Question

Consider six wires into or out of the page, all with the same current. Rank the line integral of the magnetic field(from most positive to most negative) taken counterclock wise around each loop shown as positive in accordance with right hand screw rule.

• 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 $B>A>C=D$

As line integral of the magnetic field along a closed curve is given as

$\oint \overrightarrow{B}.d\overrightarrow{l}={\mu }_{0}I$

Loop B:$\oint \overrightarrow{B}.d\overrightarrow{l}={\mu }_0(I+I-I)={\mu }_{0}I$

Loop C:$\oint \overrightarrow{B}.d\overrightarrow{l}={\mu }_0(I-I-I)=-{\mu }_{0}I$

Loop D:$\oint \overrightarrow{B}.d\overrightarrow{l}={\mu }_0(-I)=-{\mu }_{0}I$

Loop A:$\oint \overrightarrow{B}.d\overrightarrow{l}={\mu }_0(I+I+I-I-I-I)=0$

$\therefore B>A>C=D$