Consider an infinitely large sheet of thickness b lying in the xz plane with a u
ID: 2077737 • Letter: C
Question
Consider an infinitely large sheet of thickness b lying in the xz plane with a uniform current density the +z direction. (a) Draw the direction of the magnetic field above and below the sheet (use the left hand diagram above) (b) Draw the direction of the magnetic field within the sheet (use the left hand diagram above). (c) Use Ampere's law to find the magnetic field within the sheet. (d) Use Ampere's law to find the magnetic field above and below the sheet. (e) If the surface current is given by K = lim b J then the magnetic field above and below the surface is (True, False) B =Explanation / Answer
Solution:- Only Question c has been done based on student's instruction.
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?
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 = o Ienc
How much current passes through the loop? This is the current per unit length multiplied by the length h.
Therefore 2Bh = o Js h
B = (1/2) o Js
Compare this to the E = / 2o we had for the electric field from an infinite sheet of charge.