Lightning and other sparks because of an electrical charge appear when air (that

Question

Lightning and other sparks because of an electrical charge appear when air (that is normally a insulator ) becomes a conductor. The reason is that if the electrical field becomes strong enough because of the charges then the molecules and atoms tear open, and electrons and ions are left behind that form a current. The most electrical field that the atmosphere handles is E = 3.0 *106 N/C. Let´s take a look at charged, conducting ball with radius R=15 cm.

a) How much charge Q is it possible to put into the ball before sparks form?

b) Find the electrical potential of the ball (voltage) at the surface of the ball and at distance L=45 cm from the center of the ball, right before a spark forms.

Explanation / Answer

electric field due to charged conducting sphere E = k*Q/R

E = 3*10^6 N/C

R = radius = 0.15 m

Q = charge

3*10^6 = 9*10^9*Q/0.15

Q = 5*10^-5 C

(b)

potential V = k*Q/L = 9*10^9*5*10^-5/0.45 = 10^6 v

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