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

We can use the equation for the maximum charge on a conductor before breakdown:

Q = 4πε₀rE

where Q is the charge, ε₀ is the permittivity of free space, r is the radius of the conductor (which we need to find), and E is the electric field strength at breakdown.

We can rearrange this equation to solve for r:

r = Q / (4πε₀E)

Plugging in the given values:

r = (2.0 x 10^-3 C) / (4π(8.85 x 10^-12 F/m) (3.0 x 10^6 V/m))

r ≈ 4.9 m

So the diameter of the sphere is twice this radius, or about 9.8 m, which is closest to answer choice B (4.9 m).

Dielectric Breakdown Occurs in the Air at an Electric Field