If the magnitude of the electric field at a point in air exceeds about 3x 10^6 N

Question

If the magnitude of the electric field at a point in air exceeds about 3x 10^6 NlC, air, which normally isan excellent insulator, will begin to conduct electri city. What happens is this:such a strong electric field accelerates any free electrons that happen to be floating around so violently that they crash into nearby air molecules with enough energy to ionize them,creating more free electrons, and so on.This creates an avalanche of ionization that frees a huge number of electrons for conduction.

a. What is the maximum charge that you can put on the surface of a non-conducting plastic sphere 1.0 cm in diameter without causing the air to conduct electricity?

b. What is the maximum charge that you can put on the surface of a conducting metal sphere 1.0 cm in diameter without causing the air to conduct electricity?

Explanation / Answer

Here ,

electric field , E = 3 *10^6 N/C

a)

Here, the elecric field due to sphere is given as

E = k*q/R^2

3 *10^6 = 9*10^9 * q /(0.005)^2

q = 8.33 *10^-9 C

the charge is 8.33 *10^-9 C

b)

for a conducting metal sphere , as the charge is all on the surface ,

E = k*q/R^2

3 *10^6 = 9*10^9 * q /(0.005)^2

q = 8.33 *10^-9 C

the charge is 8.33 *10^-9 C

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