A wire carrying a steady current of 6 A is bent to form a circular arc of radius 2 cm. The ends of the arc are connected to two straight, semi-infinite wires that point radially outward from the center of the arc. If the magnitude of the magnetic field at the center of the arc is 10 T, the angle subtended by the arc at the center is: (Given permeability of vacuum ₀ = 4 10⁻⁷ T m A ⁻¹ )

Step-by-step solution

The straight semi-infinite wires are directed radially outward from the center, meaning the position vector of the center with respect to any point on these wires is collinear with the current element. Thus, they produce zero magnetic field at the center. The entire magnetic field at the center is due to the circular arc. The magnetic field produced by an arc of radius R subtending an angle (in radians) is given by: B = ₀ I 4 R Substitute the given values ( I = 6 A, R = 2 10⁻² m, B = 10 10⁻⁶ T): 10 10⁻⁶ = 4 10⁻⁷ 6