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 strip at distance b from the nearer edge.

Solution

Let us consider a thin strip of metal of width dx parallel to the metal strip and at a distance x from the point under consideration. Since it is thin strip of very small width, we can treat it as a long wire carrying a current I dx /w

Now the magnetic field due to this strip, dB = _oI dx / 2x

Now integrate using appropriate limits for x= 0 to x = b on one side and x = b to x = w - 2b on another

Hence, B = dB = _oI dx / 2x

Therefore the required magnetic field = B = (_oI / 2)[ln(w - 2b) - ln(b)]

NOTE: The limit of integration selected is important here. As the point under consideration is b from the one of the edges, The magnetic field generated by \'this b\' would be cancelled by another by \'another b\' on the other side of the point. Hence a total width of 2b will have zero net magnetic field at the point.
That is why we have taken the limit from b to w - 2b