Ch 22: Electric Charges and Forces

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 22: Electric Charges and Forces

Problem 4b

Chapter 22, Problem 4b

A glass rod that has been charged to +12 nC touches a metal sphere. Afterward, the rod’s charge is +8.0 nC. How many charged particles were transferred?

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Understand the problem: The glass rod initially has a charge of +12 nC, and after touching the metal sphere, its charge decreases to +8.0 nC. This means some charge was transferred from the rod to the sphere. The goal is to calculate the number of charged particles (electrons) transferred.

Calculate the amount of charge transferred: Subtract the final charge of the rod from its initial charge. The formula is ΔQ = Q_initial - Q_final, where Q_initial = 12 nC and Q_final = 8.0 nC. This will give the charge transferred in coulombs.

Convert the charge transferred from nanocoulombs (nC) to coulombs (C): Use the conversion factor 1 nC = 1 × 10⁻⁹ C. Multiply the charge transferred (ΔQ) by this factor to express it in coulombs.

Determine the number of electrons transferred: Use the relationship between charge and the elementary charge of an electron. The formula is N = ΔQ / e, where e = 1.6 × 10⁻¹⁹ C (the charge of a single electron). Divide the charge transferred (in coulombs) by the elementary charge to find the number of electrons.

Interpret the result: The value of N represents the number of electrons transferred from the rod to the sphere. Since electrons are negatively charged, the transfer of electrons reduces the positive charge on the rod.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Charge Conservation

Charge conservation is a fundamental principle in physics stating that the total electric charge in an isolated system remains constant over time. When two objects interact, such as a charged rod and a metal sphere, charge can be transferred between them, but the overall charge before and after the interaction must remain the same.

Quantization of Charge

Electric charge is quantized, meaning it exists in discrete amounts, typically in multiples of the elementary charge (approximately 1.6 x 10^-19 coulombs). This concept is crucial for understanding how many elementary charges (or charged particles) are involved in the transfer of charge between objects, as each particle carries a specific amount of charge.

Conductors and Charge Transfer

Conductors are materials that allow electric charge to flow freely due to the presence of free electrons. When a charged object, like a glass rod, touches a conductor such as a metal sphere, charge can redistribute between them, leading to a change in their respective charge states. This interaction is key to determining how many charged particles are transferred during the process.

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Textbook Question

A linear accelerator uses alternating electric fields to accelerate electrons to close to the speed of light. A small number of the electrons collide with a target, but a large majority pass through the target and impact a beam dump at the end of the accelerator. In one experiment the beam dump measured charge accumulating at a rate of −2.0 nC/s. How many electrons traveled down the accelerator during the 2.0 h run?

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Textbook Question

3.5×10¹⁰ electrons are added to a plastic rod by rubbing it with wool. What is the charge on the rod?

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Textbook Question

A plastic rod that has been charged to −15 nC touches a metal sphere. Afterward, the rod's charge is −10 nC. How many charged particles were transferred?

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What is the total charge of all the electrons in $1.0$ L of liquid water?

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Textbook Question

A plastic rod that has been charged to −15 nC touches a metal sphere. Afterward, the rod's charge is −10 nC. What kind of charged particle was transferred between the rod and the sphere, and in which direction? That is, did it move from the rod to the sphere or from the sphere to the rod?

Textbook Question

What mass of aluminum has a total nuclear charge of $1.0$ C? Aluminum has atomic number $13$ .

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