Question

A solid conducting sphere has a net charge of +23.0 microC uniformly distributed across its surface. If the sphere has a radius of 38.0 mm, what is the surface charge density on the sphere's surface?

A. 1.27 mC/m²

B. 3.80 mC/m²

C. 0.100 mC/m²

D. 5.07 mC/m²

Answer 1

The surface charge density on the sphere's surface is approximately 0.100 mC/m².

Step-by-step explanation:

The surface charge density of a conducting sphere can be found using the equation q = σ(4πR²), where q is the net charge on the sphere, σ is the surface charge density, and R is the radius of the sphere. In this question, the net charge on the sphere is +23.0 μC and the radius is 38.0 mm. Converting the radius to meters, we have R = 0.038 m. Substituting the values into the equation, we get 23.0 × 10^-6 C = σ(4π(0.038)^2 m²). Solving for σ, we find that the surface charge density on the sphere's surface is approximately 0.100 mC/m².