/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 5 An electron and a proton moving ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 26: Problem 5

An electron and a proton moving at the same speed enter a region containing a uniform magnetic field. Which is deflected more from its original path?

Short Answer

Expert verified
In a magnetic field, the electron will be deflected more from its original path than the proton. This is due to the electron's significantly smaller mass compared to the proton, which results in a higher acceleration (and hence deflection) for a given magnetic field and speed.

Step by step solution

01

Understand the Lorentz Force

In a magnetic field, moving charged particles experience a force called Lorentz force. The mathematical formulation is given by the equation \( F = qvB \sin(\Theta) \) where, \( q \) is the charge of the particle, \( v \) its speed, \( B \) the strength of the magnetic field and \( \Theta \) the angle between the direction of motion and the field.
02

Apply the 2nd Newton Law

According the 2nd Newton Law, the force exerted on a particle is the product of its mass and acceleration, \( F = ma \). We can equate the Lorentz force to this expression, obtaining \( qvB = ma \). We want to find the particle's acceleration, which results in the formula \( a = \frac{qvB}{m} \). So, the acceleration of a particle due to the magnetic field is proportional to its charge, the field strength and velocity but inversely proportional to its mass.
03

Compare Electron and Proton

Both the electron and the proton have the same magnitude of charge and enter the field at the same speed. However, the proton is about 2000 times more massive than the electron. Therefore, the acceleration (and hence the deflection) of the proton will be significantly less than that of the electron. This means that the electron will be deflected more from its original path than the proton when they enter the magnetic field.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

If a current is passed through an unstretched spring, will the spring contract or expand? Explain.

An unmagnetized piece of iron has no net magnetic dipole moment, yet it's attracted to either pole of a bar magnet. Why?

A circular wire loop of radius \(15 \mathrm{cm}\) and negligible thickness carries a 2.0 -A current. Use suitable approximations to find the magnetic field of this loop (a) in the loop plane, 1.0 mm outside the loop, and (b) on the loop axis, 3.0 m from the loop center.

Find (a) the minimum magnetic field needed to exert a \(5.4-\mathrm{fN}\) force on an electron moving at \(21 \mathrm{Mm} / \mathrm{s}\) and (b) the field strength required if the field were at \(45^{\circ}\) to the electron's velocity.

Number 12 gauge wire, commonly used in household wiring, is \(2.053 \mathrm{mm}\) in diameter and can safely carry currents of up to 20.0 A. For a wire carrying this maximum current, find the magnetic field strength (a) \(0.150 \mathrm{mm}\) from the wire's axis, (b) at the wire's surface, and (c) 0.375 mm beyond the wire's surface.
See all solutions

Recommended explanations on Physics Textbooks

Scientific Method Physics

Read Explanation

Space Physics

Read Explanation

Force

Read Explanation

Circular Motion and Gravitation

Read Explanation

Turning Points in Physics

Read Explanation

Wave Optics

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.