What Defines a Scalar Field vs a Vector Field?

[Ntip]

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?

 

[PeroK]

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.

 

[Ntip]

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.

 

[PeroK]

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.

 

[davenn]

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"