A particle with charge 5.0-µC is placed at the corner of a cube. The total electric flux in N · m2 /C through all sides of the cube is: A solid, nonconducting sphere of radius 4.0 cm has nonuniform volume charge distribution p that is a function of radial distance from the center of the sphere: p= Ar².for A-2C/m², what is the electric field at r=1,0 cm3 How we can solve these questions

A particle with charge 5.0-µC is placed at the corner of a cube. The total electric flux in N · m2 /C through all sides of the cube is: A solid, nonconducting sphere of radius 4.0 cm has nonuniform volume charge distribution p that is a function of radial distance from the center of the sphere: p= Ar².for A-2C/m², what is the electric field at r=1,0 cm3 How we can solve these questions

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 43PQ: The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R),...

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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.
A dosed surface with dimensions a = b= 0.400 111 and c = 0.600 in is located as shown in Figure 124.63. The left edge of the closed surface is located at position x = a. The electric field throughout the region is non- uniform and is given by E = (3.00 + 2.00x2)i N/C, where x is in meters. (a) Calculate the net electric flux leaving the closed surface. (b) What net charge enclosed by the surface?
A long, nonconducting, solid cylinder of radius 4.0 cm has a nonuniform volume charge density r that is a function of radial distance r from the cylinder axis: r =Ar2. For A = 2.5 mC/m5, what is the magnitude of the electric field at (a) r = 3.0 cm and (b) r = 5.0 cm?
The figure below shows a non-conducting spherical shell with a charge density of ρ = + 2 x 10-6 C/m^3. If the inner and outer radii of the sphere a = 10 cm and b = 20 cm, respectively, find the electric field strength E as a function of the distance from the center of the sphere's shell r, with r from zero to 30 cm.
A solid ball of radius R has a uniform volume charge density and produces a certain electric field magnitude E1 at point P, a distance 3.08R from the ball's center. If a core of radius 0.385R is removed from the ball, what fraction of E1 will the field magnitude at P be?
A solid conducting sphere of radius R has a uniform charge distribution, with a density = Ps * r / R where Ps is a constant and r the distance from the center of the sphere. Prove a) the total charge on the sphere is Q = πPsR ^ 3 b) the electric field of the sphere is given by E = (1 / 4πε0) * (Q / R ^ 4) * (r ^ 2)
A solid metallic sphere of radius a carries total charge Q. No other charges are nearby. The electric field just outside its surface is keQ/a2 radially outward. At this close point, the uniformly charged surface of the sphere looks exactly like a uniform flat sheet of charge. Is the electric field here given by σ/∈0 or by σ/2∈0?
Consider an imaginary cylinder with a radius of r = 0.165 mm and a length of l = 0.465 m that has an infinite line of positive charge running along its axis. The charge per unit length on the line is λ = 6.85 μC/m. What is the electric flux through the cylinder due to this infinite line of charge?
A small conducting ball that carries a charge of 30.0 nC islocated at the center of an electrically neutral hollow conductingsphere of inner radius 100 mm and outer radius 150 mm. Whatis the surface charge density (a) on the sphere’s inner surface and(b) on its outer surface? (c) Determine the electric field as a functionof r, the radial distance from the center of the sphere
A uniform charge density of 660 nC/m3 is distributed throughout a spherical volume of radius 6.00 cm. Consider a cubical Gaussian surface with its center at the center of the sphere. (a) What is the electric flux through this cubical surface if its edge length is 2.30 cm?___________N · m2/C(b) What is the electric flux through this cubical surface if its edge length is 17.0 cm? ___________N · m2/C
If a solid insulating sphere of radius 50 cm carries a total charge of 150 µC uniformly distributedthroughout its volume, what is its a) volume charge density? What is the magnitude of the electricfield at b) 10 cm and c) 65 cm from the center of the sphere.
A solid sphere of insulating material with radius R=7.62cm�=7.62cm has a uniform volume charge density given by p(r) = { (p0 for r<=R), (0 for r > R)} where ρ0=296nC/m3. What is the magnitude, in newtons per coulomb, of the electric field at a distance r=3.28cm from the center of the sphere. What is the magnitude, in newtons per coulomb, of the electric field at a distance r=11.9cm from the center of the sphere.