In Fig. a larger metal sheet of width w carries a current I(uniformly distributed in its width w). Find the magnetic field at point P which lies on the plane of the sheet.

Explanation

To find 'B' at 'P' the sheet can be considered
as collection of large number of infinitely long
wires. Take a long wire at a distance 'x' from
'P' and of width 'dx'. Due to this the magnetic
field at 'P' is 'dB'
`dB=(mu_0(I/wdx))/(2pix) ox`
due to each such wire magnetic field will be directed inwards
`:. B_(res)=intdB=(mu_0I)/(2piw)int_(x=0)^(a+w)(dx)/x=(mu_0I)/(2piw) ln((a+w)/a)`