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
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