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Consider an infinite solenoid (ideal solenoid) with n turns per length unit, through which a current () flows. The magnetic field inside the solenoid is, = (1) while the field outside the solenoid is null. From the second and third Maxwell's equations,
An infinite solenoid has infinite length but finite diameter. "Continuous" means that the solenoid is not formed by discrete finite-width coils but by many infinitely thin coils with no space between them; in this abstraction, the solenoid is often viewed as a cylindrical sheet of conductive material.
The infinite element method is a numerical method for solving problems of engineering and mathematical physics. It is a modification of finite element method . The method divides the domain concerned into sections of infinite length.
The length of is the largest length of any of its chains. If no such largest length exists, we say that M {\displaystyle M} has infinite length . Clearly, if the length of a chain equals the length of the module, one has M 0 = 0 {\displaystyle M_{0}=0} and M n = M . {\displaystyle M_{n}=M.}
A decision problem is a question which, for every input in some infinite set of inputs, requires a "yes" or "no" answer. [2] Those inputs can be numbers (for example, the decision problem "is the input a prime number?") or values of some other kind, such as strings of a formal language.
Without power, the plunger extends for part of its length outside the coil; applying power pulls the plunger into the coil. Electromagnets with fixed cores are not considered solenoids. In simple terms, a solenoid converts electrical energy into mechanical work. Typically, it has a multiturn coil of magnet wire surrounded by a frame, which is ...
A solenoid is a long, thin coil; i.e., a coil whose length is much greater than its diameter. Under these conditions, and without any magnetic material used, the magnetic flux density B {\displaystyle B} within the coil is practically constant and is given by B = μ 0 N i ℓ {\displaystyle B={\frac {\mu _{0}\,N\,i}{\ell }}}
In two dimensions, for a vortex line of infinite length, the induced velocity at a point is given by = where Γ is the strength of the vortex and r is the perpendicular distance between the point and the vortex line. This is similar to the magnetic field produced on a plane by an infinitely long straight thin wire normal to the plane.
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