Ampere's Law

The Ampère's law, was actually discovered by André-Marie Ampère in the year  1826, regarding the integrated magnetic field around  the closed loop to the electricity passing via the loop.

The first Maxwell equation determines the electric field caused by the presence of charges p and is known as Gauss' law. The form of the equation is very similar to the continuity equation discussed before. The charge density p is a source (or sink) of electric field lines. For example, if p corresponds to a positive charge q sitting at some point, the solution for E will be a purely spherically symmetric field that points radially out - away from the charge. This radial field gives rise to the Coulomb force between two charges, which is an inverse square law very similar to Newton's gravitational force law, except that the masses get replaced by charges and the proportionality constant reflecting the strength of the interaction is different.

The second equation - known as Ampere's law - is an equation that links electric and magnetic phenomena. It basically states that electric currents j (or moving charges) may cause magnetic fields around them, similar to the way static charges cause electric fields. In this equation we encounter the cross derivative of the magnetic field, in which the vector of spatial derivatives, denoted as nabla, is applied to the three components of the magnetic field vector B, and the current j acts as a source for that field. Ampere's law explains the deflection of a compass needle, if we bring it close to a wire carrying an electric current. If j corresponds to a current through a thin wire along a straight line, there will be a magnetic field B circling around this line. But the second Maxwell equation also shows that changing electric fields can cause magnetic fields, because dE/dt will be non-zero in that case.

Questionnaire:

• What is Ampere's law?
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