If the electric ficld strength in air exceeds 3.0 ×10^6 N / C , the air becomes a conductor. Usi

step 1 In this problem on the topic of electric forces and fields, we are told that any electric field

If the electric ficld strength in air exceeds 3.0 ×10^6 N /...

If the electric ficld strength in air exceeds $3.0 \times 10^{6} \mathrm{N} / \mathrm{C}$ , the air becomes a conductor. Using this fact, determine the maximum amount of charge that can be carricd by a metal sphere 2.0 $\mathrm{m}$ in radius. (See the hint in Problem 40.)

Key Concepts

Surface Electric Field of Conductors

At electrostatic equilibrium, the charges on a conductor reside on its surface, creating an electric field just outside that surface. This field is related to the surface charge density and is crucial when determining the maximum charge a conductor can hold before causing phenomena like dielectric breakdown.

Permittivity of Free Space

Denoted by ??, this constant is a measure of the resistance encountered when forming an electric field in a vacuum. It appears in Coulomb's law and Gauss's law, setting the scale for the magnitude of electric fields produced by given charges.

Gauss's Law

A principle in electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface. It is essential for calculating electric fields in symmetric situations and underpins the derivation of formulas for fields around conductors, such as spheres.

Electric Field Strength

This is a measure of the force exerted per unit charge at a point in space, commonly expressed in newtons per coulomb (N/C). It quantifies the influence that electric charges exert on each other and is fundamental in describing electrostatic interactions.

Dielectric Breakdown

This concept refers to the process in which an insulating material (dielectric) suddenly becomes conductive when the applied electric field exceeds a certain critical threshold. In the context of air, surpassing this threshold causes the air to ionize, leading to a breakdown and electrical discharge.

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