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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_forwardPositive charge is distributed in a sphere of radius R that is centered at the origin. Inside the sphere, the electric field is Ē(r) = kr-1/4 f, where k is a positive constant. There is no charge outside the sphere. a) How is the charge distributed inside the sphere? In particular, find an equation for the charge density, p. b) Determine the electric field, E(r), for r > R (outside the sphere). c) What is the potential difference between the center of the sphere (r = 0) and the surface of the sphere (r = R)? d) What is the energy stored in this electric charge configuration?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
- The 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_forwardA 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_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 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_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_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 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