Concept explainers
CP CALC A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density ρ(r) is given by
Here α is a positive constant having units of C/m3, (a) Determine α in terms of Q and R. (b) Using Gauss’s law, derive an expression for the magnitude of the electric field as a function of r. Do this separately for all three regions. Express your answers in terms of Q. (c) What fraction of the total charge is contained within the region R/2 ≤ r ≤ R? (d) What is the magnitude of
Want to see the full answer?
Check out a sample textbook solutionChapter 22 Solutions
University Physics (14th Edition)
Additional Science Textbook Solutions
The Cosmic Perspective (8th Edition)
Conceptual Physics (12th Edition)
University Physics Volume 1
College Physics (10th Edition)
Physics: Principles with Applications
Essential University Physics: Volume 1 (3rd Edition)
- QUESTION 1 Problem: An infinitely long cylindrical conductor has radius R and uniform surface charge density o. In terms of R and o, what is the charge per unit length A for the cylinder? Answer: A = 2arrow_forwardDensity, density, density. (a) A charge -328e is uniformly distributed along a circular arc of radius 6.00 cm, which subtends an angle of 72°. What is the linear charge density along the arc? (b) A charge -328e is uniformly distributed over one face of a circular disk of radius 3.50 cm. What is the surface charge density over that face? (c) A charge -328e is uniformly distributed over the surface of a sphere of radius 2.00 cm. What is the surface charge density over that surface? (d) A charge -328e is uniformly spread through the volume of a sphere of radius 3.30 cm. What is the volume charge density in that sphere? (a) Number Units (b) Number Units (c) Number Units (d) Number Unitsarrow_forwardWhat is the linear charge density of a thin wire bent into a circle (or ring) of radius 6.48 cm if the total charge on the wire is 3.86 µC? Give your answer in μC/m.arrow_forward
- O Macmillan Learning A sphere of radius R₁ = 0.340 m and uniform charge density -43.5 μC/m³ lies at the center of a neutral, spherical, conducting shell of inner and outer radii R₂ = 0.558 m and R3 = 0.770 m, respectively. Find the surface charge density on the inner and outer surfaces of the shell. inner surface charge density: 1.83 outer surface charge density: 96 μC/m² μC/m² | R₁ R₂ R3arrow_forwardA -198.7 mC charge is placed at the center of a hollow conducting sphere. Find the Charge density (in C/m²) on the outside of the sphere if its radius is 6.47 cm and if it Contains zero net charge.arrow_forwardA uniformly charged sphere has net charge Q and radius R= 20 om. What radius would a gaussian sphere need charged sphere. have order to enclose 10% of the total charge? Assume the gaussian sphere is co-centered with the Part A omarrow_forward
- Density, density, density. (a) A charge -352e is uniformly distributed along a circular arc of radius 7.40 cm, which subtends an angle of 50o. What is the linear charge density along the arc? (b) A charge -352e is uniformly distributed over one face of a circular disk of radius 3.10 cm. What is the surface charge density over that face? (c) A charge -352e is uniformly distributed over the surface of a sphere of radius 2.50 cm. What is the surface charge density over that surface? (d) A charge -352e is uniformly spread through the volume of a sphere of radius 3.60 cm. What is the volume charge density in that sphere?arrow_forwardA long copper cylindrical shell of inner radius 2 cm and outer radius 3 cm surrounds concentrically a charged long aluminum rod of radius 1 cm with a charge density of 4 pC/m. All charges on the aluminum rod reside at its surface. The inner surface of the copper shell has exactly charge to that of the aluminum rod while the outer surface of the copper shell has the same charge as the aluminum rod. Find the magnitude and direction of the electric field at points that are at the following distances from the center of the aluminum rod: (a) 0.5 cm, (b) 1.5 cm, (c) 2.5 cm, (d) 3.5 cm, and (e) 7 cm.arrow_forwardA point charge q=5.01012 C is placed at the center of a spherical conducting shell of inner radius 3.5 cm and outer radius 4.0 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 8.0 N/C. (a) What is the charge density on the inner surface of the shell? (b) What is the charge density on the outer surface of the shell? (c) What is the net charge on the conductor?arrow_forward
- The electric field 10.0 cm from the surface of a copper ball of radius 5.0 cm is directed toward the ball's center and has magnitude 4.0102 N/C. How much charge is on the surface of the ball?arrow_forwardA line of charge with a non-uniform charge density λ (lambda) = ay, where a=−10 nC/m2 lies along the y axis with one end at the origin and the other at y=h, where h=4.7 m a) What is the total charge?arrow_forwardA long cylindrical conductor of radius r= 5.0cm has a uniform charge density of ơ1 := 4.0 HC on it surface. This cylinder is surrounded by a concentric conducting cylinder of radius r2:= 8.0cm με and uniform charge density of 2:=-2.5 on its surfacearrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning