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Chapter 21: Problem 25

How many electrons would have to be removed from a coin to leave it with a charge of \(+1.0 \times 10^{-7} \mathrm{C} ?\)

Short Answer

Expert verified
Approximately \(6.25 \times 10^{11}\) electrons must be removed.

Step by step solution

01

Understanding the Problem

We are asked to find out how many electrons need to be removed from a coin to give it a charge of \(+1.0 \times 10^{-7} \text{ C}\). This means the coin will have a net positive charge, and that charge is due to missing electrons.
02

Introduction to Electron Charge

Recall that each electron carries a charge of \(-1.6 \times 10^{-19} \text{ C}\). When an electron is removed from an object, the object loses that negative charge, effectively increasing its net positive charge.
03

Setting Up the Equation

We need to calculate the number of electrons \(n\) that corresponds to a total charge of \(+1.0 \times 10^{-7} \text{ C}\). This can be calculated using the formula: \[ q = n imes e \] where \(q\) is the total charge and \(e\) is the charge of one electron, \(1.6 \times 10^{-19} \text{ C}\).
04

Solving the Equation

Rearrange the equation to solve for \(n\): \[ n = \frac{q}{e} \] Substitute the values: \[ n = \frac{1.0 \times 10^{-7} \text{ C}}{1.6 \times 10^{-19} \text{ C/electron}} \]
05

Calculating the Number of Electrons

Perform the division to find \(n\): \[ n = 6.25 \times 10^{11} \] Therefore, \(6.25 \times 10^{11}\) electrons need to be removed.

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Key Concepts

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

Electron Charge
Electrons are the basic building blocks of electric charge. Each electron carries a fundamental unit of negative charge. This is known as the elementary charge. The magnitude of this charge is approximately
  • \( -1.6 \times 10^{-19} \text{ C} \)
This negative charge plays a crucial role in electricity and magnetism.
Electrons are small, but their impact is vast. They are found in atoms orbiting the nucleus. They contribute significantly to the electrical properties of materials.
When an electron is removed, an object loses this negative charge. This changes its overall electrical balance. Understanding electron charge helps in grasping how electricity works at the atomic level.
Net Positive Charge
A net positive charge occurs when an object has more protons than electrons. Protons have a positive charge, opposite to that of electrons. If you remove electrons, an object shifts towards positive charge.
In practical terms:
  • Removing electrons increases the net positive charge.
  • Adding electrons reduces the net positive charge, making it negative.
The exercise demonstrates this by asking us to find the number of electrons removed to achieve a specified positive charge.
This highlights the delicate balance of charges. Even small changes in electron numbers can significantly affect the net charge. This concept is important in fields like electronics and chemistry.
Elementary Charge
The elementary charge is a fundamental constant of nature. It represents the smallest indivisible unit of electric charge. Both electrons and protons have magnitudes of charge equal to the elementary charge, though of opposite signs.
In more detail:
  • The charge of an electron is \( -e \), where \( e = 1.6 \times 10^{-19} \text{ C} \).
  • The charge on a proton is \( +e \).
The elementary charge is crucial for understanding atomic and subatomic interactions. It forms the basis for understanding the conservation of charge.
In equations, the elementary charge helps in quantifying and calculating electric phenomena. Recognizing its ubiquitous presence aids in solving various physical problems regarding charge distribution.

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Most popular questions from this chapter

If a cat repeatedly rubs against your cotton slacks on a dry day, the charge transfer between the cat hair and the cotton can leave you with an excess charge of \(-2.00 \mu \mathrm{C}\). (a) How many electrons are transferred between you and the cat? You will gradually discharge via the floor, but if instead of waiting, you immediately reach toward a faucet, a painful spark can suddenly appear as your fingers near the faucet. (b) In that spark, do electrons flow from you to the faucet or vice versa? (c) Just before the spark appears, do you induce positive or negative charge in the faucet? (d) If, instead, the cat reaches a paw toward the faucet, which way do electrons flow in the resulting spark? (e) If you stroke a cat with a bare hand on a dry day, you should take care not to bring your fingers near the cat's nose or you will hurt it with a spark. Considering that cat hair is an insulator, explain how the spark can appear.

Of the charge \(Q\) initially on a tiny sphere, a portion \(q\) is to be transferred to a second, nearby sphere. Both spheres can be treated as particles and are fixed with a certain separation. For what value of \(q / Q\) will the electrostatic force between the two spheres be maximized?

Three particles are fixed on an \(x\) axis. Particle 1 of charge \(q_{1}\) is at \(x=-a,\) and particle 2 of charge \(q_{2}\) is at \(x=+a .\) If their net electrostatic force on particle 3 of charge \(+Q\) is to be zero, what must be the ratio \(q_{1} / q_{2}\) when particle 3 is at (a) \(x=+0.500 a\) and (b) \(x=+1.50 a ?\)

What would be the magnitude of the electrostatic force between two \(1.00 \mathrm{C}\) point charges separated by a distance of (a) \(1.00 \mathrm{~m}\) and (b) \(1.00 \mathrm{~km}\) if such point charges existed (they do not) and this configuration could be set up?

Three charged particles form a triangle: particle 1 with charge \(Q_{1}=80.0 \mathrm{nC}\) is at \(x y\) coordinates \((0,3.00 \mathrm{~mm}),\) particle 2 with charge \(Q_{2}\) is at \((0,-3.00 \mathrm{~mm}),\) and particle 3 with charge \(q=18.0 \mathrm{nC}\) is at \((4.00 \mathrm{~mm}, 0) .\) In unit-vector notation, what is the electrostatic force on particle 3 due to the other two particles if \(Q_{2}\) is equal to (a) \(80.0 \mathrm{nC}\) and (b) \(-80.0 \mathrm{nC} ?\)
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