A sphere of radius R₁ = 0.320 m and uniform charge density 10.5 μC/m³ lies at the center of a neutral, spherical, conducting shell of inner and outer radii R₂ = 0.558 m and R3 = 0.730 m, respectively. Find the surface charge density on the inner and outer surfaces of the shell. inner surface charge density: outer surface charge density: µC/m² µC/m² R₁ R₂ R3
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- A charge of uniform linear density 2.20 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 5.40 cm, outer radius 10.0 cm). The net charge on the shell is zero. (a) What is the magnitude of the electric field at distance r = 15.4 cm from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of the shell? Stell-A cylinder of length L=5m has a radius R=2 cm and linear charge density 2=300 µC/m. Although the linear charge density is a constant through the cylinder, the charge density within the cylinder changes with r. Within the cylinder, the charge density of the cylinder varies with radius as a function p( r) =p.r/R. Here R is the radius of the cylinder and R=2 cm and p, is just a constant that you need to determine. b. Find the constant po in terms of R and 2. Then plug in values of R and 1. to find the value for the constant p. c. Assuming that L>>R, use Gauss's law to find out the electric field E inside the cylinder (rR) in terms of 1. and R. d. Based on your result from problem c, find the electric field E at r=1cm and r=4cm.A charge of uniform linear density 2.00 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 4.20 cm, outer radius = 9.80 cm). The net charge on the shell is zero. (a) What is the magnitude of the electric field at distance r = 14.0 cm from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of the shell?
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