Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 2.2, Problem 2.8P
Use your result in Prob. 2.7 to find the field inside and outside a solidsphere of radius R that carries a uniform volume charge density
Expert Solution & Answer
Learn your wayIncludes step-by-step video
schedule07:27
Students have asked these similar questions
E. When E and A were parallel, we called the quantity EA the electric flux through the surface.
For the parallel case, we found that EA is proportional to the number of field lines through the
surface.
By what trigonometric function of 0 must you multiply EA so that the product is proportional
to the number of field lines through the area for any orientation of the surface?
Rewrite the quantity described above as a product of just the vectors E and A.
Charge is distributed throughout a spherical shell of inner radius ₁ and outer radius r2 with a volume
density given by p= Por1/r, where po is a constant. Following the next few steps outlined, determine the
electric field due to this charge as a function of r, the distance from the center of the shell.
Hint
a. Let's start from outside-in. For a spherical Gaussian surface of radius r>r2, how much charge is
enclosed inside this Gaussian surface?
Hint for finding total charge
Qencl
(Answer in terms of given quantities, po, r1, 72, and physical constants ke and/or Eo. Use underscore
("_") for subscripts, and spell out Greek letters.)
b. What is the electric field as a function of r for distances greater than r₂? Finish the application of
Gauss's Law to find the electric field as a function of distance.
E(r> r₂)
c. Now let's work on the "mantle" layer, r₁
What Uniform Electric Field Strength must be developed across parallel conductive plates that are separated by 1 meter in order for a body of mass 1 microgram and
charge +1 nC to transit the plate gap in 1 ms? See illustration below.
1m
E=?
H
+
T=1 ms
1 μg
1 nC
Choose the best answer from the list below. Show your work per the problem solving rubric and submit in the following question.
A. 1X105 N/C
B. 2X106 N/C
C. 3X10 N/C
D. 4X108 N/C
Guiding Questions:
▪ Determine the acceleration, a, needed to transit in time t.
▪ Determine the force, f, needed to generate acceleration a.
▪ Determine the Electric Field necessary to generate force f.
Chapter 2 Solutions
Introduction to Electrodynamics
Ch. 2.1 - (a) Twelve equal charges,q, arc situated at the...Ch. 2.1 - Find the electric field (magnitude and direction)...Ch. 2.1 - Find the electric field a distance z above one end...Ch. 2.1 - Prob. 2.4PCh. 2.1 - Prob. 2.5PCh. 2.1 - Find the electric field a distance z above the...Ch. 2.1 - Find the electric field a distance z from the...Ch. 2.2 - Use your result in Prob. 2.7 to find the field...Ch. 2.2 - Prob. 2.9PCh. 2.2 - Prob. 2.10P
Ch. 2.2 - Use Gauss’s law to find the electric field inside...Ch. 2.2 - Prob. 2.12PCh. 2.2 - Prob. 2.13PCh. 2.2 - Prob. 2.14PCh. 2.2 - A thick spherical shell carries charge density...Ch. 2.2 - A long coaxial cable (Fig. 2.26) carries a uniform...Ch. 2.2 - Prob. 2.17PCh. 2.2 - Prob. 2.18PCh. 2.2 - Prob. 2.19PCh. 2.3 - One of these is an impossible electrostatic field....Ch. 2.3 - Prob. 2.21PCh. 2.3 - Find the potential a distance s from an infinitely...Ch. 2.3 - Prob. 2.23PCh. 2.3 - Prob. 2.24PCh. 2.3 - Prob. 2.25PCh. 2.3 - Prob. 2.26PCh. 2.3 - Prob. 2.27PCh. 2.3 - Prob. 2.28PCh. 2.3 - Prob. 2.29PCh. 2.3 - Prob. 2.30PCh. 2.4 - Prob. 2.31PCh. 2.4 - Prob. 2.32PCh. 2.4 - Prob. 2.33PCh. 2.4 - Find the energy stored in a uniformly charged...Ch. 2.4 - Prob. 2.35PCh. 2.4 - Prob. 2.36PCh. 2.4 - Prob. 2.37PCh. 2.5 - A metal sphere of radius R, carrying charge q, is...Ch. 2.5 - Prob. 2.39PCh. 2.5 - Prob. 2.40PCh. 2.5 - Prob. 2.41PCh. 2.5 - Prob. 2.42PCh. 2.5 - Prob. 2.43PCh. 2.5 - Prob. 2.44PCh. 2.5 - Prob. 2.45PCh. 2.5 - If the electric field in some region is given (in...Ch. 2.5 - Prob. 2.47PCh. 2.5 - Prob. 2.48PCh. 2.5 - Prob. 2.49PCh. 2.5 - Prob. 2.50PCh. 2.5 - Prob. 2.51PCh. 2.5 - Prob. 2.52PCh. 2.5 - Prob. 2.53PCh. 2.5 - Prob. 2.54PCh. 2.5 - Prob. 2.55PCh. 2.5 - Prob. 2.56PCh. 2.5 - Prob. 2.57PCh. 2.5 - Prob. 2.58PCh. 2.5 - Prob. 2.59PCh. 2.5 - Prob. 2.60PCh. 2.5 - Prob. 2.61P
Additional Science Textbook Solutions
Find more solutions based on key concepts
1. When is energy most evident?
Conceptual Physics (12th Edition)
Write each number in decimal form.
23. 6.31 × 10–4
Applied Physics (11th Edition)
Explain all answers clearly, with complete sentences and proper essay structure if needed. An asterisk(*) desig...
Cosmic Perspective Fundamentals
An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so t...
College Physics
When spring finally arrives in the mountains, the snow pack may be two meters deep, composed of 50 ice and 50 a...
An Introduction to Thermal Physics
19.(II) What is the net resistance of the circuit connected to the battery in Fig. 19-50?
Physics: Principles with Applications
Knowledge Booster
Similar questions
- A sphere of radius R has total charge Q. The volume charge density (C/m') within the sphere is p(r) = C/r² , where C is a constant to be determined. 1. Use the expression to find a magnitude of an electric field strenght E : a) inside the sphere (rarrow_forwardFind the electric field a distance z above the end of a wire (length L) carrying a uniform line charge lambda. Please note the field point is NOT IN FRONT of the wire! It is a distance radially outward from the end of the wire! Please list the first four steps to solve these types of problems diligently. Use metacognition, i.e. think about what you do and scrutinize your result for feasibility.arrow_forwardplease follow this criteria and try to explain everything. Include a drawing of the charge distribution and the point at which the E-field is being evaluated. Include a sample vector diagram, showing the electric-field vectors for critical do's. Use the diagrams to help explain any cancellations due to symmetry. Set up the integrals to determine the non-zero electric-field components. Show your work reasoning for constructing the integrals. Assess: is your result reasonable? Do the solutions have the correct behavior far away from the charge?arrow_forwardPositive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q. (Figure 1) Part A Calculate the x-component of the electric field produced by the charge distribution Qat points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, x, r, and appropriate constants. Part B Calculate the y-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, x, r, and appropriate constants. Part C Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms of the variables Q.Part D In what direction the charge distribution Q exerts force on q. In what direction the charge distribution exerts force on .to the left to the rightarrow_forwardConsider an infinitely long solid uniform insulating cylinder with radius R and charge density , find an expression for E(r) the electric field as a function of distance from the center axis of the cylinder. Sketch a plot of your result. Make sure to include regions r < R , r = R , and r>R ! Explain your logic and & show your work clearly.arrow_forwardng for the Electric Fields of Distributed Charge An evenly charged wire of length L has a total charge of Q distributed on it and is located on the x-axis a distance a away from the origin as drawn. Set up the integrals that could be solved to determine the -(0, yo) vector electric field components, E = (Ex, E,), at any point on the y-axis, (0, yo). You should NOT evaluate the integrals. aarrow_forwardProblem 1: What is the force F on the 1.0 nC charge at the bottom in Fig.1. Give your answer in component form. 2.OnC a) In Fig. 1, draw the vectors that represent the forces F₁, F2, and F3, exerted on the bottom charge by charges 1, 2, and 3, respectively. Pay attention to represent correctly the ratios between the magnitudes y of the forces (lengths of the vectors). Without doing calculations, try to predict the direction of the total force on the bottom charge (the total force is the vector sum of the individual forces, F = F₁+F₂ +F3). 5.0 cm 7x -6.0nC 45° 1.OnC -2.0nC 30 5.0 cm FIG. 1: The scheme for Problem 1arrow_forwardFigure shows five closed surfaces that surround various charges in a plane, as indicated. Part A Determine the electric flx through each surface, S. S, S3. S, and S, The surfaces are flat "pillbox surfaces that extend only slightly above and below the plane Express your answers in terms of the variable Q and appropriate constants. Enter your answers separated by commas. Figure Submit 1 of 1 Provide Fecgback Next> +20 Is ts P Pearson Convright O 2022 Pearson Education Inc. All nights reserved.I Terms.of Use i Privacy Policy I Permissions I Contact us Iarrow_forwardStudy the three-dimensional conductor in the figure, which has a cavity in the center. The conductor has an excess charge 1.4 uC on it. S1 What is the electric flux (in N-m2/C) through the Gaussian surface S1 shown in the figure? 91 =0 v Correct! Now put a point of charge 24.4 µC inside the cavity of the conductor. What is the flux (in N•m2/C) through the Gaussian surface S,? 1 =0 v Correct! Now consider the Gaussian surface S. With the charge still inside the cavity, what is the flux (in Nm2/C) through this surface? sin() cos() tan() 8 9 HOME cotan() asin() acos() 4 5 atan() acotan() sinh() *1|2 cosh() tanh() cotanh() +| - END O Degrees O Radians vol BACKSPACE DEL CLEARarrow_forwardTwo equal disks of external radius R and internal radius R / 2 are loaded with positive and uniform charge distributions σ. The discs lie in parallel planes separated by a distance R, but with their centers located on the same axis, as shown in figure 2. Take this axis as Z, and as the origin of coordinates or the midpoint between the rings. 2.Obtain the electric field expression for the points on the Z axis. How does the electric field for z >> R?arrow_forwardConsider the following charge configuration. What is the electric field at point P? Use a Cartesian system. +Q. +Q X L 2L 3L Write your answers as (...., .). ....... (L, 0, 0) The vector from the origin to the left source for the field is: (3L, 0, 0) The vector from the origin to the right source for the field is: (2L, O, 0) The vector to the field point P is: Answer 1: (L, 0, 0) Answer 2: (3L, 0, 0) Answer 3: (2L, 0, 0)arrow_forwardWrite-up Criteria 1. Be neat and organized. 2. Include a drawing of the charge distribution and the point at which the E-field is being evaluated. 3. Include a sample vector diagram, showing the electric-field vectors for critical dq's. 4. Use the diagrams to help explain any cancellations due to symmetry. 5. Set up the integrals to determine the non-zero electric-field components. Show your work/reasoning for constructing the integrals. 6. Solve the integrals. Box or underline your final solutions. 7. Assess: is your result reasonable? Do the solutions have the correct behavior far away from the charge? Problem A1: Two circular disks spaced 0.50 mm apart form a parallel plate capacitor. Transferring 3.0 x 109 electrons from one disk to the other causes the electric field strength to be 2.0 x 105 N/C. What are the diameters of the disks?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON