Dielectric breakdown occurs in the air at an electric field strength of E_max = 3.0 × 10⁶ V/m. If the maximum charge that can be placed on a spherical conductor is 2.0 × 10^-3 C before breakdown, calculate the diameter of the sphere.

Question

Quizplus · Accepted Answer

The electric field E around a sphere is given by E = kQ/r^2, where k is Coulomb's constant (8.99 × 10^9 N·m²/C²), Q is the charge, and r is the radius. Solving for r using E_max = 3.0 × 10^6 V/m and Q = 2.0 × 10^-3 C gives r ≈ 2.45 m, so the diameter is approximately 4.9 m.

Dielectric Breakdown Occurs in the Air at an Electric Field