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Chapter 25: Problem 85

The Tevatron accelerator at Fermilab (Illinois) is designed to carry an 11 -mA beam of protons traveling at very nearly the speed of light \(\left(3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)\) around a ring \(6300 \mathrm{~m}\) in circumference. How many protons are in the beam?

Short Answer

Expert verified
The proton beam consists of a substantial number of protons calculated using the given current and time per revolution.

Step by step solution

01

Understanding the Problem

We need to find out how many protons are in an 11-mA proton beam traveling at nearly the speed of light in a circle with a given circumference.
02

Calculate Charge per Revolution

First, find the time it takes for one revolution of the beam around the ring. This is given by the circumference of the ring divided by the speed of the protons: \[ t = \frac{6300 \text{ m}}{3.0 \times 10^{8} \text{ m/s}}. \]
03

Determine Current and Charge Relation

The relationship between current \(I\), charge \(Q\), and time \(t\) is given by \(Q = I \times t\). Since \(I = 11 \text{ mA} = 11 \times 10^{-3} \text{ A}\), the charge is: \[ Q = 11 \times 10^{-3} \text{ A} \times t. \]
04

Calculate Charge of a Single Proton

The charge of a single proton \(e\) is \(1.6 \times 10^{-19} \text{ C}\).
05

Calculate Number of Protons

To find the number of protons \(N\), divide the total charge by the charge of a single proton: \[ N = \frac{Q}{e}. \] Substitute \(Q\) from Step 3 and \(e\) from Step 4.

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Key Concepts

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

Tevatron
The Tevatron was a major particle accelerator at Fermilab, which is located in Batavia, Illinois. It was one of the most advanced machines for particle collisions.
  • Function: The main purpose of the Tevatron was to accelerate particles - specifically protons and antiprotons - nearly to the speed of light so they can collide.
  • Design: This circular accelerator had a ring design that helped particles gain the energy needed for high-impact collisions.
  • Importance: For many years, the Tevatron was crucial in the study and discovery of subatomic particles.
Understanding its design and operation is essential. The Tevatron featured a remarkable ability to speed up particles to extreme velocities, making it a valuable tool in particle physics research.
Fermilab
Fermilab, short for Fermi National Accelerator Laboratory, is a major research facility in the United States. This laboratory plays a critical role in physics, especially in studying the universe at its most fundamental level.
  • Role: Fermilab houses several accelerators, but the Tevatron was its flagship from 1983 to 2011.
  • Purpose: Fermilab is dedicated to researching many areas of particle physics, which include the structures and behaviors of elementary particles.
  • Research: Their work helps us understand the building blocks of the universe.
Around Fermilab, there's a mix of innovation and collaboration with scientists worldwide. Its impact on global scientific knowledge remains substantial, with numerous discoveries credited to its projects.
Proton Beam
A proton beam is a stream of protons used within accelerators like the Tevatron. These beams are crucial for exploring subatomic particles through collisions.
  • Composition: Made of protons, which are positively charged particles found in the nucleus of an atom.
  • Use: In particle accelerators, proton beams are accelerated close to the speed of light.
  • Impact: When these beams collide, they produce energy and new particles for study.
The manipulation and acceleration of proton beams allow scientists to recreate conditions just after the Big Bang on a small scale. This allows them to study fundamental forces and particles deeply.
Speed of Light
When trying to understand particle physics and accelerators, the speed of light is an essential concept. It is a fundamental constant used in calculations and understanding particle dynamics.
  • Value: The speed of light in a vacuum is \(3.0 \times 10^{8} \, \text{m/s}\).
  • Significance: It represents the fastest speed at which information or matter can travel.
  • Role in Accelerators: Particles accelerated in devices like the Tevatron are often pushed to speeds near this limit.
In practice, achieving speeds near that of light allows particles to have increased energy, which is necessary for creating conditions similar to those of the early universe. Understanding this concept is vital for grasping how particle accelerators operate and uncovering the mysteries of the fundamental nature of the universe.

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Most popular questions from this chapter

(II) An ordinary flashlight uses two D-cell 1.5 \(\mathrm{V}\) batteries connected in series (Fig. \(37 ) .\) The bulb draws 380 \(\mathrm{mA}\) when turned on. \((a)\) Calculate the resistance of the bulb and the power dissipated. (b) By what factor would the power increase if four D-cells in series were used with the same bulb? (Neglect heating effects of the filament.) Why shouldn't you try this?

(II) A 5.80-m length of 2.0-mm-diameter wire carries a 750 -mA current when \(22.0 \mathrm{mV}\) is applied to its ends. If the drift velocity is \(1.7 \times 10^{-5} \mathrm{~m} / \mathrm{s}\), determine \((a)\) the resistance \(R\) of the wire, \((b)\) the resistivity \(\rho,(c)\) the current density \(j,\) ( \(d\) ) the electric field inside the wire, and \((e)\) the number \(n\) of free electrons per unit volume.

(II) How many kWh of energy does a \(550-\mathrm{W}\) toaster use in the morning if it is in operation for a total of 6.0 \(\mathrm{min}\) ? At a cost of 9.0 cents/kWh, estimate how much this would add to your monthly electric energy bill if you made toast four mornings per week.

(a) A particular household uses a \(1.8-\mathrm{kW}\) heater \(2.0 \mathrm{~h} /\) day ("on" time), four 100 -W lightbulbs \(6.0 \mathrm{~h} /\) day, a \(3.0-\mathrm{kW}\) electric stove element for a total of \(1.0 \mathrm{~h} /\) day, and miscellaneous power amounting to \(2.0 \mathrm{kWh} /\) day. If electricity costs \(\$ 0.105\) per \(\mathrm{kWh}\), what will be their monthly bill \((30 \mathrm{~d}) ?(b)\) How much coal (which produces \(7500 \mathrm{kcal} / \mathrm{kg}\) ) must be burned by a \(35 \%\) -efficient power plant to provide the yearly needs of this household?

A proposed electric vehicle makes use of storage batteries as its source of energy. Its mass is \(1560 \mathrm{~kg}\) and it is powered by 24 batteries, each \(12 \mathrm{~V}, 95 \mathrm{~A} \cdot \mathrm{h}\). Assume that the car is driven on level roads at an average speed of \(45 \mathrm{~km} / \mathrm{h},\) and the average friction force is \(240 \mathrm{~N}\). Assume \(100 \%\) efficiency and neglect energy used for acceleration. No energy is consumed when the vehicle is stopped, since the engine doesn't need to idle. (a) Determine the horsepower required. (b) After approximately how many kilometers must the batteries be recharged?
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