Exercises D4
.pdf
School
Windermere Preparatory School**We aren't endorsed by this school
Course
MATH 102
Subject
Physics
Date
Dec 18, 2024
Pages
10
Uploaded by MinisterGazelle4886
D4, Page 1of 10Class D, Bellingham Academy Class D Lesson 4 Exercise Use Scantron sheet to fill in answers to multiple-choice questions.
D4, Page 2of 10Class D, Bellingham Academy 1. The electric field of a uniformly charged sphere of radius R, has a magnitude of E at a distance, d>2R, from the center of the sphere. How does the magnitude of the electric field at a point that is d/2 from the center of the sphere compare? (A) It is E/4, (B) It is E/2, (C) It is E, (D) It is 2E, (E) It is 4E 2. Calculate the electric flux through a Gaussian surface of area A enclosing an electric dipole where each charge has magnitude q. (A) 0 (B) !"#$%!(C) !""#$%!(D) !"#$%!&(E) !"#$%!&"3. The figure shows 4 point charges and the cross section of a Gaussian surface. Which of the following statement is true concerning the situation depicted? (A) The net electric flux through the Gaussian surface depends on all four charges shown, but the eclectic field at point P depends only on charges Q2 and Q3. (B) The net electric flux through the Gaussian surface depends on charges Q2 and Q3, but the eclectic field at point P depends on all four charges. (C) The net electric flux through the Gaussian surface depends on charges Q2 and Q3, but the eclectic field at point P depends on Q2, Q3, and Q4. (D) The net electric flux through the Gaussian surface depends on charges Q1 and Q4, but the eclectic field at point P depends on Q2 and Q3. (E) Both the net electric flux through the Gaussian surface and the eclectic field at point P depends on all four charges. 4. Why it is safe to be inside a car during a lightning storm? (A) The car’s rubber tires are insulators. (B) There are air and leather or fabric inside the car. They are insulators. (C) Windows and doors are closed. (D) It is dry inside a car. (E) Car’s metal frame shields the electric field between cloud and ground.
D4, Page 3of 10Class D, Bellingham Academy 5. A nonconducting sphere of radius R contains a total charge of –Q distributed uniformly throughout its volume (that is the volume charge density , r is constant. ) The magnitude of the electric field at point P, at a distance r<R from the sphere’s center, is equal to (A) ’#$%!()#࠵?.(B) ’#$%!()"࠵?*(C) ’#$%!()#࠵?+(D) ’#$%!()#&"(E) ’#$%!(&"6. The figure shows cross sections of three-dimensional closed surfaces. They have a flat top and bottom surface above and below the plane of the page. However, the electric field is everywhere parallel to the page, so there is no flux through the top or bottom surface. The electric field is uniform over each face of the surface. For each, does the surface enclose a net positive charge, a net negative charge, or no net charge? (A) (a) negative, (b) positive, (c) zero. (B) (a) positive, (b) negative, (c) zero. (C) (a) zero, (b) positive, (c) negative. (D) (a) zero, (b) negative, (c) positive. (E) (a) negative, (b) zero, (c) positive. 7. The square, circle and the semispherical shell are in the same uniform field. The diameter of the circle and the spherical shell equals the edge length of the square. Rank the pass through flux of the three surfaces, greatest first. (A) a>b>c (B) b>c>a (C) b=c>a (D) a>b=c (E) b>a>c
D4, Page 4of 10Class D, Bellingham Academy 8. Rank the magnitude of the electric field flux through each of the Gaussian surfaces in the figure (A) a>b>c (B) b>c>a (C) b=c>a (D) a>b=c (E) a=b>c 9. Rank the magnitude of the electric field flux through each of the Gaussian surfaces in the figure (A) A=B>D>C=E (B) B>C>A>E>D (C) C=E>D>A=B (D) E>D>A>B=C (E) A>B>C>D>E 10. A uniformly charged balloon in the figure expands increasing in size from the initial to final diameters shown. Do the electric field strengths at points 1, 2, and 3 increase, decrease, or stay the same? (A) 1 increased; 2 decreased; 3 unchanged. (B) 1 decreased; 2 unchanged; 3 increased. (C) 1 unchanged; 2 decreased; 3 unchanged. (D) 1 unchanged; 2 unchanged; 3 unchanged. (E) 1 increased; 2 increased; 3 unchanged.
D4, Page 5of 10Class D, Bellingham Academy 11. The two spheres in the figure surround equal charges. Three students are discussing the situation. Student1: The fluxes through spheres A and B are equal because they enclose equal charges. Student 2: But the electric field on sphere B is weaker than the electric field on sphere A. The flux depends on the electric field strength, so the flux through A is larger than the flux through B. Student 3: I thought we learned that flux was about surface area. Sphere B is larger than sphere A, so I think the flux through B is larger than the flux through A. Which of these students, if any, do you agree with? (A) A (B) B (C) C (D) Cannot be determined 12. The sphere and ellipsoid in the figure surround equal charges. Four students are discussing the situation. Student 1: The fluxes through A and B are equal because the average radius is the same. Student 2: I agree that the fluxes are equal, but that’s because they enclose equal charges. Student 3: The electric field is not perpendicular to the surface for B, and that makes the flux through B less than the flux through A. Student 4: I don’t think that Gauss’s law even applies to a situation like B, so we can’t compare the fluxes through A and B. Which of these students, if any, do you agree with? (A) A (B) B (C) C (D) D (E) Cannot be determined
D4, Page 6of 10Class D, Bellingham Academy 13. A small neutral, metal sphere hangs by an insulating thread within the larger, hollow conducting neutral sphere of the figure. A conducting wire extends from the small sphere through, but not touching, a small hole in the hollow sphere. A charged rod is used to transfer positive charge to the protruding wire. After the charged rod has touched the wire and been removed, are the following surfaces positive, negative, or not charged? (A) The small sphere is positive; The inner surface of the hollow sphere is negative; The outer surface of the hollow sphere is positive. (B) The small sphere is negative; The inner surface of the hollow sphere is positive; The outer surface of the hollow sphere is negative. (C) The small sphere is positive; The inner surface of the hollow sphere is not charged; The outer surface of the hollow sphere is not charged. (D) The small sphere is not charged; The inner surface of the hollow sphere is not charged; The outer surface of the hollow sphere is not charged. (E) The small sphere is positive; The inner surface of the hollow sphere is positive; The outer surface of the hollow sphere is negative. 14. The figure shows a section of three long charged cylinders centered on the same axis. Central cylinder A has a uniform linear charge density of ࠵?!= +3࠵?,. The cylindrical shell B has uniform linear charge density of ࠵?-= −6࠵?,. The cylindrical shell C has uniform linear charge density of ࠵?.= +6࠵?,. Rank the field strength at point 1, point 2, and point 3, greatest first. (A) 1=2=3 (B) 2>1>3. (C) 1>2>3 (D) 1>2=3 (E) 3>2>1 15. The figure shows four Gaussian surfaces consisting of identical cylindrical midsections but different end caps. The surfaces are in a uniform electric field E that is directed parallel to the central axis of each cylindrical midsection. The end caps have these shapes: S1, convex hemispheres; S2, concave hemispheres; S3, cones; S4, flat disks. Rank the surfaces according to (a) the net electric flux through them and (b) the electric flux through the top end caps, greatest first. (A) (a) 1=2=3=4; (b) 1=2=3=4; (B) (a) 1>2>3>4; (b) 1>2>3>4; (C) (a) 1<2<3<4; (b) 1<2<3<4; (D) (a) 1=2>3=4; (b) 1=2>3=4; (E) (a) 1=2<3=4; (b) 1=2<3=4;
D4, Page 7of 10Class D, Bellingham Academy Free Response Questions 1. A conducting sphere shell of inner radius a and outer radius b is inside (and concentric with ) a larger conducting spherical shell of inner radius c and outer radius d. the inner shell carries a net charge of +2q, and the outer shell has a net charge of +3q. (a) Determine the electric field for (i) r<a (ii) a<r<b (iii) b<r<c (iv) c<r<d (v) r>d (b) Show in the figure the charges that reside on or inside each of the 2 shells.
D4, Page 8of 10Class D, Bellingham Academy 2. A nonconducting sphere of radius a has excess charge distributed throughout its volume so that the volume charge density ras a function of r (the distance from the sphere’s center) is given by the equation r(r) = r0(r/a)2, where r0is a constant. Determine the electric field at points inside and outside the sphere.
D4, Page 9of 10Class D, Bellingham Academy 3. A very long, solid, nonconducting cylinder of radius R has a positive charge of uniform volume density ࠵?. A section of the cylinder far from its ends is shown in the diagram above. Let r represent the radial distance from the axis of the cylinder. Express all answers in terms of r, R, ࠵?, and fundamental constants, as appropriate. (a) Using Gauss’s law, derive an expression for the magnitude of the electric field at a radius r < R. Draw an appropriate Gaussian surface on the diagram. (b) Using Gauss’s law, derive an expression for the magnitude of the electric field at a radius r > R. (c) On the axes below, sketch the graph of electric field E as a function of radial distance r for r = 0 to r = 2R. Explicitly label any intercepts, asymptotes, maxima, or minima with numerical values or algebraic expressions, as appropriate.
D4, Page 10of 10Class D, Bellingham Academy 4. Consider a small conducting sphere with charge +Q whose center is at corner A of a cubical surface, as shown below. (a) For which faces of the surface, if any, is the electric flux through that face equal to zero? ____ ABCD ____ CDEF ____ EFGH ____ ABGH ____ BCFG ____ ADEH Explain your reasoning. (b) At which corner(s) of the surface does the electric field have the least magnitude? (c) Determine the electric field strength at the position(s) you have indicated in part (b) in terms of Q, L, and fundamental constants, as appropriate. (d) Given that one-eighth of the sphere at point A is inside the surface, calculate the electric flux through face CDEF.