Concept explainers
For a given surface, the electric flux,
C. Sketch vector
Learn your wayIncludes step-by-step video
Chapter 5 Solutions
Tutorials in Introductory Physics
Additional Science Textbook Solutions
Essential University Physics (3rd Edition)
The Cosmic Perspective
Physics for Scientists and Engineers with Modern Physics
Applied Physics (11th Edition)
Sears And Zemansky's University Physics With Modern Physics
- An insulating solid sphere of radius a has a uniform volume charge density and carries a total positive charge Q. A spherical gaussian surface of radius r, which shares a common center with the insulating sphere, is inflated starting from r = 0. (a) Find an expression for the electric flux passing through the surface of the gaussian sphere as a function of r for r a. (b) Find an expression for the electric flux for r a. (c) Plot the flux versus r.arrow_forwardConsider a thin rod which has a uniformly distributed charge Qot = -1 µC. The rod is bent into a quarter of a circle of radius R = 1 m. Find the x- and y-components of the electric field created by the rod the point O the center of the arc. Hint: The following integrals are useful: cose de = [sin@]% î sine de = [-cos0]% Rarrow_forwardThe volumetric charge density of a cylinder of radius R is proportional to the distance to the center of the cylinder, that is, ρ = Ar when r≤R, with A being a constant. (a) Sketch the charge density for the region - 3R < r < 3R. What is the dimension of A?b) Calculate the electric field for a point outside the cylinder, r > Rc) Calculate the electric field for a point inside the cylinder, r<R.d) Sketch Exrarrow_forward
- A charge distribution creates the following electric field throughout all space: E(r, 0, q) = (3/r) (r hat) + 2 sin cos sin 0(theta hat) + sin cos p (phi hat). Given this electric field, calculate the charge density at location (r, 0, p) = (ab.c).arrow_forwardCharge of a uniform density (7 pC/m2) is distributed over the entire xy plane. A charge of uniform density (10 pC/m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 3.0 m.arrow_forwardTwo very long lines of charge are parallel to each other. One with a linear charge density −λ−λ , and the other have the linear charge density +λ+λ, and they are separated by a distance RR as shown in the figure. Calculate the electric field at a point half-way between the lines of charge. r⃗ r→ is the unit radial vector in the cylindrical coordinate of the line with +λ+λ charge density.arrow_forward
- A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r 1 = 6R the electric field has a magnitude E 0. What is the magnitude of the electric field at a radial distance r 2 = R/6 as a multiple of E 0 ?arrow_forwardA solid conducting sphere of radius R carries a positive electric charge Q. For what values or r is the electric field, E(r) = 0?arrow_forwardA disk of radius 132mm is oriented with its normal unit vector at 30 degrees to a uniform electric field E of magnitude 2.23x10^3 N/C. (a) what is the electric flux through the disk? (b) What is the flux through the disk if n is parallel to Earrow_forward
- Positive electric charge Q is distributed uniformly throughout the volume of an insulating sphere with radius R. Find the magnitude of the electric field at a point P a distance r from the center of the sphere.arrow_forwardA non-conducting spherical shell has an inner radius & and an outer radius 28. There are no charges at r<& wherer is the distance from the center of the sphere. A total charge is distributed uniformly in the volume of the shell (between r=R and r=2R) Find the magnitude of the electric field at r=1718. Express your answer in units of using two decimal R² kQ placesarrow_forwardA massive non-conducting sphere of radius R has a charge Q uniformly distributed in its volume. Using Gauss's law, find an expression for the electric field inside the sphere (r < R). At spherical coordinates the volume differential of a sphere is given by dV =r2senθ dr dθ dφarrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning