Assuming the strip to be made up of a large number of elements parallel to its length, consider an element of length dx at a distance x from the point P. Treating the element as a long current-carrying wire,
\(dB = \frac {\mu _0}{4 \pi} \frac {2I'}{x}\)
Now as the current in the strip of width b is I, so the current in the element of width dx will be
\(I'= \frac {I}{b}dx\)
and hence,
\(dB = \frac {\mu _0}{4 \pi}\frac {2I}{b} \frac {dx}{x}\)
So, \(B = \frac {\mu _0}{4\pi} \frac {2I}{b} \int ^{a+b}_a \frac {dx}{x}= \frac {\mu _0}{4\pi} \frac {2I}{b} log _e 1 + \frac {b}{a}\)
