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Electromagnetic Field

A region of space around a charged particle or current-carrying conductor where a force is exerted on other charged particles; consists of electric and magnetic fields.
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The statement of the theorem

The Electromagnetic Field is represented by the four-potential Aμ=(ϕ/c,A⃗)A^\mu = (\phi/c, \vec{A}). The field strength tensor FμνF_{\mu\nu} is defined as the exterior derivative of this potential:\n\nFμν=∂μAν−∂νAμF_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu\n\nThe physical fields are extracted from the components of this tensor:\n\nE⃗=−∇ϕ−∂A⃗∂t\vec{E} = -\nabla \phi - \frac{\partial \vec{A}}{\partial t} \nB⃗=∇×A⃗\vec{B} = \nabla \times \vec{A} \n\nIn a vacuum, these fields must satisfy the wave equation, ensuring that changes in the distribution of charge or current propagate at the speed of light cc: \n\n(∇2−1c2∂2∂t2)E⃗=0\left( \nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right) \vec{E} = 0