Question

Two long conductors (shaded parts) of radius $r$ are arranged as shown in figure. Their axes are separated by a distance $d$. Current of equal density $J$ flow in both conductors, directed into the page in one conductor and directed out-of-the page in other. The magnitude and direction of magnetic field at point $A$ are

Diagram

• A. $\frac{{\mu }_{0}Jd}{2}$, in $+y$ direction
• B. $\frac{{\mu }_{0}J{d}^2}{2\pi r}$, in $-y$ direction
• C. $\frac{{\mu }_{0}Jd}{2}$, in $-y$ direction
• D. $\frac{{\mu }_{0}J{r}^2}{2\pi d}$, in $+y$ direction

Answer 1

The correct option is C $\frac{{\mu }_{0}Jd}{2}$, in $-y$ direction

Use cylindrical caivty formula,
$B=\frac{{\mu }_{0}Jd}{2}$ along $-y$ direction.