Showing 61 to 70 of 255 Questions

An infinitely long cylindrical insulating shell of inner radius a and outer radius b has a uniform volume charge density 1. A line of uniform linear charge density A is placed along the axis of the shell. Determine the electric field everywhere.
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Two infinite, nonconducting sheets of charge are parallel to each other, as shown in Figure P24.62. The sheet on the left has a uniform surface charge density a, and the one on the right has a uniform charge density 4. Calculate the electric field at points (a) To the left of, (b) In between, and (c) To the right of the two sheets
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A sphere of radius 2a is made of a nonconducting material that has a uniform volume charge density 1. (Assume that the material does not affect the electric field.) A spherical cavity of radius a is now removed from the sphere, as shown in Figure P24.64. Show that the electric field within the cavity is uniform and is given by Ex = 0 and
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A uniformly charged spherical shell with surface charge density 4 contains a circular hole in its surface. The radius of the hole is small compared with the radius of the sphere. What is the electric field at the center of the hole? (Suggestion: This problem, like Problem 64, can be solved by using the idea of superposition.)
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A closed surface with dimensions a = b = 0.400 m and c = 0.600 m is located as in Figure P24.66. The left edge of the closed surface is located at position x = a. The electric field throughout the region is nonuniform and given by E = (3.0 + 2.0x2) i N/C, where x is in meters. Calculate the net electric flux leaving the closed surface. W
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A solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression 1 = Ar 2, where A is a constant and r < R is measured from the center of the sphere. (a) Show that the magnitude of the electric field outside (r > R) the sphere is E = AR 5/5/ 0r 2. (b) Show that the magnitude of the
0603 
A point charge Q is located on the axis of a disk of radius R at a distance b from the plane of the disk (Fig. P24.68). Show that if one fourth of the electric flux from the charge passes through the disk, then R = 3b.
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A spherically symmetric charge distribution has a charge density given by p = a/r, where a is constant. Find the electric field as a function of r. (Suggestion: The charge within a sphere of radius R is equal to the integral of 1 dV, where r extends from 0 to R. To evaluate the integral, note that the volume element dV for a spherical she
0487 
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as where p0, a, and b are positive constants and r is the distance from the axis of the cylinder. Use Gaussâ€™s law to determine the magnitude of the electric field at radial distances (a) r < R and (b) r > R.
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A slab of insulating material has a nonuniform positive charge density p = Cx2, where x is measured from the center of the slab as shown in Figure P24.71, and C is a constant. The slab is infinite in the y and z directions. Derive expressions for the electric field in (a) The exterior regions and (b) The interior region of the slab (
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