Question

Two long straight conductors carry currents $4A$ and $2A$ into the plane of the paper. A circular path is imagined to be enclosing these currents. The value of $\oint \overrightarrow{B}.\overrightarrow{dl}$ is (The value of magnetic permeability of vacuum is ${\mu }_0$):

• A. $6$${\mu }_0$
• B. $7$${\mu }_0$
• C. $5$${\mu }_0$
• D. $2$${\mu }_0$

Answer 1

Answer: (A)

$6$${\mu }_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
$\varphi =\int \overrightarrow{B}\cdot d\overrightarrow{l}={\mu }_0{i}_{enclosed}$
$={\mu }_0(4+2)$
$=6{\mu }_0$