A solid spherical conductor has a radius of 12 cm. The electric field at 24 from the center of the sphere has a magnitude of 640 N/C. What is the charge density (in C/m2) on the sphere

Charge density on the sphere = 2.2 × 10⁻⁸ C/m²

Explanation:

Given:

Radius of sphere (r) = 12 cm = 0.12 m

Distance from the electric field R = 24 cm = 0.24 m

Magnitude (E) = 640 N/C

Find:

Charge density on the sphere

Computation:

Charge on the sphere (q) = (1/K)ER²            (K = 9 × 10⁹)

Charge on the sphere (q) = [1/(9 × 10⁹)](640)(0.24)²

Charge on the sphere (q) = 4 × 10⁻⁹ C

Charge density on the sphere = q / [4πr²]

Charge density on the sphere = [4 × 10⁻⁹] / [4(3.14)(0.12)²]

Charge density on the sphere = [4 × 10⁻⁹] / [0.18]

Charge density on the sphere = 2.2 × 10⁻⁸ C/m²