Consider a thin strip of metal width w and very long The cur

Consider a thin strip of metal width w and very long. The current in the strip is uniform and directed along its length and the total current is I. Find the magnetic field in the plane of strip at distance b from the nearer edge.

Solution

Consider a thin strip of metal of thickness dx parallel to the metal strip and at a distance x from point P.
this acts as a wire.
current flowing in this strip = I/w*dx
now small magnetic field due to this strip, dB = 0/4*(2Idx/wx)

now integrate using appropriate limits for B = 0 to B = B and x=b to x = b+w

(B,0) dB = 0I/2w (b+w, b) 1/x dx

or

B = 0I/2w ln(1+w/b)

this is the required solution.