Some examples of closed surfaces (left) and open surfaces (right). Left: Surface of a sphere, surface of a torus, surface of a cube. Right: Disk surface, square surface, surface of a hemisphere. (The surface is blue, the boundary is red.)
Faraday's experiment showing induction between coils of wire: The liquid battery (right) provides a current which flows through the small coil (A), creating a magnetic field. When the coils are stationary, no current is induced. But when the small coil is moved in or out of the large coil (B), the magnetic flux through the large coil changes, inducing a current which is detected by the galvanometer (G).
For an open surface Σ, the electromotive force along the surface boundary, ∂Σ, is a combination of the boundary's motion, with velocity v, through a magnetic field B (illustrated by the generic F field in the diagram) and the induced electric field caused by the changing magnetic field.
A diagram of Faraday's iron ring apparatus. The changing magnetic flux of the left coil induces a current in the right coil.
Area defined by an electric coil with three turns.
Faraday's disk, the first electric generator, a type of homopolar generator.
Alternating electric current flows through the solenoid on the left, producing a changing magnetic field. This field causes, by electromagnetic induction, an electric current to flow in the wire loop on the right.
Faraday's homopolar generator. The disc rotates with angular rate {{mvar|ω}}, sweeping the conducting radius circularly in the static magnetic field {{math|B}} (which direction is along the disk surface normal). The magnetic Lorentz force {{math|v × B}} drives a current along the conducting radius to the conducting rim, and from there the circuit completes through the lower brush and the axle supporting the disc. This device generates an emf and a current, although the shape of the "circuit" is constant and thus the flux through the circuit does not change with time.
A wire (solid red lines) connects to two touching metal plates (silver) to form a circuit. The whole system sits in a uniform magnetic field, normal to the page. If the abstract path {{math|∂Σ}} follows the primary path of current flow (marked in red), then the magnetic flux through this path changes dramatically as the plates are rotated, yet the emf is almost zero. After Feynman Lectures on Physics {{Rp|ch17}}

This induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected.

- Faraday's law of induction

The relationship is given by Faraday's law:

- Magnetic flux
Some examples of closed surfaces (left) and open surfaces (right). Left: Surface of a sphere, surface of a torus, surface of a cube. Right: Disk surface, square surface, surface of a hemisphere. (The surface is blue, the boundary is red.)

4 related topics with Alpha

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The shape of the magnetic field produced by a horseshoe magnet is revealed by the orientation of iron filings sprinkled on a piece of paper above the magnet.

Magnetic field

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Vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

Vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

The shape of the magnetic field produced by a horseshoe magnet is revealed by the orientation of iron filings sprinkled on a piece of paper above the magnet.
Right hand grip rule: a current flowing in the direction of the white arrow produces a magnetic field shown by the red arrows.
A Solenoid with electric current running through it behaves like a magnet.
A sketch of Earth's magnetic field representing the source of the field as a magnet. The south pole of the magnetic field is near the geographic north pole of the Earth.
One of the first drawings of a magnetic field, by René Descartes, 1644, showing the Earth attracting lodestones. It illustrated his theory that magnetism was caused by the circulation of tiny helical particles, "threaded parts", through threaded pores in magnets.
Hans Christian Ørsted, Der Geist in der Natur, 1854

, magnetic flux density, is measured in tesla (in SI base units: kilogram per second2 per ampere), which is equivalent to newton per meter per ampere.

are called the Ampère–Maxwell equation and Faraday's law respectively.

Gauss's law for magnetism: magnetic field lines never begin nor end but form loops or extend to infinity as shown here with the magnetic field due to a ring of current.

Maxwell's equations

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Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.

Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.

Gauss's law for magnetism: magnetic field lines never begin nor end but form loops or extend to infinity as shown here with the magnetic field due to a ring of current.
In a geomagnetic storm, a surge in the flux of charged particles temporarily alters Earth's magnetic field, which induces electric fields in Earth's atmosphere, thus causing surges in electrical power grids. (Not to scale.)
Magnetic-core memory (1954) is an application of Ampère's law. Each core stores one bit of data.
Left: A schematic view of how an assembly of microscopic dipoles produces opposite surface charges as shown at top and bottom. Right: How an assembly of microscopic current loops add together to produce a macroscopically circulating current loop. Inside the boundaries, the individual contributions tend to cancel, but at the boundaries no cancelation occurs.

Precisely, the total magnetic flux through a Gaussian surface is zero, and the magnetic field is a solenoidal vector field.

The Maxwell–Faraday version of Faraday's law of induction describes how a time-varying magnetic field corresponds to curl of an electric field.

Lorentz force acting on fast-moving charged particles in a bubble chamber. Positive and negative charge trajectories curve in opposite directions.

Lorentz force

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Combination of electric and magnetic force on a point charge due to electromagnetic fields.

Combination of electric and magnetic force on a point charge due to electromagnetic fields.

Lorentz force acting on fast-moving charged particles in a bubble chamber. Positive and negative charge trajectories curve in opposite directions.
Lorentz' theory of electrons. Formulas for the Lorentz force (I, ponderomotive force) and the Maxwell equations for the divergence of the electrical field E (II) and the magnetic field B (III), La théorie electromagnétique de Maxwell et son application aux corps mouvants, 1892, p. 451. V is the velocity of light.
Charged particle drifts in a homogeneous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (e.g. gravity) (D) In an inhomogeneous magnetic field, grad H
Right-hand rule for a current-carrying wire in a magnetic field B
Lorentz force -image on a wall in Leiden
Lorentz force -image on a wall in Leiden

Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction), and the force on a moving charged particle.

Both of these EMFs, despite their apparently distinct origins, are described by the same equation, namely, the EMF is the rate of change of magnetic flux through the wire.

U.S. NRC image of a modern steam turbine generator (STG).

Electric generator

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Device that converts motive power into electric power for use in an external circuit.

Device that converts motive power into electric power for use in an external circuit.

U.S. NRC image of a modern steam turbine generator (STG).
Early Ganz Generator in Zwevegem, West Flanders, Belgium
The Faraday disk was the first electric generator. The horseshoe-shaped magnet (A) created a magnetic field through the disk (D). When the disk was turned, this induced an electric current radially outward from the center toward the rim. The current flowed out through the sliding spring contact m, through the external circuit, and back into the center of the disk through the axle.
Hippolyte Pixii's dynamo. The commutator is located on the shaft below the spinning magnet.
This large belt-driven high-current dynamo produced 310 amperes at 7 volts. Dynamos are no longer used due to the size and complexity of the commutator needed for high power applications.
Ferranti alternating current generator, c. 1900.
A small early 1900s 75 kVA direct-driven power station AC alternator, with a separate belt-driven exciter generator.
The Athlone Power Station in Cape Town, South Africa
Hydroelectric power station at Gabčíkovo Dam, Slovakia
Hydroelectric power station at Glen Canyon Dam, Page, Arizona
Mobile electric generator
Protesters at Occupy Wall Street using bicycles connected to a motor and one-way diode to charge batteries for their electronics

The principle, later called Faraday's law, is that an electromotive force is generated in an electrical conductor which encircles a varying magnetic flux.