5. In Figure below, a conducting sphere of radius ri = 10 cm is placed at the center of a sphericalconducting shell of inner radius r2 = 20 cm and outer radius r3 = 30 cm. The inner conductingsphere carries a charge of (10 nC) and the outer surface of the conducting shell is (- 4 nC).Calculate the magnitude of the electric field at the following distances from the center of theinner sphere.(a) r = 5 cm(b) r = 15 cm(c) r = 25 cm andr = 40 cmr3r2

Answered: Image /qna-images/answer/5259fdcb-d7b5-48c8-bc3c-e0f6007a9d64.jpg

Answered: In Figure below, a conducting sphere of…

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 63PQ

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The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R), where c is a positive constant and r is the radial distance from the center of the sphere. For a spherical shell of radius r and thickness dr, the volume element dV = 4r2dr. a. What is the magnitude of the electric field outside the sphere (r R)? b. What is the magnitude of the electric field inside the sphere (r R)?
Consider a plane surface in a uniform electric field as in Figure P24.48, where d = 15.0 cm and = 70.0. If the net flux through the surface is 6.00 N find the magnitude of the electric field. Figure P24.48
A particle with charge Q is located a small distance immediately above the center of the flat face of a hemisphere of radius R as shown in Figure P19.38. What is the electric flux (a) through the curved surface and (b) through the flat face as 0?
A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of , and the cylinder has a net charge per unit length of 2. From this information, use Gausss law to find (a) the charge per unit length on the inner surface of the cylinder, (b) the charge per unit length on the outer surface of the cylinder, and (c) the electric field outside the cylinder a distance r from the axis.
Two infinite, nonconducting sheets of charge are parallel to each other as shown in Figure P19.73. The sheet on the left has a uniform surface charge density , and the one on the right hits a uniform charge density . Calculate the electric field at points (a) to the left of, (b) in between, and (c) to the right of the two sheets. (d) What If? Find the electric fields in all three regions if both sheets have positive uniform surface charge densities of value .
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 point charge of -3.00 uC is located in the center of a spherical cavity of radius 6.50 cm that, in turn, is at the center of an insulating charged solid sphere. The charge density in the solid is r = 7.35 * 10-4 C/m3. Calculate the electric field inside the solid at a distance of 9.50 cm from the center of the cavity.
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.
Figure 2 shows a nonconducting rod with a uniformly distributed charge Q. The rod forms a half-circle with radius R and produces an electric field of magnitude Earc at its center of curvature P. If the arc is collapsed to a point at distance R from P, by what factor is the magnitude of the electric field at P multiplied?
A positive static charge +10q is placed off-center inside a conducting shell of a certain thickness. The conductor has a net charge of +8q. What is the charge on the conductor's outer surface? A rectangular sheet with length 5.00 m and width 3.00 m is immersed in a uniform electric field with magnitude 14.0 N/C. If the sheet is placed at an angle 30∘ from the xy-plane and the electric field is pointing in the z-direction, what is the magnitude of the electric flux through the sheet?
Consider 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.
A solid insulating sphere of radius 0.07 m carries a total charge of 25 uC. Concentric with this sphere is a conducting spherical shell of inner radius 0.12 m and outer radius of 0.18 m, and carrying total charge of -54 uC. Find (a) the charge distribution for the insulating sphere and the conducting spherical shell, and the magnitude of the electric field at the follwing distances from the center of the two spheres and shell: (b) 0.05 m, (c) 0.10 m, (d) 0.15 m, and (e) 0.25 m.

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