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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\(\mu\) 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
2 C charge flows, with about 1.25 脳 10^19 electrons.

Step by step solution

01

Understand the problem

We need to determine the amount of charge that flows during a lightning bolt and the number of electrons that correspond to this charge. The rate of charge flow given is \(20,000\, \mathrm{C/s}\), which occurs for \(100\, \mu s\).
02

Calculate Charge Flow

The formula for charge flow is \(Q = I \times t\), where \(I\) is the current (\(20,000\, \mathrm{C/s}\)) and \(t\) is the time (\(100\, \mu s\) which is \(0.0001\, \mathrm{s}\)). Substitute the values:\[ Q = 20,000 \times 0.0001 = 2\, \text{Coulombs} \]
03

Calculate Number of Electrons

To find the number of electrons, use the formula \(n = \frac{Q}{e}\), where \(e = 1.6 \times 10^{-19}\, \mathrm{C}\) is the elementary charge of an electron. Substitute the values:\[ n = \frac{2}{1.6 \times 10^{-19}} = 1.25 \times 10^{19}\, \text{electrons} \]
04

Conclusion

The total charge that flows between the cloud and ground is \(2\, \mathrm{C}\), and approximately \(1.25 \times 10^{19}\) electrons flow in this process.

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Key Concepts

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

lightning
Lightning is a powerful natural phenomenon characterized by a sudden discharge of electricity. It typically occurs during thunderstorms when there is an imbalance of electric charges between storm clouds and the ground. These electric discharges lead to the rapid heating and expansion of air, producing the sound we know as thunder. Lightning can travel at speeds of up to one-third the speed of light, making it one of the fastest natural events.
  • Lightning is crucial for balancing electrical charges in the atmosphere.
  • It occurs primarily due to the process by which electrical charges build up in storm clouds.
  • The path of lightning is shaped by the differing air conditions and the charge distribution in clouds and on the ground.
Understanding this process can help in developing better safety measures against lightning strikes.
electric charge
An electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. Charges are of two types: positive and negative. In the context of lightning, electric charges build up within clouds due to the movement of water droplets and ice crystals.
  • Positive charges tend to accumulate at the top of the cloud, while negative charges gather at the bottom.
  • This separation of charges creates the perfect condition for lightning to occur.
  • When the electric field becomes strong enough, it overcomes the air's resistance, allowing negative charges to flow to the ground as lightning.
The balance between positive and negative charges is crucial in preventing electric discharges like lightning.
current flow
Current flow refers to the movement of electric charge, usually measured in amperes. In our context, lightning represents an extremely high current flow, translating into a brief yet immense transfer of energy.
  • The current in a lightning strike can be upwards of 20,000 amperes, making it highly destructive.
  • This massive flow only lasts a fraction of a second, usually just milliseconds.
  • The intensity of the current flow is responsible for the incredible power and brightness of lightning.
Understanding current flow helps in grasping why lightning can be so dangerous and how we might work to mitigate its impact.
electrons
Electrons are subatomic particles with a negative electric charge. They play a crucial role in many physical phenomena, including electricity and magnetism. In the process of a lightning strike, it's mainly electrons that move between the cloud and the ground.
  • An electron's charge is approximately \(1.6 \times 10^{-19} \) Coulombs.
  • The number of electrons involved in a typical lightning bolt is immense, reaching up to \(1.25 \times 10^{19}\) electrons.
  • Because electrons are so small and numerous, they can create a significant current even over a brief period.
Grasping the role of electrons allows for a deeper understanding of how electrical currents operate on a microscopic scale.

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Most popular questions from this chapter

A charge of \(-6.50 \mathrm{nC}\) is spread uniformly over the surface of one face of a nonconducting disk of radius 1.25 \(\mathrm{cm}\) . (a) Find the magnitude and direction of the electric field this disk produces at a point \(P\) on the axis of the disk a distance of 2.00 \(\mathrm{cm}\) from its center. (b) Suppose that the charge were all pushed away from the center and distributed uniformly on the outer rim of the disk. Find the magnitude and direction of the electric field at point \(P\) . (c) If the charge is all brought to the center of the disk, find the magnitude and direction of the electric field at point \(P .\) (d) Why is the field in part (a) stronger than the field in part (b)? Why is the field in part (c) the strongest of the three fields?

A ring-shaped conductor with radius \(a=2.50 \mathrm{cm}\) has a total positive charge \(Q=+0.125 \mathrm{nC}\) uniformly distributed around it, as shown in Fig. \(21.23 .\) The center of the ring is at the origin of coordinates \(O .\) (a) What is the electric field (magnitude and direction) at point \(P,\) which is on the \(x\) -axis at \(x=40.0 \mathrm{cm}\) ? (b) A point charge \(q=-2.50 \mu C\) is placed at the point \(P\) described in part (a). What are the magnitude and direction of the force exerted by the charge \(q\) on the ring?

cp Strength of the Electric Force. Imagine two 1.0 -g bags of protons, one at the earth's north pole and the other at the south pole. (a) How many protons are in each bag? (b) Calculate the gravitational attraction and the electrical repulsion that each bag exerts on the other. (c) Are the forces in part (b) large enough for you to feel if you were holding one of the bags?

Point charges \(q_{1}=-4.5 \mathrm{nC}\) and \(q_{2}=+4.5 \mathrm{nC}\) are separated by 3.1 mm, forming an electric dipole. (a) Find the electric dipole moment (magnitude and direction). (b) The charges are in a uniform electric field whose direction makes an angle of \(36.9^{\circ}\) with the line connecting the charges. What is the magnitude of this field if the torque exerted on the dipole has magnitude \(7.2 \times 10^{-9} \mathrm{N} \cdot \mathrm{m} ?\)

CP Two identical spheres are each attached to silk threads of length \(L=0.500 \mathrm{m}\) and hung from a common point (Fig. P21.68). Each sphere has mass \(m=8.00 \mathrm{g} .\) The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. One sphere is given positive charge \(q_{1},\) and the other a different positive charge \(q_{2} ;\) this causes the spheres to separate so that when the spheres are in equilibrium, each thread makes an angle \(\theta=20.0^{\circ}\) with the vertical. (a) Draw a free-body diagram for each sphere when in equilibrium, and label all the forces that act on each sphere. (b) Determine the magnitude of the electrostatic force that acts on each sphere, and determine the tension in each thread. (c) Based on the information you have been given, what can you say about the magnitudes of \(q_{1}\) and \(q_{2} ?\) Explain your answers. (d) A small wire is now connected between the spheres, allowing charge to be transferred from one sphere to the other until the two spheres have equal charges; the wire is then removed. Each thread now makes an angle of \(30.0^{\circ}\) with the vertical. Determine the original charges. (Hint: The total charge on the pair of spheres is conserved.)
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