Question 12 please 10. Write an equation for the magnitude of the displacement vector, R.11. Write an integral for the total electric field due to dq. Then, substitute in all the expressionsfor dq, R and R and rewrite the integral for E.12. The previous exercise should give two integrals. One for the x-component and one for the ycomponent. Notice the y -component integration is of an odd function about symmetriclimits. So, the y - component of the field is zero. See the document labeled "ToughIntegral.pdf to determine the x-component. Write the final expression for the electric fieldusing that document. A short, charged, thin, plastic rod of length 2a is placed on the y-axis. The total charge on therod is +Q Coulombs. We want to determine the total electric field at a general point, P locatedon the x-axis. Notice the symmetry of the source, charged object about the x-axis.+a- aYPX

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charge on th - We want to determine the total electric field at a general point, P locat e the symmetry of the source, charged object about the z-axis.

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter22: Electric Fields

Section: Chapter Questions

Problem 19P: Three point charges are located on a circular arc as shown in Figure P22.19. (a) What is the total...

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A circular ring of charge with radius b has total charge q uniformly distributed around it. What is the magnitude of the electric field at the center of the ring? (a) 0 (b) keq/b2 (c) keq2/b2 (d) keq2/b (e) none of those answers
aA plastic rod of length = 24.0 cm is uniformly charged with a total charge of +12.0 C. The rod is formed into a semicircle with its center at the origin of the xy plane (Fig. P24.34). What are the magnitude and direction of the electric field at the origin? Figure P24.34
A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are b and c as shown in Figure P19.75. We wish to understand completely the charges and electric fields at all locations. (a) Find the charge contained within a sphere of radius r a. (b) From this value, find the magnitude of the electric field for r a. (c) What charge is contained within a sphere of radius r when a r b? (d) From this value, find the magnitude of the electric field for r when a r b. (e) Now consider r when b r c. What is the magnitude of the electric field for this range of values of r? (f) From this value, what must be the charge on the inner surface of the hollow sphere? (g) From part (f), what must be the charge on the outer surface of the hollow sphere? (h) Consider the three spherical surfaces of radii a, b, and c. Which of these surfaces has the largest magnitude of surface charge density?
Three charged particles are arranged on corners of a square as shown in Figure OQ23.11, with charge Q on both the particle at the upper left corner and the particle at the lower right corner and with charge +2Q on the particle at the lower left corner. (i) What is the direction of the electric field at the upper right corner, which is a point in empty space? (a) It is upward and to the right. (b) It is straight to the right. (c) It is straight downward. (d) It is downward and to the left. (e) It is perpendicular to the plane of the picture and outward. (ii) Suppose the +2Q charge at the lower left corner is removed. Then does the magnitude of the field at the upper right corner (a) become larger, (b) become smaller, (c) stay the same, or (d) change unpredictably?
Figure P15.49 shows a closed cylinder with cross-sectional area A = 2.00 m2. The constant electric field E has magnitude 3.50 103 N/C and is directed vertically upward, perpendicular to the cylinder's top and bottom surfaces so that no field lines paw through the curved surface. Calculate the electric flux through the cylinder's (a) lop and (b) bottom surface, (c) Determine the amount of charge inside the cylinder. Figure P15.49
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.
The infinite sheets in Figure P25.47 are both positively charged. The sheet on the left has a uniform surface charge density of 48.0 C/m2, and the one on the right has a uniform surface charge density of 24.0 C/m2. a. What are the magnitude and direction of the net electric field at points A, B, and C? b. What is the force exerted on an electron placed at points A, B, and C? FIGURE P25.47
Two solid spheres, both of radius 5 cm, carry identical total charges of 2 C. Sphere A is a good conductor. Sphere B is an insulator, and its charge is distributed uniformly throughout its volume. (i) How do the magnitudes of the electric fields they separately create at a radial distance of 6 cm compare? (a) EA EB = 0 (b) EA EB 0 (c) EA = EB 0 (d) 0 EA EB (e) 0 = EA EB (ii) How do the magnitudes of the electric fields they separately create at radius 4 cm compare? Choose from the same possibilities as in part (i).
Why is the following situation impossible? A solid copper sphere of radius 15.0 cm is in electrostatic equilibrium and carries a charge of 40.0 nC. Figure P24.30 shows the magnitude of the electric field as a function of radial position r measured from the center of the sphere. Figure P24.30
Two very long, thin, charged rods lie in the same plane (Fig. P25.30). One rod is positively charged with charge per unit length +, and the other is negatively charged with charge per unit length . The perpendicular distance between the rods is R. Using the coordinate system shown in the figure, sketch the electric field as a function of r from R to +2R. FIGURE P25.30
(a) Determine the electric field strength at a point 1.00 cm to the left of the middle charge shown in Figure P15.10. (b) If a charge of 2.00 C is placed at this point, what are the magnitude and direction of the force on it?
Assume the magnitude of the electric field on each face of the cube of edge L = 1.00 m in Figure P23.32 is uniform and the directions of the fields on each face are as indicated. Find (a) the net electric flux through the cube and (b) the net charge inside the cube. (c) Could the net charge he a single point charge? Figure P23.32