### Educational Problem: Electron Beam in Electric and Magnetic Fields**Problem Statement:**An electron beam is directed horizontally into a region where there is both an electric field and a magnetic field. The electric field points upward and has a magnitude \( E = 9.4 \, \text{N/C} \), as shown in the accompanying diagram. While moving through the region, the electron beam continues in a horizontal straight line with a speed of \( 210 \, \text{m/s} \).#### Diagram Explanation:The diagram shows:- The electric field \(\vec{E}\) represented by upward arrows.- An electron beam moving horizontally from left to right.---#### (a) In which direction does the electric force act on the electrons?**Answer:** *Downward.* ✔ Correct!#### (b) In order to keep the electrons in a straight line, in which direction should the magnetic force on the electrons act?**Answer:***Upward.* ✔ Correct!#### (c) What should be the direction of the magnetic field be in order to produce the force described in part (b)?**Answer:***Into the screen.* ✔ Correct!---### Further Calculations:#### (d) Calculate the numerical value of the magnitude of the electric force in newtons.The formula for the electric force \( F_{E} \) is:\[ F_{E} = qE \]where:- \( q \) is the charge of an electron (\( q = -1.6 \times 10^{-19} \, \text{C} \)).- \( E \) is the magnitude of the electric field (\( 9.4 \, \text{N/C} \)).#### (e) Calculate the magnitude of the magnetic field in tesla, if the electron continues in a horizontal straight line.The formula for the magnetic force \( F_{B} \) is:\[ F_{B} = qvB \]where:- \( v \) is the velocity of the electron (\( 210 \, \text{m/s} \)).- \( B \) is the magnitude of the magnetic field.Since the forces are balanced (i.e., \( F_{E} = F_{B} \)):\[ qE = qvB \]Solving for \( B \):\[ B = \frac{E}{v} \]**Note

Answered: Image /qna-images/answer/870c0f5f-ad27-4f36-95a8-63d3dd1f207d.jpg

A 20% Part (d) Calculate the numerical value of the magnitude of the electric force in newtons. ▷ A 20% Part (e) Calculate the magnitude of the magnetic field in tesla, if the electron continues in a horizontal straight line. B = T

A 20% Part (d) Calculate the numerical value of the magnitude of the electric force in newtons. ▷ A 20% Part (e) Calculate the magnitude of the magnetic field in tesla, if the electron continues in a horizontal straight line. B = T

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter23: Faraday’s Law And Inductance

Section: Chapter Questions

Problem 64P

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Similar questions

A proton enters a region with a uniform electric field E=5.0kV/m and a uniform magnetic field B=5.0104kT. The proton has initial velocity v0=2.5105m/s. How far along the z axis does the proton travel after it undergoes three complete revolutions?
(a) An oxygen16 ion with a mass at 2.661026kg travels at 5.00106m/s perpendicular to a 1.20T magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the radio of this charge to the charge of an electron? (c) Discuss why the radio found in (b) should be an integer.
An electron in a TV CRT moves with a speed at 6.00107m/s, in a direction perpendicular to the Earth’s field, which has a strength of 5.00105T. (a) What strength electric field must be applied perpendicular to the Earth’s field to make the election moves in a straight line? (b) If this is done between plates separated by 1.00 cm, what is the voltage applied? (Note that TVs are usually surrounded by a ferromagnetic material to shield against external magnetic fields and avoid the need for such a correction.)
A laboratory electromagnet produces a magnetic field of magnitude 1.50 T. A proton moves through this field with a speed of 6.00 106 m/s. (a) Find the magnitude of the maximum magnetic force that could be exerted on the proton. (b) What is the magnitude of the maximum acceleration of the proton? (c) Would the field exert the same magnetic force on an electron moving through the field with the same speed? (d) Would the electron undergo the same acceleration? Explain.
Unreasonable Results A charged particle having mass 6.641027kg (that of a helium atom) moving at 8.70105m/s perpendicular to a 1.50T magnetic field travels in a circular path of radius 16.0 mm. (a) What is the charge of the particle? (b) What is unreasonable about this result? (c) Which assumptions are responsible?
Review A proton is accelerated from rest through a 5.00-V potential difference. a. What is the protons speed after it has been accelerated? b. What is the maximum magnetic field that this proton produces at a point that is 1.00 m from the proton?
What creates a magnetic field? More than one answer may be correct. (a) a stationary object with electric charge (b) a moving object with electric charge (c) a stationary conductor carrying electric current (d) a difference in electric potential (e) a charged capacitor disconnected from a battery and at rest. Note: In Chapter 24, we will see that a changing electric field also creates a magnetic field.
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(a) A physicist performing a sensitive measurement wants to limit the magnetic force on a moving charge in her equipment to less than 1.001012N. What is the greatest the charge can be if it moves at a maximum speed of 30.0 m/s in the Earth’s field? (b) Discuss whether it would be difficult to limit the charge to less than the value found in (a) by competing it with typical static electricity and noting that static is often absent.
Within a cylindrical region of space of radius 100 Mm, a magnetic field is uniform with a magnitude 25.0 T and oriented parallel to the axis of the cylinder. The magnetic field is zero outside this cylinder. A cosmic-ray proton traveling at one-tenth the speed of light is heading directly toward the center of the cylinder, moving perpendicular to the cylinders axis. (a) Find the radius of curvature of the path the proton follows when it enters the region of the field. (b) Explain whether the proton will arrive at the center of the cylinder.
What creates a magnetic Hold? More than one answer may be correct, (a) a stationary object with electric charge (b) a moving object with electric charge (c) a stationary conductor carrying electric current (d) a difference in electric potential (e) a charged capacitor disconnected from a battery and at rest Note: In Chapter 34, we will see that a changing electric field also creates a magnetic field.
(a) A proton moving with velocity v=ii experiences a magnetic force F=Fij. Explain what you can and cannot infer about B from this information. (b) What If? In terms of Fi, what would be the force on a proton in the same field moving with velocity v=ii? (c) What would be the force on an electron in the same field moving with velocity v=ii?