Fields, vectors and scalars...

[GutZ]

Walk into a bar...

 

No sorry, I am wondering if someone would like to attempt to explain what exactly is a field in terms of physics.

 

Is it a place in space that has special properties? Do all forces have a field and what the different if they are vector or scalar. EXACTLY, and as simplistic as possible. So Norman don't even think about it.

[ydoaPs]

A field is a region where every point has a value. There are vector fields(such as magnetic fields) where at every point there is a vector. There are also scalar fields(such as temperature) where at every point there is a scalar.

[Royston]

A field is a region where every point has a value.

 

That's about as succinct as you can get to describe a field (there will always be a unit with the value). However, here's some simple examples, which you can look up.

 

Isotherms, which you can find on weather reports, are an example of a scalar field, being lines that connect the same temperature. So if you had a map of Ontario, with a number of wavy lines over the top (not crossing) each with it's own value, that would be an example of a scalar field. The same is true for pressure (isobars) which I'm sure you're already familiar with.

 

A vector which has magnitude and direction, will therefore in this context be a field comprised of arrows. So take another map of Ontario, with arrows pointing in the direction of the wind stuck on top, every arrow gives you the direction and magnitude of the wind at that given point. So each arrow represents the winds velocity, at that particular point.

 

EDIT: Thread belongs in general physics

 

Mod note: moved

Edited April 3, 2009 by swansont
add mod note

[Mr Skeptic]

A scalar is your regular number (eg pi). A vector is a magnitude and direction (often written as a set of its components in the x, y, and z directions). A field is like ydoaps said, for every point (eg in 3D space) there is a value.

[GutZ]

wow it is just that simple eh? I swear it had to be harder.

[ajb]

A field is a region where every point has a value.

 

You should take the work "value" as widely as possible. A field is an assignment of a mathematical object to each point of space (a manifold).

 

It could be a number, a complex number, a matrix, something Lie algebra valued etc. The important thing is that the field itself does not need to be something observable.

 

The more high brow answer is that a field is a section of a fibre bundle over space-time.