51. A field is a quantity which can be specified everywhere in

space as a function of position.

2. The quantity that is specified may be a scalar or a vector.

3. For instance, we can specify the temperature at every point in

a room.

4. The room may, therefore, be said to be a region of

temperature field which is a scalar field because thetemperature T (x, y, z) is a scalar function of the position.

5. An example of a scalar field in electromagnetism is the electric

potential.

6 Meanwhile, at each point, the fluid will be moving with a certain speed in a certain direction

That is, each small fluid element has a particular velocity and direction, depending upon whereabouts in the fluid it is.

This is an example of a vector field since velocity is a vector. The velocity can be expressed as a vector function, i.e.

where will each be scalar functions.

kjivv ),,(),,(),,(),,( 321 zyxvzyxvzyxvzyx

321 , vvv and

71-7Example: Linear velocity vector field of

points on a rotating disk

8Physical examples of scalar fields:

Electric potential around a

charge

Temperature near a

heated wall

+

(The darker region representing higher values )