A non conducting material becomes ionized in the presence of very high electric

Question

A non conducting material becomes ionized in the presence of very high electric fields, and in such condition the material becomes a conductor. This phenomenon is called dielectric breakdown. In air for example it occurs when the E_max approximately 3 times 10^6 V/m. If a conducting sphere is charged to a potential V = 12,000 V, what is the smallest possible radius of the sphere so that the electric field E around it will not exceed the air maximum limit for the breakdown? 1.2 times 10^5 m 4.0 times 10^-3 m 250 cm 0

Explanation / Answer

Potential energy of Sphere =kQ/R

kQ/R=12000

Q=12000*R/K

Now electric field =kQ/R^2

k*(12000*R/k)/R^2=3*10^6

12000/R=3*10^6

R=4.0*10^-3 m

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