Rank the value of oint vec{B} cdot dvec{l} fo | vedclass

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(B) According to Ampere's circuital law,$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{	ext{enclosed}}$.Let the current flowing out of the plane be positiv

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$a, c, d, b$

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(B) According to Ampere's circuital law,$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{	ext{enclosed}}$.Let the current flowing out of the plane be positive and into the plane be negative.For path $a$: It encloses $2\, A$ (out) and $2\, A$ (in). Net current $I_a = 2 - 2 = 0\, A$.For path $b$: It encloses $2\, A$ (out) and $3\, A$ (out). Net current $I_b = 2 + 3 = 5\, A$.For path $c$: It encloses $2\, A$ (in) and $3\, A$ (out). Net current $I_c = 3 - 2 = 1\, A$.For path $d$: It encloses $2\, A$ (out),$2\, A$ (in),and $3\, A$ (out). Net current $I_d = 2 - 2 + 3 = 3\, A$.Comparing the net currents: $I_a = 0\, A$,$I_c = 1\, A$,$I_d = 3\, A$,$I_b = 5\, A$.Therefore,the order from smallest to largest is $a, c, d, b$.

Rank the value of $\oint \vec{B} \cdot d\vec{l}$ for the closed paths shown in the figure from the smallest to largest.

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