8Physical examples of scalar fields:

Electric potential around a

charge

Temperature near a

heated wall

+

(The darker region representing higher values )

9The flow field around an airplane

Electric field surrounding a

positive and a negative charge.

Hurricane

+

Magnetic field lines shown by iron

filings

Physical examples of vector fields:

10

Gradient of Scalar Fields

The gradient of a scalar field is a vector

field,

which points in the direction of the

greatest rate of increase of the scalar field,

and whose magnitude is the greatest rate

of change.

11

grad

x,y,z ctt

dr

Physical meaning: is the local variation of along dr. Particularly, grad is perpendicular to the line = ctt.

grad dr