# Difference between Scalar and Vectorial fields ?

1. Oct 5, 2014

### mark_usc

Dear all!

I think the main difference between scalar and vector fields is that vectorial fields are composed of vector elements that varies among them.

Scalar fields are fields that have large regions of equal magnitude, variations are just presented in different regions.

Please bring me help to make an exact differentiation in essence of what makes an scalar or vector fields.

With all the best

Marco Uscanga

2. Oct 5, 2014

### Staff: Mentor

No your understanding is wrong scalar fields means simply that at every point in the space there is assigned a value. If you were to take the gradient of the scalar field as an example, you would have a vector field where there is now a vector for every point in the space. The vector happens to point in the direction where the scalar value increases the most.

Think of a topological map of some island with a mountain somewhere on it. You could define a scalar elevation value for every GPS coordinate on the island. That's a scalar field. Now if you perform the gradient on the scalar field you'd get a vector pointing in the direction of greatest slope.

I'm sure there's a more mathematical definition for scalar and vector fields that someone will post shortly.

3. Oct 5, 2014

### Matterwave

To understand the difference between a scalar field and a vector field, one must first understand the difference between a scalar and a vector. A scalar or vector field is then simply a scalar or vector attached at each point in space (or space-time as is the case in relativity).

The most basic distinction is that a scalar is one single number, it only has a magnitude, while a vector has magnitude and direction, and is described by n-numbers where n is the dimension of your underlying space (n=3 for regular 3 dimensional space that we are familiar with).

There are some more mathematically precise formulations of these ideas, but at this point, I don't think they will do you any good.