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 symmetrically 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 0 direction. Suppose this field has magnitude B.

The field on the opposite side of the sheet at the same distance will also be B but in opposite direction . Applying Ampere 's law to the rectangle shown in figure.
`2Bl=mu_(0)Kl " " or, " " B=(1)/(2)mu_(0)K`.
Note that it is independent of x.