Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 19: Problem 23

An electron moves at speed \(8.0 \times 10^{5} \mathrm{m} / \mathrm{s}\) in a plane perpendicular to a cyclotron's magnetic field. The magnitude of the magnetic force on the electron is \(1.0 \times 10^{-13} \mathrm{N}\) What is the magnitude of the magnetic field?

Short Answer

Expert verified
Answer: The magnitude of the magnetic field is approximately \(7.81 \times 10^{-5}\,T\).

Step by step solution

01

Write down the given variables

We are given these variables: - Speed of the electron: \(v = 8.0 \times 10^{5}\,\mathrm{m/s}\) - Magnetic force on the electron: \(F = 1.0 \times 10^{-13}\,\mathrm{N}\) - Charge of the electron: \(q = -1.6 \times 10^{-19}\,\mathrm{C}\) - Angle between the velocity vector and the magnetic field vector is \(θ = 90^{\circ} ⟹ sin(θ) = 1\)
02

Solve for the magnetic field strength

Using the magnetic force formula \(F = qvBsinθ\), we can solve for the magnetic field strength \(B\). Since \(sin(θ) =1\), the equation simplifies to \(F=qvB\). Rearrange the formula to isolate the magnetic field strength: \(B= \cfrac{F}{q \times v}\) Now, plug in the given values: \(B = \cfrac{1.0 \times 10^{-13}\,\mathrm{N}}{(-1.6 \times 10^{-19}\,\mathrm{C) \times (8.0 \times 10^{5}\,\mathrm{m/s})}}\)
03

Calculate the magnetic field strength

Now, calculate the strength of the magnetic field: \(B= \cfrac{1.0\,\times\,10^{-13}\,\mathrm{N}}{((-1.6\,\times\, 10^{-19}\mathrm{C) (8.0\,\times\, 10^{5}\, \mathrm{m/s})}} \approx \boxed{7.81\,\times\,10^{-5}\,T}\) So, the magnitude of the magnetic field is approximately \(7.81 \times 10^{-5}\,T\).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing ions (primarily Na") flows through an artery with a diameter of \(0.50 \mathrm{cm} .\) The artery is in a magnetic field of $0.35 \mathrm{T}\( and develops a Hall voltage of \)0.60 \mathrm{mV}$ across its diameter. (a) What is the blood speed (in \(\mathrm{m} / \mathrm{s}\) )? (b) What is the flow rate (in \(\mathrm{m}^{3} / \mathrm{s}\) ) \(?\) (c) If the magnetic field points west and the blood flow is north, is the top or bottom of the artery at the higher potential?
Crossed electric and magnetic fields are established over a certain region. The magnetic field is 0.635 T vertically downward. The electric field is $2.68 \times 10^{6} \mathrm{V} / \mathrm{m}$ horizontally east. An electron, traveling horizontally northward, experiences zero net force from these fields and so continues moving in a straight line. What is the electron's speed?
You want to build a cyclotron to accelerate protons to a speed of $3.0 \times 10^{7} \mathrm{m} / \mathrm{s} .$ The largest magnetic field strength you can attain is 1.5 T. What must be the minimum radius of the dees in your cyclotron? Show how your answer comes from Newton's second law.
An early cyclotron at Cornell University was used from the 1930 s to the 1950 s to accelerate protons, which would then bombard various nuclei. The cyclotron used a large electromagnet with an iron yoke to produce a uniform magnetic field of \(1.3 \mathrm{T}\) over a region in the shape of a flat cylinder. Two hollow copper dees of inside radius \(16 \mathrm{cm}\) were located in a vacuum chamber in this region. (a) What is the frequency of oscillation necessary for the alternating voltage difference between the dees? (b) What is the kinetic energy of a proton by the time it reaches the outside of the dees? (c) What would be the equivalent voltage necessary to accelerate protons to this energy from rest in one step (say between parallel plates)? (d) If the potential difference between the dees has a magnitude of $10.0 \mathrm{kV}$ each time the protons cross the gap, what is the minimum number of revolutions each proton has to make in the cyclotron?
Find the magnetic force exerted on an electron moving vertically upward at a speed of \(2.0 \times 10^{7} \mathrm{m} / \mathrm{s}\) by a horizontal magnetic field of \(0.50 \mathrm{T}\) directed north.
See all solutions

Recommended explanations on Physics Textbooks

Waves Physics

Read Explanation

Fluids

Read Explanation

Oscillations

Read Explanation

Linear Momentum

Read Explanation

Mechanics and Materials

Read Explanation

Thermodynamics

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.

Sign-up for free