# What is a Force Field in Physics?

## 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.

### 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:

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 **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.

## 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 vectorâ€”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.

### 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:

- Gravitational force field â€“ Gravity is everywhere. It is a force that accelerates objects toward the earth with a magnitude of 9.81 {eq}m/s^2 {/eq}, and no matter where on the planet earth a person travels, gravity will always act the same. These observations imply that gravity has a magnitude, 9.81 {eq}m/s^2 {/eq}, a direction, toward the earth, and gravity is continuous. Since these conditions are met, the gravitational force can be represented as a force field.

- Magnetic force field â€“ As in the magnet example above, magnetism is considered to be a force field because it is a continuous force, and magnetism acts on every point in spacetime that the force comes into contact with. Another example of a magnetic force field is the earth's own magnetic field. The charged ions in the earth's core create a magnetic field as the earth spins, and this magnetic field is felt everywhere. In fact, it is the earth's magnetic field that penetrates into space and deflects cosmic particle radiation and solar storms. Figure 3 is a representation of earth's magnetic force field.

- Electric force field â€“ The electric force arises from a charged particle such as an electron or a proton, and, just like the magnetic force, the electric force from one charged particle has the ability to attract or repel another charged particle. Imagine an electron and a proton orbiting a nucleus. These two particles circle the nucleus, changing their relative positions to one another, yet, at no time, do they not feel a repulsive force. The repulsion between the electron and the proton is always felt no matter how the particles are oriented, and this is the electric force field. If the electric force field did not exist, only in certain positions would the proton and electron be repulsed.

## Lesson Summary

In physics, a field is a region where every point in spacetime is well defined, and the concept of fields is used to describe the action of forces, called a **force field**. A force field represents all of the points in spacetime where a force is present. For example, the gravitational force draws every particle on earth toward its surface, and the area that the gravitational force acts on is represented as a force field. Other common force field examples are the magnetic force field which is responsible for the attraction and repulsion felt by magnetic objects and the electric force field which is responsible for phenomena such as the repulsion between an electron and a proton orbiting a nucleus.

There are two types of fields found in physics. A field can either be a **vector field**, or it can be a **scalar field**. A vector is a quantity that has a magnitude and a direction. Since a force must act at an angle and with a non-zero magnitude to be felt, all force fields are vector fields. Scalar fields are fields where every point in spacetime is represented by a scalar quantity. A map of the United States displaying the regional temperature is an example of a scalar vector field.

## 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**.

A magnetic field is a force field that represents the force that moving charges inside metals feel at different points in space. If you're closer to the magnet, the magnetic field is stronger. If you're further away, it's weaker. Or in other words, the force that the compass needle feels is stronger when it's closer to the magnet.

The magnetic field of a bar magnet looks something like this:

The Earth also has a magnetic field, which is why compasses point towards geographical north.

When you drop a baseball and let it fall to the ground, it feels the force of gravity. This is because the Earth has its own force field, which we call a **gravitational field.** Just as we did with the bar magnet, we could drop the baseball at different locations, and draw arrows (vectors) to show the size and direction of the force it feels. This map of arrows would be the Earth's gravitational field, shown below. (Technically the baseball should be exactly 1 kilogram, since this is how we define gravitational fields.)

## Lesson Summary

- A
**force field**in physics is a map of a force over a particular area of space. This could be a map of the force the charges inside a compass needle feels, in which case we call it a magnetic field. Or it could be the force on a 1-kilogram mass near to the Earth, in which case we call it a gravitational field. But since both of these fields are maps of forces, they are both force fields. - There are two main types of fields: scalar fields and vector fields. Since force is a vector - it has both size and direction, like an arrow - all force fields are vector fields.
- Examples of force fields include magnetic fields, gravitational fields, and electrical fields.

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## 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:

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 **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**.

A magnetic field is a force field that represents the force that moving charges inside metals feel at different points in space. If you're closer to the magnet, the magnetic field is stronger. If you're further away, it's weaker. Or in other words, the force that the compass needle feels is stronger when it's closer to the magnet.

The magnetic field of a bar magnet looks something like this:

The Earth also has a magnetic field, which is why compasses point towards geographical north.

When you drop a baseball and let it fall to the ground, it feels the force of gravity. This is because the Earth has its own force field, which we call a **gravitational field.** Just as we did with the bar magnet, we could drop the baseball at different locations, and draw arrows (vectors) to show the size and direction of the force it feels. This map of arrows would be the Earth's gravitational field, shown below. (Technically the baseball should be exactly 1 kilogram, since this is how we define gravitational fields.)

## Lesson Summary

- A
**force field**in physics is a map of a force over a particular area of space. This could be a map of the force the charges inside a compass needle feels, in which case we call it a magnetic field. Or it could be the force on a 1-kilogram mass near to the Earth, in which case we call it a gravitational field. But since both of these fields are maps of forces, they are both force fields. - There are two main types of fields: scalar fields and vector fields. Since force is a vector - it has both size and direction, like an arrow - all force fields are vector fields.
- Examples of force fields include magnetic fields, gravitational fields, and electrical fields.

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- Activities
- FAQs

## 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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