A closed loop is formed by two concentric circular arcs of radii cm and 2 cm, connected by two straight radial segments. Both arcs subtend an angle of 90^ at their common center. If a steady current of 16 A flows through the loop, the magnitude of the net magnetic field at the common center is: (Given permeability of vacuum ₀ = 4 10⁻⁷ T m A ⁻¹ )

Step-by-step solution

The magnetic field at the center of a circular arc of radius R subtending an angle is given by B = ₀ I 4 R . The straight radial segments of the loop lie along the lines passing through the center, so they produce zero magnetic field at the center. For the inner arc ( R₁ = cm = 10⁻² m, = 2 rad): B₁ = 4 10⁻⁷ 16 4 10⁻² 2 = 16 10⁻⁵ 2 = 80 T. For the outer arc ( R₂ = 2 cm = 2 10⁻² m, = 2 rad): B₂ = 4 10⁻⁷ 16 4 2 10⁻² 2 = 8 10⁻⁵ 2 = 40 T. Since the loop is closed, the current flows in opposite angular directions in the