/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 Lightning occurs when there is a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: 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 C/s; this lasts for \(100 \mu s\) 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
2 Coulombs of charge flow and approximately 1.25 x 10^{19} electrons transfer.

Step by step solution

01

Understand the Problem

We need to calculate the total charge that flows between the ground and a thundercloud in a given time and then find out the number of electrons corresponding to this charge. We are given a charge flow rate of 20,000 C/s and a duration of 100 microseconds ( \(100 \mu s = 100 \times 10^{-6} s\)).
02

Calculate the Total Charge

The total charge ( \(Q\)) is calculated by multiplying the charge flow rate ( \(I\)) with the time duration ( \(t\)). Formula to use: \[Q = I \times t\]Plug in the values:\[Q = 20,000\ C/s \times 100 \times 10^{-6}\ s = 2\ C\]So, the total charge that flows is 2 Coulombs.
03

Calculate the Number of Electrons

To find the number of electrons, we use the relation between charge and the elementary charge of an electron ( \(e = 1.602 \times 10^{-19}\ C\)). The number of electrons ( \(n\)) is given by \[n = \frac{Q}{e}\]Substituting the known values:\[n = \frac{2\ C}{1.602 \times 10^{-19}\ C/electron} \approx 1.25 \times 10^{19}\ electrons\]This gives the total number of electrons flowing during this interval.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Lightning and Charge Flow
Lightning is a dazzling natural phenomenon where electric charge moves rapidly between a thundercloud and the ground. It often occurs during intense storms, creating a majestic yet powerful light show we observe. The process involves a flow of electric charges, primarily electrons, from one point to another. In a typical lightning bolt, the sky and earth connect through this swift and temporary exchange of charges, allowing electrons to move across a potential difference.

The flow rate of this charge can reach staggering heights, sometimes about 20,000 Coulombs per second. This rapid flow takes place over incredibly short durations, such as \(100\ \mu s = 100 \times 10^{-6}\) seconds, resulting in enormous amounts of electric energy being transferred in the blink of an eye.

The dynamics of a lightning bolt allow us to comprehend the immense power and potential danger this natural occurrence holds. Lightning serves as a powerful reminder of nature's forces and the significance of electrical charge flow.
Understanding Elementary Charge
At the core of understanding electric charges lies the concept of the elementary charge. It is the smallest unit of charge, symbolized by 'e', and is the charge carried by a single proton or the positive charge equivalent carried by an electron with a negative sign.

The value of the elementary charge is approximately \(1.602 \times 10^{-19}\) Coulombs. This value is a fundamental constant in physics, bridging the microscopic world of particles and macroscopic electric phenomena. To conceptualize electric interactions, considering the elementary charge enables us to comprehend the aggregation of tiny charges into sizable ones, such as those in lightning.

For instance, when a lightning bolt discharges 2 Coulombs of electric charge, we can determine the number of individual charges that moved by dividing the total charge by the elementary charge. This shows how even a single bolt involves countless individual electrons acting in concert.
Electrons: The Charge Carriers
Electrons are the primary charge carriers in many electrical phenomena, including lightning. These subatomic particles have a negative charge and are found orbiting the nucleus of an atom. Their mobility allows them to flow between different points, which is essential for all electric and electronic functions.

In scenarios like lightning, electrons accumulate in the clouds, creating a charge imbalance with the earth. Once the electric field's strength reaches a threshold, electrons leap across the sky, forming a lightning strike.

The number of electrons involved in such a natural event is vast. For a 2-Coulomb charge movement, approximately \(1.25 \times 10^{19}\) electrons are involved! Visualizing such numbers illustrates the immense scale of particles involved, even in a singular momentary event like a lightning flash.

Understanding electrons' role in electricity extends beyond theory, as it is foundational to practical applications like electronics, electrochemistry, and lightning protection systems.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In an inkjet printer, letters are built up by squirting drops of ink at the paper from a rapidly moving nozzle. The ink drops, which have a mass of \(1.4 \times 10^{-8} \mathrm{~g}\) each, leave the nozzle and travel toward the paper at \(20 \mathrm{~m} / \mathrm{s}\), passing through a charging unit that gives each drop a positive charge \(q\) by removing some electrons from it. The drops then pass between parallel deflecting plates \(2.0 \mathrm{~cm}\) long where there is a uniform vertical electric field with magnitude \(8.0 \times 10^{4} \mathrm{~N} / \mathrm{C}\). If a drop is to be deflected \(0.30 \mathrm{~mm}\) by the time it reaches the end of the deflection plates, what magnitude of charge must be given to the drop?

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.

Particles in a Gold Ring. You have a pure (24-karat) gold ring with mass \(19.7 \mathrm{~g}\). Gold has an atomic mass of \(197 \mathrm{~g} / \mathrm{mol}\) and an atomic number of 79. (a) How many protons are in the ring, and what is their total positive charge? (b) If the ring carries no net charge, how many electrons are in it?

Positive charge \(+Q\) is distributed uniformly along the \(+x\)-axis from \(x=0\) to \(x=a\). Negative charge \(-Q\) is distributed uniformly along the \(-x\)-axis from \(x=0\) to \(x=-a\). (a) A positive point charge \(q\) lies on the positive \(y\)-axis, a distance \(y\) from the origin. Find the force (magnitude and direction) that the positive and negative charge distributions together exert on \(q\). Show that this force is proportional to \(y^{-3}\) for \(y \gg a\). (b) Suppose instead that the positive point charge \(q\) lies on the positive \(x\)-axis, a distance \(x>a\) from the origin. Find the force (magnitude and direction) that the charge distribution exerts on \(q\). Show that this force is proportional to \(x^{-3}\) for \(x \gg a\).

proton is traveling horizontally to the right at \(4.50 \times 10^{6}\) \(\mathrm{m} / \mathrm{s} .\) (a) Find the magnitude and direction of theweakest electric field that can bring the proton uniformly to rest over a distance of \(3.20 \mathrm{~cm}\). (b) How much time does it take the proton to stop after entering the field? (c) What minimum field (magnitude and direction) would be needed to stop an electron under the conditions of patt (a)?
See all solutions

Recommended explanations on Physics Textbooks

Thermodynamics

Read Explanation

Scientific Method Physics

Read Explanation

Electricity

Read Explanation

Work Energy and Power

Read Explanation

Measurements

Read Explanation

Oscillations

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.