An infinitely long straight conductor carrying current ' I ' is bent into a shape as shown in figure. The radius of the circular loop is ' r '. The magnetic induction at the centre of the loop at point ' o ' is ( ₀= permeability of free space)

Step-by-step solution

Magnetic induction at the center of the loop is found by superposition of contributions from the semicircular arc and both straight conductors. The semicircular loop of radius r with clockwise current I contributes a field directed into the page. For a semicircular arc, the field magnitude is half that of a full loop: B_ loop = ₀ I 4r . The two semi-infinite straight conductors, each carrying current I to the right, are at perpendicular distance r from the center. Each contributes a field directed out of the page w