Figure shows a cross section of a large metal. Sheet carrying an electric current along its surface. The current in a strip of width dl is Kdl where K is a constant. Find the magnetic field at a point P at a distance x from the metal sheet.

Explanation

Consider two strips `A` and `C` of the sheet situated symeetrically on the two sides of `P` (figure).The magnetic field at `P` due to the strip `A` is `B_(0)` perpendicular to `AP` and that due to the strip `C` is `B_(c)` perpendicular to `CP`,The resultant of these two is parallel to the width `AC` of the sheet.The field due to the whole sheet will also be in this direction.Suppose this field has magnitude `B`.The field on the opposite side of the sheet at the same distance wll also be `B` but in opposite direction.Applying Ampere's law to the rectangle shown in figure.
`2Bl=mu_(0)lambda l` or `B=1/2mu_(0)lambda`
Note that it is independent of `y`.