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You are working on a laboratory device that includes a small sphere with a large electric charge Q. Because of this charged sphere, there is a strong electric field surrounding your device. Other researchers in your laboratory are complaining that your electric field is affecting their equipment. You think about how you can obtain the large electric field that you need close to the sphere but prohibit the field from reaching your colleagues. You decide to surround your device with a spherical transparent plastic shell. The nonconducting shell is given a uniform charge distribution. (a) The shell is placed so that the small sphere is at the exact center of the shell. Determine the charge that must he placed on the shell to completely eliminate the electric field outside of the shell. (b) What if the shell moves? Does the small sphere have to be at the center of the shell for this scheme to work?
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Chapter 23 Solutions
Physics for Scientists and Engineers
- 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?arrow_forwardTwo infinite, nonconducting sheets of charge are parallel to each other as shown in Figure P19.73. The sheet on the left has a uniform surface charge density , and the one on the right hits a uniform charge density . Calculate the electric field at points (a) to the left of, (b) in between, and (c) to the right of the two sheets. (d) What If? Find the electric fields in all three regions if both sheets have positive uniform surface charge densities of value .arrow_forwardFigure 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 P15.49arrow_forward
- 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 e as shown in Figure P24.45. 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? Figure P24.45 Problems 43 and 47.arrow_forwardFigure 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 P15.49arrow_forwardA pyramid has a square base with an area of 4.00 m2 and a height of 3.5 m. Its walls are four isosceles triangles. The pyramid is in a uniform electric field of 655 N/C pointing downward (Fig. P25.13). What is the electric flux through the square base?arrow_forward
- Find the net electric flux through (a) the closed spherical surface in a uniform electric field shown in Figure P23.22a and (b) the closed cylindrical surface shown in Figure P23.22b. (c) What can you conclude about the charges, if any, inside the cylindrical surface? Figure P23.22arrow_forwardA slab of insulating material has a nonuniform positive charge density = Cx2, where x is measured from the center of the slab as shown in Figure P23.45 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 (|x| d/2) and (b) the interior region of the slab (d/2 x d/2). Figure P23.45arrow_forwardA positively charged sphere and a negatively charged sphere are in a sealed container. The only way the charged spheres can be examined is by observing the electric field outside the container. a. Given the depiction of the electric fields in Figure P25.7A, is the net electric flux through the container zero, positive, or negative? Explain your answer. b. Two different spheres are placed inside a container. Given the depiction of the electric fields in Figure P25.7B, is the net electric flux through the container zero, positive, or negative? Explain your answer.arrow_forward
- 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 P25.47arrow_forwardTwo positively charged spheres are shown in Figure P24.70. Sphere 1 has twice as much charge as sphere 2. If q = 6.55 nC, d = 0.250 m, and y = 1.25 m, what is the electric field at point A?arrow_forwardA solid insulating sphere of radius a = 5.00 cm carries a net positive charge of Q = 3.00 C uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius b = 10.0 cm and outer radius c = 15.0 cm as shown in Figure P24.54, having net charge q = 1.00 C Prepare a graph of the magnitude of the electric field due to this configuration versus r for O r 25.0 cm.arrow_forward
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