An infinitely long wire, located on the \( z \)-axis, carries a current \( I \) along the \( +z \)-direction and produces the magnetic field \( \vec{B} \). The magnitude of the line integral \( \int \vec{B}\cdot d\vec{l} \) along a straight line from the point \( \left(-\sqrt{3}\,a,\,a,\,0\right) \) to \( (a,\,a,\,0) \) is given by: \([ \mu_{0} \text{ is the magnetic permeability of free space.}]\)
