Question

Consider six long wires with current coming 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 counterclockwise 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

Answer: (C)

$B>A>C=D$

Loop $B:{\mu }_0(2i-i)=\oint B.dl$
Loop $C:{\mu }_0(i-2i)=\oint B.dl$
Loop $A:{\mu }_0(3i-3i)=\oint B.dl$
Loop $D:{\mu }_0(0-i)=\oint B.dl$
$B>A>C=D$