What Defines a Scalar Field vs a Vector Field?

AI Thread Summary
A scalar field is defined by a quantity that has magnitude but no direction, such as temperature in a pan of water, while a vector field includes both magnitude and direction. The discussion highlights confusion around isotropic radiation fields, which decrease in intensity radially but can still be considered scalar fields if they are described by a single intensity value at each point. The key distinction lies in whether the field requires a vector to fully describe it; if only a scalar value suffices, it remains a scalar field. The participants emphasize the importance of understanding these definitions in the context of antenna theory. Clarifying these concepts is essential for grasping the nature of different fields in physics.
Ntip
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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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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.
 
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.
 
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.
 
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:
 

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