As a crude model for lightning, consider the ground to be one plate of a paralle

Question

As a crude model for lightning, consider the ground to be one plate of a parallel-plate capacitor and the cloud to be the other plate. The altitude of the cloud is 600m and its area is 5 km2. How much charge can the cloud hold before the dielectric strength of air is exceeded and the lightning results?

E= 3 000 000 V/m

e0=1.00059

The way I thought you did it was that you find the C first by :

C= (k•e0•A)/d

Then Q=C•E•d to find the charge....

Is this right because I seem to be getting the wrong answer...

Explanation / Answer

I solved the similar problem with different numbers please see the process a ) Side of a square is s = 0.50km Area of a square A = s2 ( 0.5 *103 m ) 2 seperated distance d = 550 m dielectric constant of airis k = 1.00059 Capacitance of a Capacitor is C = ke0 A / d = 1.00059 *8.85*10-12 * ( 0.5*103 m ) 2 / 550 m = 4.0 n F b ) Dielectric strength of air is E = 3*106 V /m V = E * d V = 3*106 V /m *550 m = 1650*106 V Charge on the cloud is Q = CV = 4.0 nF * 1650*106 V = 6.6 C

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