Concept explainers
An electron beam in a cathode-ray tube passes between two parallel plates that have a voltage difference of 500 V across them and are separated by a distance of 4 cm. as shown in the following diagram.
a. In what direction will the electron beam deflect as it passes between these plates? Explain.
b. Using the expression for a uniform field. ΔV = Ed, find the value of the electric field in the region between the plates.
c. What is the magnitude of the force exerted on individual electrons by this field? (F = qE, q = 1.6 × 10–19C)
d. What are the magnitude and direction of the acceleration of an electron? (m = 9.1 × 10–31 kg)
e. What type of path will the electron follow as it passes through the region between the plates? Explain.
(a)
The direction in which the electron beam will deflect as is passes between the plates.
Answer to Problem 1SP
The electron beam will deflect upward.
Explanation of Solution
Electron is the first discovered fundamental particles. It was discovered by J. J. Thomson in 1897. The mass of electron is
Electrons are negatively charged particles. The magnitude of the charge of electron is
One of the fundamental property of the electric charges is that the like charges repel whereas the unlike charges attract. Thus it will be attracted towards the upward plate which has positive charge. In another way, the direction of the electric field is from positive to negative and the force on a negative charge is opposite to the direction of electric field. This implies the force on the electron is towards the positive plate.
Conclusion:
Thus the electron beam will deflect upward.
(b)
The value of the electric field in the region between the plates.
Answer to Problem 1SP
The value of the electric field in the region between the plates is
Explanation of Solution
Given Info: The distance between the plates is
Write the equation for the electric field between the plates.
Here,
Substitute
Conclusion:
Thus the value of the electric field in the region between the plates is
(c)
The magnitude of the force exerted on individual electron by the electric field.
Answer to Problem 1SP
The magnitude of the force exerted on individual electron by the electric field is
Explanation of Solution
Write the equation for the magnitude of the force on the electron.
Here,
The magnitude of
Substitute
Conclusion:
Thus the magnitude of the force exerted on individual electron by the electric field is
(d)
The magnitude and direction of the acceleration of an electron.
Answer to Problem 1SP
The magnitude of acceleration of an electron is
Explanation of Solution
Write the equation for the force on a body.
Here,
Rewrite the above equation for
Substitute
The direction of acceleration will be in the direction force on the particle. In part (b) it is found that the force on the particle is toward upward so that the direction of acceleration will also be upward.
Conclusion:
Thus the magnitude of acceleration of an electron is
(e)
The type of path the electron will follow as it passes through the region between the plates.
Answer to Problem 1SP
The type of path the electron will follow as it passes through the region between the plates will be parabolic and it will be towards the positively charged plate.
Explanation of Solution
The path followed by a particle under the action of given forces is called the trajectory of the particle. The trajectory may have different shapes. It can be expressed by a particular equation.
In the given situation, the electrons are in a uniform electric field between the plates. This implies the electron will have constant acceleration. This is similar to the situation where a body is under the influence of gravitational force where the constant acceleration is equal to the acceleration due to gravity.
A body falling under gravitational force will follow a parabolic path. Similarly the electron moving with the constant acceleration will also follow a parabolic path and it will be directed towards the positive plate situated upward.
Conclusion:
Thus the type of path the electron will follow as it passes through the region between the plates will be parabolic and it will be towards the positively charged plate.
Want to see more full solutions like this?
Chapter 18 Solutions
Physics of Everyday Phenomena
- You are working on a research project in which you must control the direction of travel of electrons using deflection plates. You have devised the apparatus shown in Figure P22.28. The plates are of length = 0.500 m and are separated by a distance d = 3.00 cm. Electrons are fired at vi = 5.00 106 m/s into a uniform electric field from the left edge of the lower, positive plate, aimed directly at the right edge of the upper, negative plate. Therefore, if there is no electric field between the plates, the electrons will follow the broken line in the figure. With an electric field existing between the plates, the electrons will follow a curved path, bending downward. You need to determine (a) the range of angles over which the electron can leave the apparatus and (b) the electric field required to give the maximum possible deviation angle. Figure P22.28arrow_forwardIn a Millikan oil-drop experiment, a particular oil drop weighs 4.37×10^−14 N. The parallel plates are separated by a distance of 1.80 cm.When the potential difference between the plates is 546 V, the drop is suspended. a. What is the net charge on the oil drop? b. If the upper plate is positive, how many excess electrons are on the oil drop?arrow_forwardThe electrons that are used in an electron microscope are accelerated through a potential difference of 70 kV.a. Calculate the speed of the electrons using the Newtonian formula for kinetic energy.b. Calculate the speed of the electrons using the relativistic formula for kinetic energy.c. By what factor does the Newtonian result exceed the relativistic result?arrow_forward
- Atoms have an equal number of electrons and protons so are electrically neutral. Atoms that have a net electrical charge are known as "ions". Positive ions - have "missing" electrons Negative ions - have "excess" electrons 3. The net charge of an object can be found be summing the individual charges. Since charge is quantized, all net charges are just an integer multiple of the elementary charge. q-ne where q is the net charge and n is an integer. For example, sodium can be a +1 ion and chlorine can be a -1 ion. What does this mean concerning their charge and structure? Revised 1/20 L2 D Ctlo But, what if you want to look at larger objects that are charged; e.g., objects made up of a huge number of atoms/molecules. How do these objects become charged?arrow_forwardThree charged particles with charges {-q, q, -q} are placed on the z axis at z = {-d,0, d}. See the diagram below. d d a. (4 pts) List as many symmetries associated with this arrangement of charges as you can identify. b. (6 pts) Calculate the electric field on the x axis: i.e. determine E(x, 0,0). c. (6 pts) Evaluate the electric potential on the x axis. i.e. determine $(x,0,0). d. (5 pts) Show that Ex e. (3 pts) Why were we able to apply E = -Vø as we did in part d without having obtained the full functional form for ø(x, y, z). Be explicit. f. (3 pts) What is E(x,0,0) in the limit x >> d to zeroth order in d/x? g. (3 pts) What is ø(x,0,0) in the limit x >> d to zeroth order in d/x?arrow_forwardIdentify the following objects as being either ... a. positive b. negative c. neutral If there is no conclusive evidence, then select all that could be true. Description of Object a, b, or c? i. An object possesses more protons than electrons. ii. An object possesses more neutrons than electrons. iii. A formerly neutral object that just lost some electrons. iv. A formerly neutral object that just gained some electrons. v. An object which attracts a negatively-charged balloon. vi. An object which attracts neutral paper bits and attracts a negatively-charged balloon. vii. An object which attracts neutral attracts paper bits and repels a negatively-charged balloon. viii. An object which attracts a negatively-charged balloon and attracts a positively-charged balloon. ix. An object which attracts a charged balloon (balloon A) which is attracted to a negatively-charged balloon (balloon B). x. An object which attracts a…arrow_forward
- le11: Finding the Charge on an Oil Drop In a Millikan oil-drop experiment, a drop has been found to weigh 2.41014 N. The parallel plates are separated by a distance of 1.2 cm. When the potential difference between the plates is 450 V, the drop is suspended, motionless. a. What is the charge on the oil drop? b. If the upper plate is positive, how many excess electrons are on the oil drop?arrow_forwardConsider a model of an electron as a hollow sphere with radius R and the electron charge -e spread uniformly over that surface. a. Calculate the electric field inside and outside of the sphere. b. Calculate the electric potential that creates this field, and has a zero value at infinity. c. Calculate the work required to create this electron. d. Use Einstein’s equation relating rest mass to energy to derive a value for R. Unfortunately, your answer will be model-dependent. The traditional “Classical radius of the electron” is derived by setting the electrostatic work to be e2/(4pi e0 R)arrow_forwardA completely ionized beryllium atom (net charge = +4e) is accelerated through a potential difference of 6.0 V. What is the increase in kinetic energy of the atom? a. 0 eV b. 0.67 eVc. 12 eVd. 24 eVarrow_forward
- Describe your approach to determining the distance between the electron and proton in an atom if the potential energy U of the electron is known to be 14 eV. а. Use the law of conservation of energy. b. Use Coulomb's law. С. Use the definition of electrostatic potential energy U of one point charge q at position r in the presence of an electric potential. d. Use Newton's second law.arrow_forward1. An iron atom has 26 protons, 30 neutrons and 26 electrons. a. What is the total charge of its nucleus? b. What is the total charge of its electrons? c. What is the magnitude of the electric force of attraction between an iron nucleus and its innermost electron id the distance between them is 1.5 x 1012?arrow_forwardAn oil droplet is sprayed into a uniform electric field of adjustable magnitude. The 0.0400g droplet hovers motionless when the electric field is set to 370N/C and directed downward. a. What was the charge of the oil droplet in Coulombs? b. Determine the approximate number of excess or defecit electrons on the droplet.arrow_forward
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College