Question

Find the greatest surface charge density that can exist on a conductor before dielectric breakdown of the air occurs. The dielectric strength of the air is 3 × 106 V/m and permittivity of free space is 8.85 × 10−12 C 2 /N · m2 .

Answer 1

Answer:

$\sigma_{max}=3*10^{-5}\frac{C}{m^2}$

Explanation:

The electric field on the surface of a conductor is given by:

$E=\frac{\sigma}{\epsilon_0}$

Here $\sigma$ is the surface charge density and $\epsilon_0$ the permittivity of free space. Thus, the highest surface charge density that can exist in a conductor is given by the value of the dielectric breakdown of the air multiplied by the permittivity of free space:

$\sigma_{max}=\epsilon_oE_{breakdown}\\\sigma_{max}=(8.85*10^{-12}\frac{C^2}{N\cdot m^2})(3*10^6\frac{V}{m})\\\sigma_{max}=3*10^{-5}\frac{C}{m^2}$