A spherical, non-conducting shell of inner radius r₁ = 10 cm and outer radius r₂ = 15 cm carries a total charge Q = 15 μC distributed uniformly throughout the volume of the shell. What is the magnitude of the electric field at a distance r = 12 cm from the center of the shell? (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²) A) 5.75 × 10³ N/C B) zero C) 2.87 × 10⁶ N/C D) 5.75 × 10⁶N/C E) 2.87 × 10³ N/C

Question

Quizplus · Accepted Answer

According to Gauss's law, the electric field at any point outside the shell is the same as if all the charge were concentrated at the center of the shell. Thus, we can consider the shell to be a point charge Q located at the center of the shell. Then, the electric field at a distance r from the center is given by:
E = kQ/r^2
Substituting the given values, we get:
E = (8.99 × 10^9 N ∙ m^2/C^2) × (15 × 10^-6 C) / (0.12 m)^2
E = 2.87 × 10^6 N/C
Therefore, the magnitude of the electric field at a distance of 12 cm from the center of the shell is 2.87 × 10^6 N/C, which is closest to option C (2.87 × 10^13 N/C).

A Spherical, Non-Conducting Shell of Inner Radius R1 = 10

A Spherical, Non-Conducting Shell of Inner Radius R₁ = 10