- #1
Mathmos6
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Homework Statement
Hi there - I'm wondering about how you can actually show the existence of a scalar potential for an irrotational vector field E - if [itex] \nabla \times E = 0[/itex] everywhere, then how does one show there exists a scalar potential [itex] \phi(x) [/itex] such that [itex]E=- \nabla \phi [/itex]?
The Attempt at a Solution
By Stokes' theorem we can see that [itex] \int_C E dx = \int_S \nabla \times E dS = 0 [/itex] everywhere so our integral is path independent, but does path independence necessarily prove the existence of a scalar potential?
Thanks a lot, Mathmos6