This is a consequence of symmetry and Ampère's circuital law.

Ampère's circuital law, connects the direction of an electric current and its associated magnetic currents.

In its original form, Ampère's circuital law relates a magnetic field to its electric current source.

Equation (112) is Ampère's circuital law, with Maxwell's addition of displacement current.

Therefore, from Ampere's circuital law, the intensity of the B field must be zero outside the windings.

This version of the rule is used in two complementary applications of Ampère's circuital law:

Hence derive a generalized form of Amp res circuital law that will apply in general even if circuits are not closed.

Faraday's law of induction is the dual of Ampère's circuital law.

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It was also in this 1861 paper that Maxwell first introduced the displacement current term which is now included in Ampère's circuital law.

The laws of primary interest are Ampère's circuital law (with the displacement current density neglected) and the magnetic flux continuity law.

The London penetration depth results from considering the London equation and Ampère's circuital law.

The equations in each vertical column are balance equations, circuital equations and gradient-forming equations.

He added this displacement current to Ampère's circuital law at equation (112) in his 1861 paper On Physical Lines of Force.

In 1826 André-Marie Ampère developed Ampère's circuital law showing that electric current produces a magnetic field.

In electrostatics and electrodynamics, Gauss's law and Ampère's circuital law are respectively:

Ampère's equation was extended by including the polarization current, thereby remedying the limited applicability of the original Ampère's circuital law.

The current density is an important parameter in Ampère's circuital law (one of Maxwell's equations), which relates current density to magnetic field.

The first tensor equation is an expression of the two inhomogeneous Maxwell's equations, Gauss's law and Ampere's circuital law.

The other three are Gauss's law for magnetism, Faraday's law of induction, and Ampère's circuital law.

Ampère's circuital law, discovered by André-Marie Ampère in 1826, relates the magnetic field around a closed loop to the electric current passing through the loop.

Magnetostatics covers calculations of the magnetic field and the Lorentz force using the Biot-Savart law and Ampere's circuital law.

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That equation is another way of writing the two inhomogeneous Maxwell's equations (namely, Gauss's law and Ampère's circuital law) using the substitutions:

However, an improved understanding of electromagnetism in the nineteenth century showed that the magnetism of lodestones was properly explained by Ampère's circuital law, not magnetic monopole fluids.