Question

Charge is continuously fed to a conductor. What should the minimum charge density at any point be to give corona discharge when the conductor is kept in air?
(Dielectric strength of air is $3,000,000\frac{V}{m}$

• A. $4,000,000{\epsilon }_0$
• B. $3,000,000{\epsilon }_0$
• C. $2,000,000{\epsilon }_0$
• D. $1,000,000{\epsilon }_0$

Answer 1

The correct option is B $3,000,000{\epsilon }_0$

Corona discharge takes place when there is dielectric breakdown around a conductor. The dielectric strength of air is given to be $3,000,000\frac{V}{m}$ So, if the conductor creates an electric field more than $3,000,000\frac{V}{m}$ then dielectric breakdown will take place. The electric field produced by a conductor is given by $\frac{\sigma }{{\epsilon }_0}$ , where $\sigma$ is the local charge density
So, $\frac{\sigma }{{\epsilon }_0}$ > 3,000,000
$\Rightarrow \sigma$ > $3,000,000{\epsilon }_0$
So the minimum charge density is $3,000,000{\epsilon }_0$