A current $\backslash ($ I $\backslash )$ flows around the rectangular loop shown in the accompanying figure. For which of the paths shown is the integral $\backslash (\backslash$oint $\backslash$vec$\{$B$\}\backslash$cdot d $\backslash$vec$\{$l$\}\backslash )$ the same?

Hints: Paths A $\backslash$& C are "linked" to the rectangular loop like smaller key rings on a big key ring. Path B is as if it were a large hula hoop through which the rectangular loop is passing. Path D is like a hula hoop that is dangling off the corner of a table $($the rectangular loop being the edge of the table$).$

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Select the correct answer

The integrals around $\backslash ($ A B $\backslash )$ and $\backslash ($ C $\backslash )$ are all the same, but the integral around $\backslash ($ D $\backslash )$ is

different.

The integrals around $\backslash ($ A $\backslash )$ and $\backslash ($ C $\backslash )$ are the same and the integrals around $\backslash ($ B $\backslash )$ and $\backslash ($ D $\backslash )$ are the same.

Only the integrals around $\backslash ($ A $\backslash )$ and $\backslash ($ C $\backslash )$ are the same

The integral is the same around every path.

The integral is different around each path.