Air becomes a conductor when the electric field strength...

Air becomes a conductor when the electric field strength exceeds $3.0 \times 10^{6} \mathrm{N} / \mathrm{C}$. Determine the maximum amount of charge that can be carried by a metal sphere $2.0 \mathrm{m}$ in radius.

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Key Concepts

Conductors

Conductors are materials in which electric charges can move freely. In a charged conductor, any excess charge resides on its surface, and the electric field just outside the surface can be determined using symmetry and Gauss's law, which is essential for understanding the limits imposed by phenomena like dielectric breakdown.

Dielectric Breakdown

Dielectric breakdown is the process by which an insulating material, like air, becomes conductive when subjected to an electric field that exceeds a critical threshold. This concept sets practical limits to the maximum electric field that a material can withstand before it permits the flow of current.

Electric Field

The electric field is a vector field representing the force per unit charge exerted on a test charge in its vicinity. It is fundamental in determining how charges interact and is calculated from charge distributions using principles such as Coulomb's law or Gauss's law.

Gauss's Law

Gauss's Law is a key concept in electromagnetism that relates the electric flux through a closed surface to the total charge enclosed by that surface. It simplifies the calculation of electric fields, especially around symmetric distributions such as spheres.

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