y-components of the electric field at P (dEx and dE,) produced by just this segment? SOLUTION GUIDE See MasteringPhysics® study area for a Video Tutor solution. MP EXECUTE 4. Integrate your expressions for dE, and dE, from 0 = 0 to 0 = . The results will be the x-component and y-component of the IDENTIFY and SET UP 1. The target variables are the components of the electric field at P. 2. Divide the semicircle into infinitesimal segments, each of which electric field at P. is a short circular arc of radius a and angle d0. What is the 5. Use your results from step 4 to find the magnitude and direc- length of such a segment? How much charge is on a segment? tion of the field at P. 21.34 EVALUATE 6. Does your result for the electric-field magnitude have the cor- y rect units? 7. Explain how you could have found the x-component of the electric field using a symmetry argument. 8. What would be the electric field at P if the semicircle were а extended to a full circle centered at P? P

y-components of the electric field at P (dEx and dE,) produced by just this segment? SOLUTION GUIDE See MasteringPhysics® study area for a Video Tutor solution. MP EXECUTE 4. Integrate your expressions for dE, and dE, from 0 = 0 to 0 = . The results will be the x-component and y-component of the IDENTIFY and SET UP 1. The target variables are the components of the electric field at P. 2. Divide the semicircle into infinitesimal segments, each of which electric field at P. is a short circular arc of radius a and angle d0. What is the 5. Use your results from step 4 to find the magnitude and direc- length of such a segment? How much charge is on a segment? tion of the field at P. 21.34 EVALUATE 6. Does your result for the electric-field magnitude have the cor- y rect units? 7. Explain how you could have found the x-component of the electric field using a symmetry argument. 8. What would be the electric field at P if the semicircle were а extended to a full circle centered at P? P

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 75PQ: A solid sphere of radius R has a spherically symmetrical, nonuniform volume charge density given by...

See similar textbooks

Similar questions

Part D. Integrate your expressions for dEx and dEy from θ=0 to θ=π. The results will be the x-component and y-component of the electric field at P. Express your answers separated by a comma in terms of some, all, or none of the variables Q and a and the constants k and π. Part E. Use your results from part D to find the magnitude and direction of the field at P. Part F. What would be the electric field at P if the semicircle were extended to a full circle centered at P?
Positive 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 right
Consider a wire made of a good conductor with a length, L, radius, R, and a total charge of +Q. a. What assumptions can be made about area if the wire is very long? ? >> ? (Hint: recall surface area of a cylinder) b. Calculate the Electric Field at the surface of the conducting wire. Convert the final answer to units of “k”. Is this the same as the Electric Field of a point charge or a conducting sphere? Distance (r) Electric Field Strength (E) c. Calculate the Electric Flux at the surface of the wire. How does the Electric Flux of the wire compare the Electric Flux of the sphere? Why? d. Calculate the Electric Field strength at a distance, a (such that a > 0) away from the conducting wire. e. Calculate the Electric Flux at a distance, a (such that a > 0) How does the Electric Flux compare to the Electric Flux calculated in part c? f. What should be the Electric Field inside the wire?
Charge is distributed throughout a spherical volume of radius R with a density p = ar², where a is a constant (of unit C/m³, in case it matters). Determine the electric field due to the charge at points both inside and outside the sphere, following the next few steps outlined. Hint a. Determine the total amount of charge in the sphere. Hint for finding total charge Qencl = (Answer in terms of given quantities, a, R, and physical constants ke and/or Eg. Use underscore ("_") for subscripts, and spell out Greek letters.) b. What is the electric field outside the sphere? E(r> R) = c. What is the electric field inside the sphere? Hint for E within sphere #3 Question Help: Message instructor E(r < R) = Submit Question E с $ 4 R G Search or type URL % 5 T ^ MacBook Pro 6 Y & 7 U * 8 9 0 0
A solid conducting sphere carrying charge q has radius a. It is inside a concentric hollow conducting sphere with inner radius b and outer radius c. The hollow sphere has no net charge. Part A Derive an expression for the electric-field magnitude in terms of the distance r from the center for the region r < a. Express your answer in terms of some or all of the variables q, r, and appropriate constants. 17 ΑΣΦ E₁ = Submit Part B Request Answer E₂ = Review | Constants ? Derive an expression for the electric-field magnitude in terms of the distance r from the center for the region a
The electric field strength at the surface of a flat negative electrode in 20° C salt water is 20 kV/m The field strength is 10 kV/m at a distance of 2.0 nm from the surface. Part A What is the electrode's surface charge density in nC/cm²? Express your answer in nanocoulombs per square centimeter. VAX 77- Submit Part B Bequest Answer co= ? What is the molarity of the salt solution? Assume the salt is NaCl Express your answer in terms of molarity. 195] ΑΣΦ nC/cm³ 2 M
Electric Fields 3. A plastic rod is bent into the quarter circle of radius R as shown below. A total positive charge of Q is evenly distributed along the rod. a. In terms of the given quantities, what is the linear charge density A? b. Set up the two integrals you would evaluate to find the components of the electric field. The integrals should be written in terms of the given quantities {Q and R} Ex Ey с. Evaluate your integrals to write down the electric field vector at the origin. y E = -f 10 + +
Explain, giving detailed steps, how you would determine the electric field vector at point P. Give an expression for the electric field vector at point P if |g |= 0.1 nC and a = 0.01 metre.
A. What is the strength of the electric field at point 4 cm from the center? Express your answer to three significant figures and include the appropriate units. B. What is the strength of the electric field at point 8 cm from the center? Express your answer as an integer and include the appropriate units. C. What is the strength of the electric field at point 12 cm from the center? Express your answer to three significant figures and include the appropriate units.
A glass rod that has been charged to +12.0 nC touches a metal sphere. Afterward, the rod’s chargeis +8.0 nC. In both cases the fractional uncertainty is 1%. a. What kind of charged particle was transferred between the rod and the sphere, and in whichdirection? That is, did it move from the rod to the sphere or from the sphere to the rod? b. How many charged particles were transferred? Give full explanations
+Y ↑ +X In figure-1, the coordinate of charge g = 17 µAs R (4,4), the coordinate of charge = 12 uAs P (11, 4) and the coordinate of charge 9 = 15 µas P (11,9) The coordinates have centimeters as unit. a Find the vector pointing from g to 2. This vector is denoted by 712- rcomponent of 12 Give your answer to at least three significance digits. ст y component of 12 Give your answer to at least three significance digits. bFind the unit vector 12. rcomponent of Ê12 Give your answer to at least three significance digits. cm y component of 12 Give your answer to at least three significance digits. cm Submit
4mm Q, 3 mm Smm FIGURE 1.1 FIGURE 1.1 shows a system of three point charges. and Q3 ) Calculate the electre potentral energy for the ystem.