Magnetic Field of An Infinite Current Sheet
An infinite current sheet can be modelled as an infinite number of parallel wires all carrying the same current. Assuming each wire carries current I, and there are N wires per unit length, the magnetic field can be derived using Ampère's law:
R is a rectangular loop surrounding the current sheet. In the two sides perpendicular to the sheet, since . In the other two sides, so if S is one parallel side of the rectangular loop of dimensions L x W, the integral simplifies to:
Since B is constant due to the chosen path, it can be pulled out of the integral:
The integral is evaluated:
Solving for B, plugging in for Ienc (total current enclosed in path R) as I*N*L, and simplifying:
Notably, the magnetic field strength of an infinite current sheet does not depend on the distance from it.
The direction of B can be found via the right-hand rule.
Read more about this topic: Current Sheet
Famous quotes containing the words magnetic, field, infinite, current and/or sheet:
“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)
“He stung me first and stung me afterward.
He rolled me off the field head over heels
And would not listen to my explanations.”
—Robert Frost (1874–1963)
“My belief is that science is to wreck us, and that we are like monkeys monkeying with a loaded shell; we don’t in the least know or care where our practically infinite energies come from or will bring us to.”
—Henry Brooks Adams (1838–1918)
“We hear the haunting presentiment of a dutiful middle age in the current reluctance of young people to select any option except the one they feel will impinge upon them the least.”
—Gail Sheehy (b. 1937)
“You take the lake. I look and look at it.
I see it’s a fair, pretty sheet of water.
I stand and make myself repeat out loud
The advantages it has....”
—Robert Frost (1874–1963)