3.1 Vector fields

Vector fields

A vector field can be considered a map of vectors over some space. . For example if one were to show wind vectors on a weather map; that would be avector field. The electric field surrounding a charge is a vector field (were is the potential around the charge is a scalar field).

The flux of a vector field through a closed surface is the average outward normal component of the vector times the area of thesurfaceflux = (average normal component ) $\cdot$ (surface area)

Three vector fields are shown below. Which represents the electric field eminating from a positive point charge in the middle? (Note that vectors ofsimilar magnitude are colored similarly in these plots)