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## Homework Statement

(a) Find faraday tensor in terms of ##\vec E## and ## \vec B ##.

(b) Obtain two of maxwell equations using the field relation. Obtain the other two maxwell equations using 4-potentials.

(c) Find top row of stress-energy tensor. Show how the b=0 component relates to j.

## Homework Equations

## The Attempt at a Solution

__Part (a)__

[/B]

The relations between the potentials and fields are:

[tex] \vec B = \nabla \times \vec A [/tex]

[tex]\vec E = -\nabla \phi - \frac{\partial \vec A}{\partial t} [/tex]

The four-vector potential is given by ## A = \left( \frac{\phi}{c}, \vec A \right)##.

From the relation given: ## F^{ab} = \partial^{a} A ^b - \partial^b A^a ##, it looks something like ##\nabla \times A##. How do I show this? I've read the basics of tensor notation and seems alright, but I can't seem to apply the knowledge.