain spacelike character, associated sources, and the property of locality.

  • Locality is the key aspect of fields. It allows us to do a lot of physics with them, but it also poses some problems, which are yet to be solved.

  • Gravitation and electromagnetism are two of the basic fields in physics.

Frequently Asked Questions about Fields in Physics

It is an entity depending on space and time that causes physical interactions.

The source of a field is the entity generating the field. It may be a physical quantity, like mass for gravity, or the action of some phenomenon or device, such as a fan generating wind.

Some examples are the field associated with the wind, the gravitational field (or gravity), the electric field, and the magnetic field (or the unified electromagnetic field).

Final Fields in Physics Quiz

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What are fields in physics?

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Fields are physical entities extended in spacetime, which model interactions.

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Has the idea of field been the same throughout history?


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No, although it was quickly observed that some phenomena depended on spacetime, the idea of sources causing these phenomena or how local they were has changed over time.

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Two key features of fields are locality and a spacelike character.

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Temperature does not have a characteristic source.

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Is locality a principle fully accepted as universal?

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No, but it is believed to be approximately universal as a characteristic of nature.

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Fields depend on time and space.

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What is an example of a field without a specific source?

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The field associated with the wind.

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Was temperature always conceived as a field generated at the microscopic level?

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 No, historically, it was believed that it was generated in ‘bubbles’.

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Are there physical particles carrying the interaction of fields?

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Yes, but not for every field.

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What is an example of a particle carrying a field’s interaction?

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The photon, which is the responsible particle for carrying the electromagnetic interaction.

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Do point-like particles exist?

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This is unknown.

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Is differential calculus used in field theory?

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Yes, as well as integral calculus.

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The gravitational field is generated by masses.

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The magnetic field and the electric field are not independent.

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Are magnets point-like particles sourcing the magnetic field?

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They do source the magnetic field, but they are not point-like particles.

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Newton’s second law of motion is the law that relates the net force to the rate of change of momentum.

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Newton’s first law of motion implies that moving objects in space move with constant velocity.

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Newton’s law of gravity states that the force of attraction between two bodies is the same for each of them.

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Rockets move because they expel particles with momenta, and, due to Newton’s third law of motion, momentum is generated on the rocket.

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Is the formulation ‘the total force equals the mass times the acceleration’ always true?

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No, ‘the total force equals the mass times the acceleration’ is only true if the mass is constant.

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According to Newton’s laws, can we decelerate light by exerting a force?

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According to Newton’s laws, we cannot decelerate light by exerting a force because light does not have mass.

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Why do objects lying on a surface remain still (not move) according to Newton’s laws?

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Objects lying on a surface do not move because there is no net force acting on them to change their resting state.

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What is the inertial mass?

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The inertial mass is the name given to the mass appearing in Newton’s laws.

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Why do objects moving at a certain speed usually stop at some point? Choose the correct answer.

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Because there are no ideal conditions for Newton’s first law to be applied. There is always some force, usually friction.

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Explain in terms of Newton’s third law of motion why we can swim? Choose the correct answer.

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When we move our arms and legs in the water, we displace particles of water that exert a force back at us, causing us to move.

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If an object is spinning in circles in a no-friction circular motion and the circular motion suddenly stops, what happens to the object? Choose the correct answer.

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If an object suddenly stops spinning, it will remain moving in a straight line tangent to the original circle at constant velocity.

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What is the principle of equivalence?

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It is the principle that states that the mass measuring the intensity of the gravitation interaction and the inertial mass are the same.

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Do the masses in Newton’s law of gravitation play an equivalent role?

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Yes, exchanging them amounts to a global sign in the formula, which accounts for the opposite direction consistent with Newton’s third law.

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The gravitational field strength is sourced by mass.

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The gravitational field strength is sourced by mass and affects masses.

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Newton’s description of the gravitational field strength is compatible with more modern descriptions.

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Radial dependence is a sign of isotropy, i.e. equivalence of all spatial directions.

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The gravitational field strength on the Sun is greater than on Jupiter.

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Who stated the first rigorous formulation of the gravitational field strength?

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Newton stated the first rigorous formulation of the gravitational field strength.

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What are two characteristics of a theory to describe the gravitational field strength?

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The two characteristics of a theory to describe the gravitational field strength are 

  • sourced by masses 
  • attractive (decaying with distance from the source)

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Do masses play an equivalent role when computing the forces caused by the gravitational field strength?

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Yes, masses play an equivalent role when computing the forces caused by the gravitational field strength because one can describe the attractive force from the point of view of one mass or the other.

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Can you name another theory about gravitational field strength that is more fundamental than Newton’s?

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Einstein’s theory of general relativity.

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Is the gravitational field strength constant on the surface of planets and stars?

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Yes, the gravitational field strength is constant on the surface of planets and stars because they have an approximately spherical shape and the surface is at a constant radial distance.

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Is Earth’s gravitational field strength constant when an object is inside it and travelling towards its core?

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No, Earth’s gravitational field strength is not constant when an object is inside it and travelling towards its core because the radial distance is decreasing (as well as the amount of mass attracting towards the core).

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Is Earth’s gravitational field strength constant while getting away from the surface?

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No, Earth’s gravitational field strength is not constant while getting away from the surface because the radial distance is increasing.

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Which astronomical object in the Solar System has the biggest surface gravitational field strength?

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The Sun has the biggest surface gravitational field strength (it is the biggest astronomical object in the Solar System, but this is not the only variable because its mass is important too).

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Which planet in the Solar System has the biggest surface gravitational field strength?

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Jupiter has the biggest surface gravitational field strength (it is the biggest planet in the Solar System, (but this is not the only variable because its mass is important too).



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Does the gravitational field strength have an infinite range?

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Yes, the gravitational field strength has infinite range. It can reach arbitrarily long distances with a non-zero value of intensity.

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The gravitational field has an associated gravitational potential field.

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The gravitational potential energy is sourced by masses.

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The gravitational potential energy decreases with radial distance.

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Gravitational potential energy explains why we get tired when going up a hill.

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The gravitational potential energy can be approximated through a simpler equation for points close to the earth’s surface.

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What is the feature of the gravitational field that ensures the existence of a gravitational potential?

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The gravitational field is conservative.

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Why does the gravitational potential have spherical symmetry?

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Because there are no special spatial directions.

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