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)
“Swift blazing flag of the regiment,
Eagle with crest of red and gold,
These men were born to drill and die.
Point for them the virtue of slaughter,
Make plain to them the excellence of killing
And a field where a thousand corpses lie.”
—Stephen Crane (1871–1900)
“The traditional American husband and father had the responsibilities—and the privileges—of playing the role of primary provider. Sharing that role is not easy. To yield exclusive access to the role is to surrender some of the potential for fulfilling the hero fantasy—a fantasy that appeals to us all. The loss is far from trivial.”
—Faye J. Crosby (20th century)
“God is a being of transcendent and unlimited perfections: his nature therefore is incomprehensible to finite spirits.”
—George Berkeley (1685–1753)
“I can never get people to understand that poetry is the expression of excited passion, and that there is no such thing as a life of passion any more than a continuous earthquake, or an eternal fever. Besides, who would ever shave themselves in such a state?”
—George Gordon Noel Byron (1788–1824)