Question

Three long straight conductors are kept perpendicular to the plane of paper. Currents $2A$, $3A$ are passing through the two conductors into the plane of paper in first two conductors and $5A$ current passes through third conductor, directed out of the paper. A closed loop encloses the conductors, then the value of $\int \overrightarrow{B}.d\overrightarrow{l}$ over the closed loop is (assume current into the paper as negative and out of the paper as positive)

• A. $2\mu$
• B. $0$
• C. $10\mu$
• D. $+\mu$

Answer 1

The correct option is B $0$

Using ampere's circuital law,
The line integral of magnetic field in a closed loop equals ${\mu }_{0}i$ , where i is the current enclosed by the loop
$\overrightarrow{B}.d\overrightarrow{l}={\mu }_{0}i$
$={\mu }_0(2+3-5)$
$=0$