Oersted's Law

In electromagnetism, Ørsted's law, also spelled Oersted's law, is the physical law stating that an electric current creates a magnetic field.

This was discovered on 21 April 1820 by Danish physicist Hans Christian Ørsted (1777–1851), when he noticed that the needle of a compass next to a wire carrying current turned so that the needle was perpendicular to the wire. Ørsted investigated and found the physical law describing the magnetic field, now known as Ørsted's law. Ørsted's discovery was the first connection found between electricity and magnetism, and the first of two laws that link the two; the other is Faraday's law of induction. These two laws became part of the equations that govern electromagnetism, Maxwell's equations.

Ørsted found that, for a straight wire carrying a steady (DC) current

The direction of the magnetic field at a point, the direction of the arrowheads on the magnetic field lines, which is the direction that the "North pole" of the compass needle points, can be found from the current by the right hand rule. If the right hand is wrapped around the wire so the thumb points in the direction of the current (conventional current, flow of positive charge), the fingers will curl around the wire in the direction of the magnetic field.

The above rules can be generalized to give the modern vector form of Ørsted's law

The line integral of the magnetic field ${\displaystyle \mathbf {B} (\mathbf {x} )\,}$ around any closed curve ${\displaystyle C\,}$ is proportional to the total current ${\displaystyle I\,}$ passing through any surface bounded by the curve.

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