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For a given surface, the electric flux,
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- 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_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 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_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 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_forwardConsider two thin disks, of negligible thickness, of radius R oriented perpendicular to the x axis such that the x axis runs through the center of each disk. The disk centered at x=0 has positive charge density η, and the disk centered at x=a has negative charge density −η, where the charge density is charge per unit area. What is the magnitude E of the electric field at the point on the x axis with x coordinate a/2? Express your answer in terms of η, R, a, and the permittivity of free space ϵ0.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
- A 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 disk of radius 196 mm is oriented with its normal unit vector n̂ at 60º to a uniform electric field of magnitude 5.87 x 103 N/C. (a)What is the electric flux through the disk? (b) What is the flux through the disk if n̂ is parallel toarrow_forwardA cylinder has a length L and radius R. It has a non-uniform charge distribution p such that p = por? for rR Find the electric field both inside and outside the cylinder.arrow_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