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 1

The Correct Option is A

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}} $