This is a test given in the past - it is a sample - to show you what the tests are like Physics 223 Name ____________________ - it is not meant for practice and these particular problems will probably not be on the test Exam #1(a) Student # _________________ No Work! No Credit! 1. A long cylindrical conductor has a radius ra and a linear charge density +λ. It is surrounded by a coaxial cylindrical conducting shell with inner radius rb and linear charge density – λ. To receive credit, each response must include a complete derivation of the electric field or the electric potential. a. Compute the electric field in the region r < ra. (4) b. Compute the electric field in the region ra < r < rb. (7) c. Compute the potential difference between the cylinders. (7) Physics 223 Exam #1(a) No Work! No Credit! Name ____________________ Student # _________________ 2. The drawing shows a plastic rod having a uniformly distributed charge of –Q. The rod has been bent in a 120º circular arc of radius r. The point P is at the center of curvature of the rod. a. Compute the electric field due to the rod at point P. (9) b. Compute the electric potential at point P (Assume V = 0 at infinity). (9) Physics 223 Exam #1(a) No Work! No Credit! Name ____________________ Student # _________________ 3. Three point charges –Q, –Q, and +3Q are arranged along a line as shown in the sketch. Assume that Q = 4 µC and R = 2.0 m. P R −Q +3Q −Q R R a. Compute the electric field at point P. (6) b. Compute the electric potential at point P. (6) c. At a particular instant, an electron is placed at point P. Compute the electron’s acceleration at this instant. (3) d. Compute the electron’s potential energy when it is located at point P. Assume U = 0 when the electron is infinitely far away. (3) Physics 223 Name ____________________ Exam #1(a) Student # _________________ No Work! No Credit! 4. A very large flat plate is charged so that it produces a uniform electric field of r E = (− 720 N / C ) yˆ in the region above the plate. Protons are then projected with an initial speed of vi = 9.55 × 10 3 m / s into the region where the electric field is present. The protons are to strike a target that lies at a horizontal distance of 1.27 mm from the point where the protons cross the plate and enter the electric field. a. Determine the surface charge density of the plate. (4) b. Compute one of the two projection angles that will result in the proton striking the target. (6) c. Compute the time of flight for the projection angle determined in part (b). (4) d. Compute the second projection angle that will result in the proton striking the target. (4) Physics 223 Exam #1(a) No Work! No Credit! Name ____________________ Student # _________________ 5. Each of three objects has a net charge. Objects A and B attract one another. Objects B and C also attract one another, but objects A and C repel one another. Which one of the following table entries is a possible combination of the signs of the net charges on these three objects? (4) (a) (b) (c) (d) (e) A + − + − − B + + − + − C − + − − + 6. Two particles of the same mass carry charges +3Q and –2Q, respectively. They are shot into a region that contains a uniform electric field as shown. The particles have the same initial velocities in the positive x direction. The lines, numbered 1 through 5, indicate possible paths for the particles. If the electric field points in the negative y direction, what will be the resulting paths for these particles? (4) 1 y 2 x 3 point of entry (a) (b) (c) (d) (e) E 4 5 Path 1 for +3Q and path 4 for –2Q Path 2 for +3Q and path 5 for –2Q Path 3 for +3Q and path 2 for –2Q Path 5 for +3Q and path 2 for –2Q Path 4 for +3Q and path 3 for –2Q 7. Two positive charges are located at points A and B as shown in the figure. The distance from each charge to the point P is a = 2.0 m. (4) A +3.0 µC a P a +3.0 µC B Which statement is true concerning the direction of the electric field at P? (a) (b) (c) (d) (e) The direction is toward A. The direction is toward B. The direction is directly away from A. The direction makes a 45° angle above the horizontal direction. The direction makes a 135° angle below the horizontal direction. Physics 223 Exam #1(a) No Work! No Credit! Name ____________________ Student # _________________ 8. Suppose that the charges from #3 are rearranged as shown in this figure. (4) A P a a B Which one of the following statements is true for this new arrangement? (a) (b) (c) (d) (e) The electric field will be zero, but the electric potential remains unchanged. Both the electric field and the electric potential are zero at P. The electric field will remain unchanged, but the electric potential will be zero. The electric field will remain unchanged, but the electric potential will decrease. The electric field will remain unchanged, but the electric potential will increase. 9. Calculate the total electric flux through the paraboloidal surface due to a uniform electric field of magnitude E0 in the direction shown in the figure. (5) 10. A charge Q exerts a 12 N force on another charge q. If the distance between the charges is doubled, what is the magnitude of the force exerted on Q by q ? (5)