Magnetic Field and Vector Potential For Finite Continuous Solenoid
A finite solenoid is a solenoid with finite length. Continuous means that the solenoid is not formed by discrete coils but by a sheet of conductive material. We assume the current is uniformly distributed on the surface of it, and it has surface current density K. In cylindrical coordinates:
The magnetic field can be found by vector potential. The vector potential for a finite solenoid with radius a, length L in cylindrical coordinates is is:
where
The, and are complete elliptic integral of first, second, and third kind.
By using
the magnetic flux density is:
Read more about this topic: Solenoid
Famous quotes containing the words magnetic, field, potential, finite and/or continuous:
“We are in great haste to construct a magnetic telegraph from Maine to Texas; but Maine and Texas, it may be, have nothing important to communicate.”
—Henry David Thoreau (1817–1862)
“It is through attentive love, the ability to ask “What are you going through?” and the ability to hear the answer that the reality of the child is both created and respected.”
—Mary Field Belenky (20th century)
“Children are potentially free and their life directly embodies nothing save potential freedom. Consequently they are not things and cannot be the property either of their parents or others.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“All finite things reveal infinitude:”
—Theodore Roethke (1908–1963)
“For good and evil, man is a free creative spirit. This produces the very queer world we live in, a world in continuous creation and therefore continuous change and insecurity.”
—Joyce Cary (1888–1957)