The figure shows a cross -section of along thin ribbon of width b that is carrying a uniformly disturbed total current i into the page. Calculate the magnitude and direction of the magnetic field →B at a point P in the plane of the ribbon at a distance afrom its edge.
Take a small element of thickness dx at a distance x from P. The current in the element is di=ibdx,
and magnetic at P, dB=μ02πdix=μ02π(ib)dxx
The total field B=μ02πib∫(a+b)adxs=μ02πib|lnx|(a+b)a=μ02πib In (a+b)a