Consider a small black surface of area A = 3.5 cm² maintained at 600 K. Determine the rate at which radiation energy is emitted by the surface through a ring-shaped opening defined by 0 ≤ ϕ ≤ 2π and 40 ≤ θ ≤ 50°, where ϕ is the azimuth angle and u is the angle a radiation beam makes with the normal of the surface.