Calculating Capacitance and Charge for Lightning Formation

In summary, the capacitance of the parallel-plate capacitor representing lightning is 3.3x10^-7 F and the maximum charge it can hold before producing a spark is 9.9x10^-1 C. These values are obtained by using the formula C = k(8.85x10^-12)A/d and considering the dielectric strength of air to be 3x10^6 V/m.
  • #1
mli273
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1. 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 520 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 0.30 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?


2. C=k(8.85x10^-12)A/d
C=Q/V
Dielectric Strength of air = 3x10^6 V/m
 
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  • #2
a) The capacitance of the capacitor is C = k(8.85x10^-12)(0.3x10^3 m^2)/520 m C = 3.3x10^-7 Fb) The charge held by the cloud before spark (lightning) results can be obtained by solving for Q in the expression C=Q/V. Substituting the values Q = 3.3x10^-7 F x (3 x 10^6 V/m) Q = 9.9x10^-1 C
 

What is "Lightning as a Capacitor"?

"Lightning as a Capacitor" refers to the concept that a lightning bolt acts as a large capacitor, storing and releasing electrical energy in a short period of time.

How does a lightning bolt act as a capacitor?

When a lightning bolt forms, it creates an electric field between the negatively charged bottom of the cloud and the positively charged ground. This electric field acts as a capacitor, storing energy until it is released in a sudden discharge of lightning.

What is the capacitance of a lightning bolt?

The capacitance of a lightning bolt can vary depending on the size and intensity of the storm, but it is estimated to be in the range of 100-200 picofarads (pF).

Why is it important to understand "Lightning as a Capacitor"?

Understanding the concept of "Lightning as a Capacitor" can help us better predict and protect against the potential dangers of lightning strikes. It can also aid in the development of technologies for harnessing lightning's energy.

What other natural phenomena can act as capacitors?

Other natural phenomena that can act as capacitors include the Earth's ionosphere, which stores electrical energy from the sun, and the Van Allen radiation belts, which store and release high-energy particles from the sun.

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