Positive charge Q is distributed uniformly throughout an insulating sphere of radius R, centered at the origin. A particle with a positive charge Q is placed at x = 2R on the x axis. The magnitude of the electric field at x = R/2 on the x axis is:

Question

Quizplus · Accepted Answer

The electric field inside a uniformly charged sphere at a distance r from the center is given by E = (Q * r) / (4πε₀R³). At x = R/2, the field due to the sphere is (Q * (R/2)) / (4πε₀R³) = Q / (8πε₀R²). The field due to the point charge at x = 2R is Q / (4πε₀(3R/2)²) = Q / (9πε₀R²). The net field is the vector sum of these fields: Q / (8πε₀R²) - Q / (9πε₀R²) = 7Q / (72πε₀R²) = 7Q / (18πε₀R²).

Positive Charge Q Is Distributed Uniformly Throughout an Insulating Sphere π\piπ

Positive Charge Q Is Distributed Uniformly Throughout an Insulating Sphere $\pi$