Chapter 28, Problem 23P

(III) A very long flat conducting strip of width d and negligible thickness lies in a horizontal plane and carries a uniform current I across its cross section. (a) Show that at points a distance y directly above its center, the field is given by

     $B=\frac{{\mu }_{0}I}{\pi d}{\tan }^{-1}\frac{d}{2y},$

assuming the strip is infinitely long. [Hint: Divide the strip into many thin “wires,” and sum (integrate) over these.] (b) What value does B approach for $y\gg d$? Does this make sense? Explain.