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)
“The field of doom bears death as its harvest.”
—Aeschylus (525–456 B.C.)
“Much of what contrives to create critical moments in parenting stems from a fundamental misunderstanding as to what the child is capable of at any given age. If a parent misjudges a child’s limitations as well as his own abilities, the potential exists for unreasonable expectations, frustration, disappointment and an unrealistic belief that what the child really needs is to be punished.”
—Lawrence Balter (20th century)
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)
“For Lawrence, existence was one continuous convalescence; it was as though he were newly reborn from a mortal illness every day of his life. What these convalescent eyes saw, his most casual speech would reveal.”
—Aldous Huxley (1894–1963)