A very long cylindrical wire is carrying a current $I_{o}$ distributed uniformly over its cross-section area. $O$ is the centre of the cross-section of the wire and the direction of current in into the plane of the figure. The value of $\int_{A}^{B} \vec{B} . \vec{dI}$ along the path $AB$ (from $A$ to $B$ ) is

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According to Ampere's circuital law ∮ B → . dl → = μ 0 I net For the closed path OAB ∮ B → . dl → = ∫ O A B → . dl → + ∫ A B B → . dl → + ∫ B O B → . dl → = μ 0 - I 0 6 Since the magnetic field is perpendicular to the paths OA and BO ∫ A B B → . dl → = - μ 0 I 0 6

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