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

`\sigma_(max)=3*10^(-5)(C)/(m^2)`

Step-by-step explanation:

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

`E=(\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)(C^2)/(N\cdot m^2))(3*10^6(V)/(m))\\\sigma_(max)=3*10^(-5)(C)/(m^2)`