Summary: What is a Vector Field?
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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
)
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)
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