Two wires with currents (2,A) and (1,A) are enclosed in a ci... | Physics | SolveeIt | Solveeit

Today, August 18

Question

Two wires with currents $2\,A$ and $1\,A$ are enclosed in a circular loop. Another wire with current $3\, A$ is situated outside the loop as shown. Then $\oint{\overrightarrow{B}}.\overrightarrow{dl}$ around the loop is

A

${{\mu }_{0}}$

B

$3{{\mu }_{0}}$

C

$6{{\mu }_{0}}$

D

$2{{\mu }_{0}}$

Answer

${{\mu }_{0}}$

Explanation

Solution

Amperes law states that the line integral of $\overrightarrow{B}$ around any closed path or circuit is equal to ${{\mu }_{0}}$ times the total current crossing the area bounded by the closed path provided the electric field inside the loop remain constant. Thus,
$\int{\overrightarrow{B}}.\overrightarrow{dl}={{\mu }_{0}}{{i}_{net}}$ $={{\mu }_{0}}(3-2)={{\mu }_{0}}$