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Chapter 21: Problem 2

Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about \(20,000 \mathrm{C} / \mathrm{s} ;\) this lasts for \(100 \mu \mathrm{s}\) or less. How much charge flows between the ground and the cloud in this time? How many electrons flow during this time?

Short Answer

Expert verified
The total charge that flows from the ground to the cloud is \(2 \, C\). The total number of electrons transferred is approximately \(1.25 \times 10^{19}\) electrons.

Step by step solution

01

Calculate the Total Charge

The total charge can be calculated using the formula for charge (\(Q\)) given by \(Q = It\), where \(I\) is the current (rate of charge flow) and \(t\) is the time. Here, \(I = 20000 \, C/s\) and \(t = 100 \, \mu s = 100 \times 10^{-6} \, s\). Substituting these values into the formula, we calculate the total charge.
02

Determine the Number of Electrons

The total number of electrons can be found by dividing the total charge calculated in the previous step by the charge of a single electron, which is approximately \(1.6 \times 10^{-19} \, C\).
03

Final Answer

Performing these calculations will give the total charge transferred and the total number of electrons that flow during this time.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coulomb's Law
Coulomb's Law is fundamental to understanding the mechanics behind lightning. This law states that the force between two stationary, electrically charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it is expressed as:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
Here, \(F\) is the electrostatic force, \(k\) is Coulomb's constant, \(q_1\) and \(q_2\) are the amounts of the charges, and \(r\) is the distance between the centers of the two charges. Coulomb's law is crucial because it helps us understand why charges accumulate and discharge in the phenomenon of lightning, as a result of interactions between charged particles in clouds and the ground.
Electric Current
Electric current refers to the flow of electric charge and is essential for the transfer of energy during a lightning strike. It is measured in amperes (A), where one ampere is one coulomb of charge passing a point in one second. To grasp the scale of electric current in lightning, consider that a household light bulb might use about 0.5A, whereas a lightning bolt involves currents upwards of tens of thousands of amperes. This immense current is what powers the bright flash and thunder we perceive during a storm.
Flow of Electrons
The flow of electrons is the movement of negatively charged particles within a conductor, such as a lightning bolt. Electrons originate at the negative charge center and move towards the positive charge center, which could be the ground or another part of a cloud. In the context of our example, approximately \(20,000\) coulombs of electrons per second flow in the lightning bolt. This flow is what creates the electric current. Understanding electron flow helps us appreciate the dynamic and powerful nature of electricity, especially in such dramatic events as lightning strikes.
Charge Flow Rate
Charge flow rate, often synonymous with electric current, is the amount of charge that passes through a point in the circuit per unit time. For the lightning bolt example, the stated rate is \(20,000\) coulombs per second (\(C/s\)), which indicates an incredibly high rate of charge transfer. This rate determines the level of electric charge that moves between the cloud and the ground during the short duration of a lightning strike. Given the extremely brief time of a lightning flash, quantifying the charge flow rate is essential to calculate the significant amounts of charge and energy being transferred in mere microseconds.

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Most popular questions from this chapter

Point charge \(q_{1}=-5.00 \mathrm{nC}\) is at the origin and point charge \(q_{2}=+3.00 \mathrm{nC}\) is on the \(x\) -axis at \(x=3.00 \mathrm{~cm} .\) Point \(P\) is on the \(y\) -axis at \(y=4.00 \mathrm{~cm} .\) (a) Calculate the electric fields \(\vec{E}_{1}\) and \(\vec{E}_{2}\) at point \(P\) due to the charges \(q_{1}\) and \(q_{2}\). Express your results in terms of unit vectors (see Example 21.6 ). (b) Use the results of part (a) to obtain the resultant field at \(P\), expressed in unit vector form.

A +2.00 nC point charge is at the origin, and a second \(-5.00 \mathrm{nC}\) point charge is on the \(x\) -axis at \(x=0.800 \mathrm{~m}\). (a) Find the electric field (magnitude and direction) at each of the following points on the \(x\) -axis: (i) \(x=0.200 \mathrm{~m} ;\) (ii) \(x=1.20 \mathrm{~m} ;\) (iii) \(x=-0.200 \mathrm{~m}\). (b) Find the net electric force that the two charges would exert on an electron placed at each point in part (a).

A -3.00 nC point charge is on the \(x\) -axis at \(x=1.20 \mathrm{~m}\). A second point charge, \(Q,\) is on the \(x\) -axis at \(-0.600 \mathrm{~m}\). What must be the sign and magnitude of \(Q\) for the resultant electric field at the origin to be (a) \(45.0 \mathrm{~N} / \mathrm{C}\) in the \(+x\) -direction, (b) \(45.0 \mathrm{~N} / \mathrm{C}\) in the \(-x\) -direction?

In a rectangular coordinate system a positive point charge \(q=6.00 \times 10^{-9} \mathrm{C}\) is placed at the point \(x=+0.150 \mathrm{~m}, y=0,\) and an identical point charge is placed at \(x=-0.150 \mathrm{~m}, y=0 .\) Find the \(x\) - and \(y\) -components, the magnitude, and the direction of the electric field at the following points: (a) the origin; (b) \(x=0.300 \mathrm{~m}, y=0\) (c) \(x=0.150 \mathrm{~m}, y=-0.400 \mathrm{~m}\) (d) \(x=0, y=0.200 \mathrm{~m}\)

In an experiment in space, one proton is held fixed and another proton is released from rest a distance of \(2.50 \mathrm{~mm}\) away. (a) What is the initial acceleration of the proton after it is released? (b) Sketch qualitative (no numbers!) acceleration-time and velocity-time graphs of the released proton's motion.
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