Vector Fields vs Scalar Fields

In summary, scalar fields are fields that do not have a direction. An isotropic radiation field is a scalar field because it decreases in intensity radially as you move away from the source.
  • #1
Ntip
53
5
I am looking at antenna theory and just came upon scalar fields. I found an site giving an example of a scalar field as measuring the temperature in a pan on a stove with a small layer of water. The temperature away from the heat source will be cooler than near it but it doesn't have a direction. That would be a scalar field. Then they said if you stir it it would have direction so be a scalar field.

I don't quite understand this which is why I also don't understand how an isotropic radiation field is a scalar field. If it decreases in intensity radially as your move away from the source, how is this not a vector field?
 
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  • #2
Ntip said:
I am looking at antenna theory and just came upon scalar fields. I found an site giving an example of a scalar field as measuring the temperature in a pan on a stove with a small layer of water. The temperature away from the heat source will be cooler than near it but it doesn't have a direction. That would be a scalar field. Then they said if you stir it it would have direction so be a scalar field.

I don't quite understand this which is why I also don't understand how an isotropic radiation field is a scalar field. If it decreases in intensity radially as your move away from the source, how is this not a vector field?
I suspect there are a few typos in there.

A field is a quantity defined at every point in spacetime. If that quantity is a scalar, it's a scalar field; if that quantity is a vector, then it's a vector field.
 
  • #3
PeroK said:
I suspect there are a few typos in there.

A field is a quantity defined at every point in spacetime. If that quantity is a scalar, it's a scalar field; if that quantity is a vector, then it's a vector field.
So since an isotropic radiation field is uniform in the radial direction you can ignore the direction and that makes it a scalar field? It seems like it should be a vector field to me because the direction is in the radial direction. I'll go back and read more on this but I just haven't wrapped my head around it yet.
 
  • #4
Ntip said:
So since an isotropic radiation field is uniform in the radial direction you can ignore the direction and that makes it a scalar field? It seems like it should be a vector field to me because the direction is in the radial direction. I'll go back and read more on this but I just haven't wrapped my head around it yet.
If the radiation field is described by a single number (the intensity) at every point, then it's a scalar field. It's only a vector field if you need a vector at every point to describe the radiation field.
 
  • #5
PeroK said:
I suspect there are a few typos in there.

A field is a quantity defined at every point in spacetime. If that quantity is a scalar, it's a scalar field; if that quantity is a vector, then it's a vector field.

That didnt answer the Q for the OP
"what makes it a scaler or vector field" :wink:
 

What is the difference between a vector field and a scalar field?

A vector field is a mathematical function that assigns a vector to each point in space, while a scalar field assigns a scalar value to each point in space. In other words, a vector field has both magnitude and direction, while a scalar field only has magnitude.

How are vector fields and scalar fields used in science?

Vector fields are used to represent physical quantities such as velocity, force, and electric and magnetic fields. Scalar fields are used to represent physical quantities such as temperature, pressure, and concentration. These fields are essential in understanding and modeling various phenomena in science and engineering.

What are some examples of vector fields and scalar fields?

An example of a vector field is the wind velocity field, which assigns a direction and magnitude to each point in space. An example of a scalar field is the temperature field, which assigns a temperature value to each point in space.

How are vector fields and scalar fields represented?

Vector fields are typically represented using arrows or lines, with the length and direction of the arrows or lines indicating the magnitude and direction of the vector at that point. Scalar fields are represented using a color map or contour lines, with the color or contour level indicating the scalar value at that point.

Can a vector field and a scalar field exist together?

Yes, a vector field and a scalar field can exist together. In fact, many physical phenomena involve both a vector field and a scalar field, such as fluid flow (velocity field and pressure field) and electromagnetic waves (electric and magnetic fields).

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