Determine the magnetic field due to an infinite sheet of current.
Answers
Consider an infinite vertical sheet carrying current out of the page. The sheet has a uniform current per unit length Js.
We should assume the field is uniform on either side of the sheet. What direction is the field to the right of the sheet?
right
left
up
down
The field is up on the right of the sheet and down on the left.
Apply Ampere's Law to determine the magnetic field. What shape should we choose for our amperian loop?
We'll go with a loop a height h. For both the top and bottom sides B • ds is zero because the field is perpendicular to those sides.
If we go counter-clockwise around the loop both the right and left sides of the loop give:
∫ B • ds = B h
Since there are two of these, 2Bh = μo Ienc
How much current passes through the loop? This is the current per unit length multiplied by the length h.
Therefore 2Bh = μo Js h
B = (1/2) μo Js
Compare this to the E = σ/ 2εo we had for the electric field from an infinite sheet of charge.