Vector Calculus for Electromagnetism 42 : Gradient of One Over the Separation Vector
Channel: Adam Beatty
Date: 13/06/2013

In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I work out the gradient of the inverse of the magnitude of the separation vector. This is required in order to prove the Helmholtz Theorem

The Helmholtz theorem is vital to simplify the study of electric and magnetic fields; permitting the introduction of a scalar and magnetic potential. The proof of which is often overlooked, or in my opinion it's just shown to be true.  The proof follows from the Dirac Delta Function (or distribution) which is how I do it. I prove all the necessary machinery required for the proof (which is quite involved in that regard).

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