Storm Cloud – Interesting Problems (Electrostatics)

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1972

A positively charged cloud is located at an altitude of 400 m and, together with the surface of the Earth, forms a plate capacitor (the surface area of one “plate” is 8 km²). There is a strong electric field between the cloud and the ground, which is so intense that it immediately leads to electrical discharge and the occurrence of lightning. The strength of the electric field is:

In this problem, we need to calculate the following:

1. What is the charge of the cloud?
2. What is the voltage between the cloud and the ground?
3. What charge would a spherical water droplet with a diameter of 1mm need to have if it was hovering just before the cloud discharge, assuming there was no wind? (Ignore buoyancy in the air).
4. How long would the cloud discharge last if the average lightning current strength was 4kA?Task Analysisa) The electric field strength of a parallel plate capacitor is given by the expression:

The capacitance of the parallel plate capacitor is given by the expression:

1. The amount of charge on the capacitor plates is:

b) For the droplet to float in the air, the gravitational force and the electric force must have the same intensity because they have the same direction but opposite directions. The forces are given by the expressions:

the condition of the task is:

To calculate the amount of charge on the droplet from the expression, we must first calculate the mass of the droplet

the acceleration due to gravity is: , the condition for the droplet to float is given by the expression:

from this condition, we can determine the amount of charge on the droplet.

The unit for the electric field strength of a parallel plate capacitor is , the electric field strength of the droplet is expressed in:

c) The time for the electric discharge to occur can be determined from the relation:

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