Can a Vector Be Expanded into a Field in Physics?

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SUMMARY

A vector can indeed be expanded into a field in physics, specifically when discussing vector fields such as gravitational potential. The equation F = -∇V illustrates that a vector field is derived from a scalar potential function V. By expanding a vector across a plane with a point of attraction at the origin, it transforms into a vector field, demonstrating the relationship between vectors and fields in physics.

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maburne2
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Hey everyone,
I was just wondering can a vector be expanded into a field? I.e. take a gravitational potential that can be described by a vector (F = -[tex]\nabla[/tex]V). Can this vector then be expanded into a field given a plane with the point of attraction at the origin, for simplicity.

Thanks
 
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Vectors by themselves are just something that has both magnitude and direction. But what you described (F = - del(V)) is a vector field, which... yeah, is a field.
 
So if I take a vector and expand it throughout some arbitrary plane it makes a field?
 

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