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)
“Raising a daughter is an extremely political act in this culture. Mothers have been placed in a no-win situation with their daughters: if they teach their daughters simply how to get along in a world that has been shaped by men and male desires, then they betray their daughters’ potential But, if they do not, they leave their daughters adrift in a hostile world without survival strategies.”
—Elizabeth Debold (20th century)
“Sisters define their rivalry in terms of competition for the gold cup of parental love. It is never perceived as a cup which runneth over, rather a finite vessel from which the more one sister drinks, the less is left for the others.”
—Elizabeth Fishel (20th century)
“We read poetry because the poets, like ourselves, have been haunted by the inescapable tyranny of time and death; have suffered the pain of loss, and the more wearing, continuous pain of frustration and failure; and have had moods of unlooked-for release and peace. They have known and watched in themselves and others.”
—Elizabeth Drew (1887–1965)