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Vector Fields

Module by: Paul Padley

Summary: What is a Vector Field?

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

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 a vector 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 the surfaceflux = (average normal component ) ⋅ ⋅ (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 of similar magnitude are colored similarly in these plots)

Figure 1
Figure 1 (VectorFields.gif)

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