A long wire carrying a current i is bent to create a plane angle . Determine the magnetic field B at a point located on the angle bisector at a distance x from the vertex.

Step-by-step solution

The bent wire can be considered as two semi-infinite straight wires joined at the vertex. Let the point on the angle bisector be P , located at a distance x from the vertex. The perpendicular distance d from P to each semi-infinite wire is given by: d = x ( 2 ) For each semi-infinite wire, the magnetic field at P is determined by the angles subtended by its ends at P with respect to the perpendicular. One end extends to infinity, subtending an angle ₂ = 2 . The other end is at the vertex, subtending an angle ₁ = 2