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)
“Last night I watched my brothers play,
The gentle and the reckless one,
In a field two yards away.
For half a century they were gone
Beyond the other side of care
To be among the peaceful dead.”
—Edwin Muir (1887–1959)
“Views of women, on one side, as inwardly directed toward home and family and notions of men, on the other, as outwardly striving toward fame and fortune have resounded throughout literature and in the texts of history, biology, and psychology until they seem uncontestable. Such dichotomous views defy the complexities of individuals and stifle the potential for people to reveal different dimensions of themselves in various settings.”
—Sara Lawrence Lightfoot (20th century)
“God is a being of transcendent and unlimited perfections: his nature therefore is incomprehensible to finite spirits.”
—George Berkeley (1685–1753)
“There was a continuous movement now, from Zone Five to Zone Four. And from Zone Four to Zone Three, and from us, up the pass. There was a lightness, a freshness, and an enquiry and a remaking and an inspiration where there had been only stagnation. And closed frontiers. For this is how we all see it now.”
—Doris Lessing (b. 1919)