The production of an → electromotive force in a circuit
caused by a variation in the magnetic flux through the circuit.
If this variation is produced by a change in the current flowing in the circuit
itself, it is called → self-induction. If due to
the variation in a current in some other circuit, it is called
mutual induction. See also
→ Faraday's law of induction.

The production of stationary electric charges on an uncharged object
as a result of a charged body being brought near it without touching it.
A positive charge will induce a negative charge, and vice versa.

The induced → electromotive force in a circuit is
equal in magnitude and opposite in sign to the rate of change of the
→ magnetic flux through the surface bounded by the
circuit. Mathematically, it is expressed as:
∇ x E = -∂B/∂t, which is one of the
four → Maxwell's equations.

1) General: The act of inducing, bringing about, or causing.
2) Electromagnetism: A common term for the process by which a body having electric
or magnetic properties produces magnetism, an electric charge, or an
→ electromotive force in a neighboring body without contact.
For more details, see
→ electromagnetic induction;
→ electrostatic induction;
→ magnetic induction.
3) Math.: A method of mathematical proof typically used to establish that a
given statement is true of all natural numbers. It is done by proving that
the first statement in the infinite sequence of statements is true,
and then proving that if any one statement in the infinite sequence of
statements is true, then so is the next one.
4) Logic: Any form of reasoning in which the conclusion, though supported by the
premises, does not follow from them necessarily.
→ inductive reasoning.

A device for producing high-voltage pulses by means of
→ electromagnetic induction. It consists of a primary coil
of a few turns of wire, wound on an iron core, and insulated from a secondary coil of
many turns which surrounds it coaxially. The current in the primary, which is
interrupted periodically, sets up a magnetic field, first big, then zero. This changing
field induces a large voltage in the secondary.

In magnetohydrodynamics, an equation that describes the transport of plasma and magnetic
field lines over time: ∂B/∂t = ∇ x (v x B) +
η∇^{2}B,
where B
is the → magnetic induction, v is the
plasma velocity, and η = (μσ)^{-1} the
→ magnetic diffusivity.
The first term on the right side represents → magnetic advection
and the second term → magnetic diffusion.
The induction equation can also be expressed as: ∂B/∂t = -(v.∇)B + (B.∇)v -
B(∇.v),
where the terms of the right-hand side stand for advection,
stretching, and compression, respectively. Among these terms, net
increase of the field can be done only through the stretching and
compression.

A component of an electromagnetic field which is
the region close to the source (an antenna) where steady-state magnetic and electrostatic forces
can be detected. → radiation field.

1) Same as → magnetic flux density.
2) The production of a magnetic field in a piece of un-magnetized iron or other
→ ferromagnetic substance when a magnet is brought near it.
The magnet causes the individual particles of iron, which act like tiny magnets,
to line up so that the sample as a whole becomes magnetized.