Maxwell's equations

Maxwell's equations are the set of four equations, attributed to James Clerk Maxwell (written by Oliver Heaviside), that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter.

Maxwell's equations in CGS units

The above equations are given in the International System of Units, or SI for short. In a related unit system, called cgs (short for centimeter-gram-second), the equations take on a more symmetrical form, as follows:

Related Topics:
International System of Units - Centimeter-gram-second

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: abla cdot mathbf{E} = 4pi ho

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: abla cdot mathbf{B} = 0

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: abla imes mathbf{E} = -rac{1}{c} rac{partial mathbf{B}} {partial t}

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: abla imes mathbf{B} = rac{1}{c} rac{ partial mathbf{E}} {partial t} + rac{4pi}{c} mathbf{J}

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Where c is the speed of light in a vacuum. The symmetry is more apparent when the electromagnetic field is considered in a vacuum. The equations take on the following, highly symmetric form:

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: abla cdot mathbf{E} = 0

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: abla cdot mathbf{B} = 0

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: abla imes mathbf{E} = -rac{1}{c} rac{partial mathbf{B}} {partial t}

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: abla imes mathbf{B} = rac{1}{c} rac{partial mathbf{E}}{partial t}

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The force exerted upon a charged particle by the electric field and magnetic field is given by the Lorentz force equation:

Related Topics:
Electric field - Magnetic field - Lorentz force

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: mathbf{F} = q (mathbf{E} + rac{mathbf{v}}{c} imes mathbf{B}),

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where q is the charge on the particle and mathbf{v} is the particle velocity. This is slightly different from the SI-unit expression above. For example, here the magnetic field mathbf{B} has the same units as the electric field mathbf{E} .

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