Figure shows a cross-section of a large metal sheet carrying an electric current along its axis. The current in a strip of width is k where k is a constant. Find the magnetic field at apoint P at a distance x From the metal sheet.

Explanation

Consider two strips R and S of the sheet situated symmetrically on the two sides of P. The magnetic field at P above sheet and below sheet is parallel to sheet as shown in figure. There is no field perpendicular to the sheet.


Now applying Ampere.s law to the closed path 1-2-3-4-1 as shown in fig.
`oint vecB.d vec(l) = mu_0 i_("in")`
`int_(1)^(2)vecB.vec(dl) + int_(2)^(3) vecB.vec(dl) + int_(3)^(4) vecB.vec(dl) = mu_0 (kl)`
or `Bl + 0 + Bl +0 = mu_0kl or B = (mu_0k)/(2)`