Oersted's law

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In

This was discovered on 21 April 1820 by Danish physicist

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's rules

Ørsted found that, for a straight wire carrying a steady direct current (DC):^[5]

• The magnetic field lines encircle the current-carrying wire.
• The magnetic field lines lie in a plane perpendicular to the wire.
• If the direction of the current is reversed, the direction of the magnetic field reverses.
• The strength of the field is directly proportional to the magnitude of the current.
• The strength of the field at any point is inversely proportional to the distance of the point from the wire.

Direction of the magnetic field

right hand rule

to find the direction of the magnetic field

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

, flow of positive charge), the fingers will curl around the wire in the direction of the magnetic field.

Vector form of the law

The above rules can be generalized to give the modern vector form of Ørsted's law^[2][6]

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.

${\displaystyle \oint _{C}\mathbf {B} \cdot \mathrm {d} {\boldsymbol {\ell }}=\mu _{0}I\,}$

where ${\displaystyle \mu _{0}\,}$ = 4π×10⁻⁷ V·s/(A·m) is the

magnetic constant

, and the direction of integration around ${\displaystyle C\,}$ is related to the direction of current by the right hand rule. The law can be expressed in terms of the current density ${\displaystyle \mathbf {J} (\mathbf {x} )\,}$ through the surface ${\displaystyle S\,}$ instead of the total current ${\displaystyle I\,}$ through it^[2]

${\displaystyle \oint _{C}\mathbf {B} \cdot \mathrm {d} {\boldsymbol {\ell }}=\mu _{0}\iint _{S}\mathbf {J} \cdot \mathrm {d} \mathbf {S} \,}$

where ${\displaystyle S\,}$ is any surface spanning ${\displaystyle C\,}$.

Ørsted's law only holds for steady currents, which don't change with time. Therefore, it only holds for DC

.

Footnotes

References

• F. W. Sears and M. W. Zemansky 1964 University Physics Third Edition (Complete Volume), Addison-Wesley Publishing Company, Inc. Reading, MA, LCCCN: 63-15265 (no ISBN).