A uniformly charged conducting sphere of 0.2 m diameter has a surface charge density of 70 Cm ⁻² . The electric flux leaving the surface of the sphere is:

Step-by-step solution

The diameter of the sphere is d = 0.2 m, so the radius is r = 0.1 m. The surface area of the sphere is A = 4 r^2 = 4 (0.1)^2 = 0.04 m ^2 . The total charge Q on the sphere is given by Q = A , where = 70 10⁻⁶ C m ⁻² . Q = 70 10⁻⁶ 0.04 = 2.8 10⁻⁶ C. According to Gauss's Law, the electric flux leaving the surface is = Q ₀ . Using ₀ = 8.854 10⁻¹² C ^2 N ⁻¹ m ⁻² : = 2.8 10⁻⁶ 8.854 10⁻¹² = 2.8 3.14159 10⁻⁶ 8.854 10⁻¹² 8.796 10⁻⁶ 8.854 10⁻¹² 0.993 10^6 N C ⁻¹ m ^2 . Rounding to the nearest value, 9.9 10^5 N C ⁻¹ m ^2 . An