Scalar and vector fields
This chapter describes the main characteristics of a scalar field from a given sketch of the contours and the main characteristics of a vector field from a given sketch of the field lines. It examines the base vectors of a cylindrical or spherical polar coordinate system in terms of the Cartesian base vectors. Some examples of scalar fields are the barometric pressure in the atmosphere, the distribution of mass in a material body, and the electrostatic potential in the region near an electrically charged object. Other examples of vector fields are the gravitational field of a planet and the magnetic field produced by a magnet. The chapter explores two quantities, flux and circulation, that encompass the physically significant properties of a vector field and play important roles in the description of many physical processes. It discusses two other useful pictorial devices: scalar field contours and vector field lines.