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Laws of Electromagnetism

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Faraday's Law of Electromagnetic Induction

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Faraday's law states that the induced electromotive force (EMF) in any closed circuit is equal to the negative rate of change of the magnetic flux through the circuit. It is integral in understanding how electric generators and transformers work.

ext{EMF} = - rac{d ext{flux}}{dt}

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Gauss's Law for Electricity

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Gauss's law states that the net electric flux through a closed surface is directly proportional to the enclosed electric charge. Used broadly in electric field calculations.

abla ullet E = rac{ ho}{ ext{ε}_0}

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Gauss's Law for Magnetism

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Gauss's law for magnetism states that the net magnetic flux through a closed surface is zero. This implies that there are no 'magnetic charges' analogous to electric charges, and that magnetic field lines are closed loops.

abla ullet B = 0

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Ampère's Circuital Law

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Ampère's law states that the integral of the magnetic field B around a closed loop is proportional to the electric current I passing through the loop. It's fundamental in electromagnetism for calculating the magnetic field generated by a current.

igoint B ullet dl = ext{μ}_0(I + ext{ε}_0 rac{d ext{flux}}{dt})

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Lorentz Force Law

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The Lorentz force law describes the force on a charged particle moving in an electric (E) and magnetic (B) field. This fundamental law is the basis for many electric devices like motors and particle accelerators.

F=q(E+vimesB)F = q(E + v imes B)

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