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Physics / Physics with MasteringPhysics 4 / Chapter 20 / Problem 61P

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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Lightning As a crude model for lightning, consider the

Chapter 20, Problem 61P

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QUESTION:

Problem 61P

Lightning As a crude model for lightning, consider the ground to be one plate of a parallel-plate capacitor and a cloud at an altitude of 550 m to be the other plate. Assume the surface area of the cloud to be the same as the area of a square that is 0.50 km on a side, (a) What is the capacitance of this capacitor? (b) How much charge can the cloud hold before the dielectric strength of the air is exceeded and a spark (lightning) results?

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QUESTION:

Problem 61P

Lightning As a crude model for lightning, consider the ground to be one plate of a parallel-plate capacitor and a cloud at an altitude of 550 m to be the other plate. Assume the surface area of the cloud to be the same as the area of a square that is 0.50 km on a side, (a) What is the capacitance of this capacitor? (b) How much charge can the cloud hold before the dielectric strength of the air is exceeded and a spark (lightning) results?

ANSWER:

Step 1 of 2:-

Here, we have to find the capacitance of the capacitor.

The plates have are of,

$A=0.50\ \times{}0.50\ k{m}^{2}$

$=0.25\ k{m}^{2}$

$=250000\ {m}^{2}$ .

The separation is,

$d=550\ m$ .

So, the capacitance will be,

$C=\frac{{\epsilon{}}_{0}A}{d}$

$=\frac{8.85\times{}1{0}^{-12}\times{}250000}{550}$

$=4.02\times{}1{0}^{-9}\ F$

$=4.02\times{}1{0}^{-3}\ \mu{}F$

So, the capacitance is $4.02\times{}1{0}^{-3}\ \mu{}F$ .

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