Textbook Question
If a proton and an electron are released when they are m apart (a typical atomic distance), find the initial acceleration of each particle.
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Ch 21: Electric Charge and Electric Field
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
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 C/s; this lasts for ms or less. How much charge flows between the ground and the cloud in this time? How many electrons flow during this time?
Verified step by step guidance1
First, identify the given values in the problem: the maximum rate of charge flow (current) is 20,000 C/s, and the time duration is 100 ms. Convert the time from milliseconds to seconds by dividing by 1000, so 100 ms = 0.1 s.
To find the total charge that flows, use the formula for charge flow: \( Q = I \times t \), where \( Q \) is the charge in coulombs, \( I \) is the current in amperes (C/s), and \( t \) is the time in seconds. Substitute the given values into the formula.
Calculate the total charge \( Q \) by multiplying the current (20,000 C/s) by the time (0.1 s). This will give you the total charge in coulombs that flows between the ground and the cloud.
Next, to find the number of electrons, use the relationship between charge and electrons: \( Q = n \times e \), where \( n \) is the number of electrons and \( e \) is the elementary charge (approximately \( 1.602 \times 10^{-19} \) C). Rearrange the formula to solve for \( n \): \( n = \frac{Q}{e} \).
Substitute the total charge \( Q \) calculated in the previous step and the value of the elementary charge \( e \) into the formula to find the number of electrons that flow during this time.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Electric Charge
Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It is measured in coulombs (C), and electrons carry a negative charge. Understanding charge flow is crucial for calculating the total charge transferred during lightning.
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Electric Charge
Current and Charge Flow
Current is the rate of flow of electric charge, measured in amperes (A), where 1 A equals 1 C/s. In the context of lightning, the current is given as 20,000 C/s, indicating the rapid movement of charge. To find the total charge transferred, multiply the current by the duration of the flow.
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Electron Charge
The charge of a single electron is approximately -1.602 x 10^-19 coulombs. To determine the number of electrons transferred during lightning, divide the total charge by the charge of one electron. This calculation helps quantify the microscopic flow of electrons in the macroscopic event of lightning.
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Related Practice
Textbook Question
Two small aluminum spheres, each having mass kg, are separated by cm. How many electrons does each sphere contain? (The atomic mass of aluminum is g/mol, and its atomic number is .)
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Textbook Question
Two small spheres spaced cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is N?
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