•5 In Fig. 23-33, a proton is a dis- tance d/2 directly above the center of a square of side d. What is the magnitude of the electric flux through the square? (Hint:Think of the square as one face of a cube with edge d.) d/2 Figure 23-33 Problem 5.

•5 In Fig. 23-33, a proton is a dis- tance d/2 directly above the center of a square of side d. What is the magnitude of the electric flux through the square? (Hint:Think of the square as one face of a cube with edge d.) d/2 Figure 23-33 Problem 5.

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 53PQ

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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.
•34 In Fig. 23-45, a small circular hole of radius R = 1.80 cm has been cut in the middle of an infinite, flat, nonconducting surface that has uniform charge density o = 4.50 pC/m?. A z axis, with its origin at the hole's center, is perpendicular to the surface. In unit- vector notation, what is the electric field at point Pat z = 2.56 cm? (Hint: See Eq. 22-26 and use superposition.) Figure 23-45 Problem 34.
*•32 a0 In Fig. 22-50, positive charge q = 7.81 pC is spread uni- formly along a thin nonconducting rod of length L= 14.5 cm. What are the (a) magnitude and (b) di- rection (relative to the positive di- rection of the x axis) of the electric field produced at point P, at dis- tance R= 6.00 cm from the rod along its perpendicular bisector? -x L
•13 ao Figure 22-40 shows a proton (p) on the central axis through a disk with a uniform charge density due to excess electrons. The disk is seen from e, an edge-on view. Three of those elec- trons are shown: electron e, at the disk center and electrons e, at oppo- site sides of the disk, at radius R from -R ER- Figure 22-40 Problem 13. the center. The proton is initially at distance z = R =2.00 cm from the disk. At that location, what are the magnitudes of (a) the electric field E, due to electron e̟ and (b) the net electric field Esnet due to electrons e,? The proton is then moved to z = R/10.0. What then are the magnitudes of (c) E, and (d) Esnet at the proton's location? (e) From (a) and (c) we see that as the proton gets nearer to the disk, the magnitude of Ē increases, as expected. Why does the magnitude of Enet from the two side electrons decrease, as we see from (b) and (d)?
-24 Figure 23-40 shows a section of a long, thin-walled metal tube of radius R= 3.00 cm, with a charge per unit length of A = 2.00 x 10-8 C/m. What is the magnitude E of the electric field at radial distance (a) r= R2.00 and (b) r= 2.00R? (c) Graph E versus r for the range r = 0 to 2.00R.
In Fig.89 the metallic wire has a uniform linear charge density λ = 4 x 10-⁹C/m, the rounding radius R=10cm is much smaller than the length of the wire. Find the magnitude of the electric field at point "0". 001|2 R Fig-89
54 o In Fig. 22-61, an electron is shot at an initial speed of Detecting screen Vo = 2.00 x 10° m/s, at angle 6 = 40.0° from an x axis. It moves through a uniform electric field E = (5.00 N/C)j. A screen for de- tecting electrons is positioned par- allel to the y axis, at distance x = 3.00 m. In unit-vector notation, what is the velocity of the electron when it hits the screen? Figure 22-61 Problem 54.
8 Figure 23-27 shows four solid spheres, each with charge Q uniformly distributed through its volume. (a) Rank the spheres according to their volume charge density, greatest first. The figure also shows a point P for each sphere, all at the same distance from the center of the sphere. (b) Rank the spheres according to the mag- nitude of the electric field they produce at point P, greatest first. P. Pe P. P. (a) (b) (c) (d)
•13 O Figure 22-40 shows a proton (p) on the central axis through a disk with a uniform charge density due to excess electrons. The disk is seen from e, an edge-on view. Three of those elec- trons are shown: electron e, at the disk center and electrons e, at oppo- Figure 22-40 Problem 13. -R- site sides of the disk, at radius R from the center. The proton is initially at distance z = R = 2.00 cm from the disk. At that location, what are the magnitudes of (a) the electric field E̟ due to electron e and (b) the net electric field Enet due to electrons e,? The proton is then moved to z = R/10.0. What then are the magnitudes of (c) E, and (d) E,net at the proton's location? (e) From (a) and (c) we see that as the proton gets nearer to the disk, the magnitude of E, increases, as expected. Why does the magnitude of E, net from the two side electrons decrease, as we see from (b) and (d)?
18) Po O' A R R/2 A very long, soli d insulating cylinder of radius R = 1.2 m has a cylindrical empty hole with radius R/2 centered at 0' along its entire length. The solid material of the cylinder has a uniform volume charge density p = 0.5x10-9 m3 The di stance solidin between O' and A points is R/4 and the Point B is 10R away from the point O. ius R/ What is the potential di fference between points A and B, that is, V- V3? = 8.85x10-12 (C2/N.m²)). as a un nd Ap otentia A) 536.1 V B) 178.7 V C) 571.8 V D) 64.33 V E) 128.6 V 1-12
•23 Figure 22-47 shows two paral- lel nonconducting rings with their central axes along a common line. Ring 1 has uniform charge qi and ra- dius R; ring 2 has uniform charge q2 and the same radius R. The rings are separated by distance d = 3.00R. The net electric field at point P on the common line, at distance R from ring 1, is zero. What is the ratio qlq,? Ring 1 Ring 2 42 'R -d- Figure 22-47 Problem 23.
7 Figure 23-26 shows four situations in which four very long rods extend into and out of the page (we see only their cross sec- tions). The value below each cross section gives that particular rod's uniform charge density in microcoulombs per meter. The rods are separated by either d or 2d as drawn, and a central point is shown midway between the inner rods. Rank the situations ac- cording to the magnitude of the net electric field at that central point, greatest first. (a) +3 +2 (6) +2 -4 -4 +2 (c) +8 +8 (d) -6 +5 +5 -6