Two long conductors are arranged as shown above to form overlapping cylinders, each of raidus $r$, whose centers are separated by a distance $d$. Current of density $J$ flows into the plane of the page along the shaded part of one conductor and an equal current flows out of the plane of the page along the shaded portion of the other, as shown. What are the magnitude and direction of the magnetic field at point $A?$
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Field due to one conducts is $B$ By Ampere circuit law
$\oint_{s} \vec{B} \cdot \overrightarrow{d l}=\mu_{0} \Sigma I$
$B_{1} \times\left(2 \pi \frac{d}{2}\right)=\mu_{0} J \times \pi\left(\frac{d}{2}\right)^{2}=\frac{\mu_{0} d J}{4}$
$B=2 B_{1}=\left(\frac{\mu_{0}}{2 \pi}\right) 2 d J$
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