A wire has three different sections as shown in figure. The magnitude of the magnetic field produced at the centre ' 0 ' of the semicircle by three sections together is ( ₀= permiability of free space)

Step-by-step solution

The magnetic field at point O results from summing contributions from all three wire segments. Since O lies along the axis of both straight segments (i) and (iii), the Biot-Savart Law indicates d l r , so d l r = 0 and B_i = B_ iii = 0 . The semicircular arc (ii) of radius R produces a field at its center. For an arc of angle , B = ₀ I 4 R . With = , B_ ii = ₀ I 4 R = ₀ I 4R . The right-hand rule indicates this field is directed into the page. The total field is B_ total = 0 + ₀ I 4R + 0 = ₀ I 4R . A