Consider an infinite vertical sheet carrying current out of the page. The sheet has a uniform current per unit length J_s.

We should assume the field is uniform on either side of the sheet. What direction is the field to the right of the sheet?

1. right
2. left
3. up
4. 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 = μ_o I_enc

How much current passes through the loop? This is the current per unit length multiplied by the length h.

Therefore 2Bh = μ_o J_s h

B = (1/2) μ_o J_s

Compare this to the E = σ/ 2ε_o we had for the electric field from an infinite sheet of charge.