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 distnace ‘x’ from ‘P’ and of width ‘dx’. Due to this the magnetic field at ‘P’ is ‘dB’
`dB=(mu_(0)((I)/(w)dx))/(2pix)ox`
due to each such wire `vecB` will be directed inwards
`therefore B_(res)=intdB=(mu_(0)I)/(2piw)`
`underset(x=a)overset(a+w)int(dx)/(x)=(mu_(0)I)/(2piw).ln.(a+w)/(a)`