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)
“While each child is born with his or her own distinct genetic potential for physical, social, emotional and cognitive development, the possibilities for reaching that potential remain tied to early life experiences and the parent-child relationship within the family.”
—Bernice Weissbourd (20th century)
“For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
—Ralph Waldo Emerson (1803–1882)
“The habit of common and continuous speech is a symptom of mental deficiency. It proceeds from not knowing what is going on in other people’s minds.”
—Walter Bagehot (1826–1877)