Biot–Savart law

The Biot–Savart law gives the magnetic field produced at a point by steady electric currents, expressing each current element’s contribution in terms of its direction, strength, and distance.

Magnetic field: A vector field describing magnetic influence and the forces it exerts on moving charges and magnetic materials. The law calculates this field from steady electric currents.
Ampère's circuital law: An integral law relating the circulation of a magnetic field around a closed path to the enclosed electric current. Symmetry often makes it faster than direct Biot–Savart integration.
Electric current: The rate at which electric charge passes through a surface. Steady current is the source quantity distributed along conductors in the law.
Ampère–Maxwell law: A Maxwell equation relating magnetic-field circulation to electric current and changing electric flux. Unlike the magnetostatic Biot–Savart law, it accounts directly for changing electric fields.
Current element: An idealized infinitesimal segment of a conductor carrying electric current. The law assigns a differential magnetic-field contribution to each segment.
Magnetic field of a straight wire: The magnetic field surrounding a long, straight conductor carrying steady current. Integrating the law along a straight wire gives a field that circles the wire.
Coulomb's law: A law giving the electrostatic force between stationary point charges as proportional to their charge product and inversely proportional to distance squared. It offers a useful comparison: the Biot–Savart law describes magnetic fields from currents rather than electric forces between charges.
Maxwell's equations: A set of four equations describing how electric and magnetic fields arise and interact with charges and currents. The law is consistent with their magnetostatic limit, but is not the general time-dependent field solution.
Cross product: A vector operation whose result is perpendicular to two input vectors, with direction set by the right-hand rule. It makes each field contribution perpendicular to both the current element and the displacement to the observation point.
Magnetic field of a circular loop: The magnetic field produced by steady current flowing around a circular conductor. The law gives the field along the loop’s symmetry axis by summing its current elements.

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