Question

Consider six wires coming into or out of the page as shown in figure, all with the same current. Rank the line integral of the magnetic field from most positive to most negative taken counterclockwise around each loop shown in the figure given below :

• A. B > C > D > A
• B. B > C = D > A
• C. B > A > C = D
• D. C > B = D > A

Answer 1

The correct option is C B > A > C = D

By Ampere's law, we have $\int \overrightarrow{B}.\overrightarrow{dl}={\mu }_{0}I$
For loop $A,\int \overrightarrow{B}.\overrightarrow{dl}={\mu }_0\left(0\right)=0$
For loop B, $\int \overrightarrow{B}.\overrightarrow{dl}={\mu }_0(1+1-1)I={\mu }_{0}I$
For loop C, $\int \overrightarrow{B}.\overrightarrow{dl}=-{\mu }_{0}I$
For loop D, $\int \overrightarrow{B}.\overrightarrow{dl}=-{\mu }_{0}I$
$\Rightarrow B>A>C=D$