Question

Consider six wires carrying same current coming into or out of the page. Rank the line integral of the magnetic field (from most positive to most negative) taken counter-clockwise around each loop shown.

• 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 $B>A>C=D$

According to Ampere's integral law, we know that
$\oint \overrightarrow{B}.dl={\mu }_0{I}_{en}$
Taking current going into the plane as negative and whereas taking current out of the plane as positive,
In loop A, $I_{en}=-3I+3I=0$
In loop B, $I_{en}=2I-I=I$
In loop C, $I_{en}=-2I+I=-I$
In loop D, $I_{en}=-I$

So line integral of the magnetic fields in all loop will be such that,
$B>A>C=D$