48 O A charged particle is held at the center of a sphericalshell. Figure 23-53 gives the magnitude E of the electric field ver-sus radial distance r. The scale of the vertical axis is set by E, =10.0 x 10' N/C. Approximately, what is the net charge on theshell?E,3.r (cm)4.(5/N ,01) 7

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Answered: 48 O A charged particle is held at the…

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 48PQ

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Example 23.3 derives the exact expression for the electric field at a point on the axis of a uniformly charged disk. Consider a disk of radius R = 3.00 cm having a uniformly distributed charge of +5.20 C. (a) Using the result of Example 23.3, compute the electric field at a point on the axis and 3.00 mm from the center. (b) What If? Explain how the answer to part (a) compares with the field computed from the near-field approximation E = /20. (We derived this expression in Example 23.3.) (c) Using the result of Example 23.3, compute the electric field at a point on the axis and 30.0 cm from the center of the disk. (d) What If? Explain how the answer to part (c) compares with the electric field obtained by treating the disk as a +5.20-C charged particle at a distance of 30.0 cm.
An aluminum spherical ball of radius 4 cm is charged with 5C of charge. A copper spherical shell of inner radius 6 cm and outer radius 8 cm surrounds it. A total charge of 8C is put on the copper shell. (a) Find the electric field at all points in space, including points inside the aluminum and copper shell when copper shell and aluminum sphere are concentric. (b) Find the electric field at all points in space, including points inside the aluminum and copper shell when the centers of copper shell and aluminum sphere are 1 cm apart.
ne electric field at 2 cm from the center of long copper rod of radius 1 cm has a magnitude 3 N/C and directed outward from the axis of the rod. (a) How much charge per unit length exists on the rod? (b) What would be the electric flux through a cube of side 5 cm situated such that the rod passes through opposite sides of the cube perpendicularly?
Suppose the conducting spherical shell of Figure 15.29 carries a charge of 3.00 nC and that a charge of -2.00 nC is at the center of the sphere. If a = 2.00 m and b = 2.40 m. find the electric field at (a) r = 1.50 m, (b) r = 2.20 m, and (c) r = 2.50 m. (d) What is the charge distribution on the sphere?
A uniformly charged disk of radius 35.0 cm carries charge with a density of 7.90 10-3 C/m2. Calculate the electric field on the axis of the disk at (a) 5.00 cm, (b) 10.0 cm, (c) 50.0 cm, and (d) 200 cm from the center of the disk.
A charged rod is placed in the center along the axis of a neutral metal cylinder (Fig. F25.57). The rod has a total charge of 38.3 C uniformly distributed. What are the charges on the inner and outer surfaces of the metal cylinder? (Ignore the ends.) FIGURE P25.57 Problems 57 and 58.
A uniformly charged spherical shell with positive surface charge density contains a circular hole in its surface. The radius r of the hole is small compared with the radius R of the sphere. What is the electric field at the center of the hole? Suggestion: This problem can be solved by using the principle of superposition.
A thin, square, conducting plate 50.0 cm on a side lies in the xy plane. A total charge of 4.00 108 C is placed on the plate. Find (a) the charge density on each face of the plate, (b) the electric field just above the plate, and (c) the electric field just below the plate. You may assume the charge density is uniform.
Figure P23.23 represents the top view of a cubic gaussian surface in a uniform electric field E oriented parallel to the top and bottom faces of the cube. The field makes an angle with side , and the area of each face is A. In symbolic form, find the electric flux through (a) face , (b) face , (c) face , (d) face , and (e) the top and bottom faces of the cube. (f) What is the net electric flux through the cube? (g) How much charge is enclosed within the gaussian surface? Figure P23.23
(a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in Figure 18.53, given that qa= 1.00C and qc=qd= +1.00 C. (b) Calculate the magnitude of the electric field at the location of q, given that the square is 5.00 cm on a side.
The electric field everywhere on the surface of a charged sphere of radius 0.230 m has a magnitude of 575 N/C and points radially outward from the center of the sphere. (a) What is the net charge on the sphere? (b) What can you conclude about the nature and distribution of charge inside the sphere?
Determine if approximate cylindrical symmetry holds for the following situations. State why or why not. (a) A 300-cm long copper rod of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (b) A 10-cm long copper of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (c) A 150-cm wooden rod is glued to a 150-cm plastic rod to make a 300 cm long rod, which is then painted with a charged paint so that one obtains a uniform charge density. The radius of each rod is 1 cm, and we seek an electric field at a point that is 4 cm from the center of the rod. (d) Same rod as (c), but we seek electric field at a point that is 500 cm from the center of the rod.

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48 O A charged particle is held at the center of a spherical shell. Figure 23-53 gives the magnitude E of the electric field ver- sus radial distance r. The scale of the vertical axis is set by E, = 10.0 x 10' N/C. Approximately, what is the net charge on the shell? E, 3. r (cm) 4. (5/N ,01) 7