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What is a Force Field in Physics?

Katherine Kaylegian-Starkey, David Wood, Will Welch
  • Author
    Katherine Kaylegian-Starkey

    Katherine has a bachelor's degree in physics, and she is pursuing a master's degree in applied physics. She currently teaches struggling STEM students at Lane Community College.

  • Instructor
    David Wood

    David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

  • Expert Contributor
    Will Welch

    Will has a doctorate in chemistry from the University of Wyoming and has experience in a broad selection of chemical disciplines and college-level teaching.

Learn what a force field is. Explore the difference between a scalar and a vector field, and look at examples of force fields. Updated: 02/24/2022

What is a Force Field?

In physics, a field is a region where every point within that region is defined in spacetime. For example, imagine watching the weather report on the morning news. Chances are that the weatherman will bring up an imagine like that pictured in Figure 1. Figure 1 is a United States map with the local temperatures labeled by region. This is also an example of a visual representation of a field because every point on the map is affected by the temperature. Now think about the gravitational force. There is no place on earth that gravity's effects are not visible. This is an example of a force field.

So that leads to the question, what is a force field and how is it defined? In simple terms, a force field in physics is the area that is affected by another force.


Figure 1. This temperature map is an example of a field in physics.

An example of a field in physics.


Are Force Fields Possible?

Are force fields possible? Yes, force fields are a real physical phenomena. How do force fields form? A force field is a direct response to non-discrete natural phenomena such as gravity or magnetism. Recall that discrete means that something is well defined and distinct. Forces such as gravity and magnetism are not discrete because they occur continuously. To illustrate this point, imagine a magnet. Now bring another magnet close to the first, and notice the attraction or repulsion felt between the magnets. Move the second magnet to a different location near the first, and notice that there is also an attraction or repulsion between the magnets. This could be repeated endlessly and the two magnets, no matter how they are oriented, will always attract or repeal each other. If the magnetic force was discrete instead of continuous, the second magnet would only feel an attraction or repulsion at a single place on the first magnet. Since forces are not discrete, a force field represents all of the points that the force affects.

Definition

A force field is a map of the force felt over a particular area of space. To explain this better, we should first describe a field. While it might sound mysterious, a field, in physics, is really just a map of a particular quantity over an area of space. For example, if you walked around an actual farmer's field and took temperature measurements, and then wrote those measurements on a map, you would have just drawn a temperature field. Below is an example of a temperature field of the United States:

A temperature field (map) of the USA
A Temperature Field (Map) of the USA

Instead, if you walked around that same farmer's field and measured the wind speed and direction, you would create a wind velocity field. In these kinds of maps, the length of the arrow represents the speed of the wind - longer means faster. Whenever we have the length of an arrow represent a number, the arrows are called vectors. So such a wind speed map would be called a vector field, and it is also a force field, because it is a map of the force of the wind felt over the area. The aforementioned temperature field on the other hand, since it contains only numbers and no arrows with direction, is called a scalar field.

A prevailing wind map of the world
A Prevailing Wind Map of the World

A vector is a quantity with a number and a direction, like wind speed. A scalar is a quantity that is just a number, with no direction. Force is a vector, because it has both a size and direction - you feel a force, or a push, in a particular direction. Because of this, all force fields are vector fields.

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Types of Force Fields

There are two types of fields that exist in physics and mathematics. A field can be a vector field, or it can be a scalar field. Recall that a vector is a quantity that has a magnitude, or size, and a direction. A scalar is a quantity that has magnitude and no direction.

For example, driving 50 miles East to Grandma's house is a vector because there is a size, 50 miles, and a direction, East. On the other hand, driving 50 miles to Grandma's house is a scalar quantity because there is only a distance given.

Vector Fields

All forces are vectors because forces act on an object. Imagine pushing a cart. To affect the cart with the force of the push two things must happen: first, contact must be made with the cart from some direction, and second, a non-zero force must be applied. These two conditions that must be met for a force to act are also the conditions that must be met to classify a quantity as a vector—a direction and magnitude. Vector fields are graphically represented using arrows of varying lengths. The arrows point in the direction of the applied force, and the varying lengths indicate the intensity of the force in that region of space. Figure 2 is an example of the graph of a vector field where F labels the force, and S labels the surface the force originates from.


Figure 2. This is an example of a force field. The arrows point in the direction of the force, and the varying lengths of the arrows indicate the intensity of the force in that region.

An example of a vector field.


Scalar Field

A scalar field is a field where every point in spacetime is represented by a scalar quantity, and, since force fields are always vector fields, what types of things can be represented using a scalar field?

To illustrate this, return to the U.S. temperature map in Figure 1. Temperature is a scalar quantity, and Figure 1 represents a scalar field. Thus, this is not a force field.

Why is Temperature a Scalar Quantity?
Temperature is a scalar because temperature has no direction. If it did, thermostats would be set to a temperature and direction! Other examples of scalar fields include pressure fields, humidity fields, and potential fields such as those of the electric potential.

Force Field Examples

There are countless force field examples in physics. Among the force fields most commonly known are the gravitational force field, the magnetic force field, and the electric force field. The following list expounds on these fields in greater detail:

Examples of Force Fields

In physics we talk about magnetic fields, electric fields, and gravitational fields. All these things sound impressive, but really they're just ways of showing a force felt over an area of space.

If you move a compass near to a magnet, the needle will move. Magnets apply forces to certain magnetic materials, including the compass needle. If you move that compass to lots of different places, and note down the direction it points, you are drawing a magnetic field.

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Video Transcript

Definition

A force field is a map of the force felt over a particular area of space. To explain this better, we should first describe a field. While it might sound mysterious, a field, in physics, is really just a map of a particular quantity over an area of space. For example, if you walked around an actual farmer's field and took temperature measurements, and then wrote those measurements on a map, you would have just drawn a temperature field. Below is an example of a temperature field of the United States:

A temperature field (map) of the USA
A Temperature Field (Map) of the USA

Instead, if you walked around that same farmer's field and measured the wind speed and direction, you would create a wind velocity field. In these kinds of maps, the length of the arrow represents the speed of the wind - longer means faster. Whenever we have the length of an arrow represent a number, the arrows are called vectors. So such a wind speed map would be called a vector field, and it is also a force field, because it is a map of the force of the wind felt over the area. The aforementioned temperature field on the other hand, since it contains only numbers and no arrows with direction, is called a scalar field.

A prevailing wind map of the world
A Prevailing Wind Map of the World

A vector is a quantity with a number and a direction, like wind speed. A scalar is a quantity that is just a number, with no direction. Force is a vector, because it has both a size and direction - you feel a force, or a push, in a particular direction. Because of this, all force fields are vector fields.

Examples of Force Fields

In physics we talk about magnetic fields, electric fields, and gravitational fields. All these things sound impressive, but really they're just ways of showing a force felt over an area of space.

If you move a compass near to a magnet, the needle will move. Magnets apply forces to certain magnetic materials, including the compass needle. If you move that compass to lots of different places, and note down the direction it points, you are drawing a magnetic field.

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  • Activities
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Visualizing Gravitational Fields

Read the following visualization exercises and answer the questions.

1.) The Sun has a big gravitational force field. Because the sun is a sphere it exerts its gravitational force equally in all directions around it so that the value of the field is dependent on the distance from the sun, but not the direction.

  • The Earth's orbit is an oval. Draw an oval and place a dot as close to the center as possible. Does the planet feel the same gravitational force from the sun at all times of the year? Explain in terms of the Sun's gravitational field.
  • What shape would the planet's orbit have to be and where would the sun have to be in order for the planet to feel the same gravitational pull at any place in its orbit?

2.) Your weight is actually a measurement of the Earth's gravitational field gravitational field acting on your mass.

  • Think about astronauts orbiting the Earth in a space ship. Is the Earth's gravitational field stronger at the surface or in the orbit of the space station.
  • Is the sun's gravitational field stronger near Mercury of Pluto?

Answers

1.) Since the value of the field is dependent on the radius, the sun's gravitational field will have the same value along circles with the sun at the center.

  • There is no way to put the sun in an oval such that every point on the oval is equidistant from the sun. The Earth does not feel the exact same gravitational field at all points in the year.
  • The orbit would have to be a perfect circle.

2.) Astronauts float in the space station. They are effectively weightless, so they are not experiencing a very strong force due to the Earth's gravitational field.

  • The field is strong at the surface and weak in the space station's orbit.
  • Similarly, the sun's gravitational field gets weaker the further away from it you go. Mercury, the closes planet, feels a stronger gravitational field than Pluto, the furthest planet.

What is a force field in physics?

In physics, a force field is a representation of the area that a force effects. For example, the attraction and repulsion of magnets can be felt even before the magnets are touching. This is an example the magnetic force field.

What is an example of a force field?

All forces are represented as force fields. The most well-known examples of force fields in physics are the gravitational force field, the magnetic force field, and the electric force field.

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