PHYS 211 Exam 1, Fall 2012

Score:________ Check if solution is continued on the back. 1 PHYSICS 211 Quiz I TIME: 60 minutes November 18, 2012 DO NOT OPEN THIS EXAM BEFORE YOU ARE TOLD TO BEGIN NAME________________________________________________ ID Number ________________________ Useful information 0=8.85x10-12 C2/N.m2. 0=4 x 10-7 Tm/A. q = 1.6  1019 C me= 9.1x10-31 kg. mp= 1.67×10-27 kg. ke=8.9875x109 Nm2/C2 Grading A B TOTAL Score:________ Check if solution is continued on the back. 2 Part A: Multiple choice questions (12) 1. (3) If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = –80 nC, and q = 36 nC in the figure, what is the magnitude of the total electric force on q? a. 5.0 N b. 4.4 N c. 3.8 N d. 5.7 N e. 0.60 N 2. (3) Charge Q is distributed uniformly along a semicircle of radius a. Which formula below gives the correct magnitude of the electric field at the center of the circle? a. a Q E 0  4 1  . b. 2 0 4 1 a Q E    . c. a Q E   2 4 1 0  . d. 2 0 2 4 1 a Q E    . e. 2 0 2 4 1 a Q E   . 3. (5) Which one of the following cannot be a statement of Gauss’s Law for some physical situation? a. Q E r  0 2 4   . b. Q rL E  0 2   . c.     dV d   A 0 E . d.      A 0 E d . e.   dA EA  20 . 4. (3) A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface? a. R2E b. 4R2E/3 c. 2R2E/3 d. R2E/2 e. R2E/3 Score:________ Check if solution is continued on the back. 3 Part B: Problems (88) 2. (44%) Gauss’s law A solid insulating sphere of radius a carries a net positive charge +3Q , uniformly distributed throughout its volume. Concentric with this sphere, is a conducting spherical shell with inner radius b and outer radius c, and having a net charge –Q, as shown in the figure below. (a) (10) Show (in details) that the electric field in the region r < a is E=3keQr/a3 (b) (7) Find the electric field in the region b > r > a. (c) (5) Find the electric field in the region c > r > b. Score:________ Check if solution is continued on the back. 4 (d) (6) Determine the charge on the inner surface of the conducting shell (at r=b). (e) (6) Find the electric field at r > c. (f) (5) Make a plot of the magnitude of the electric field versus r. (g) (5) What is the flux across a cube concentric to the two spheres with side l>2c? Score:________ Check if solution is continued on the back. 5 3.(24%) The x-axis is the symmetry axis of a stationary uniformly charged ring of radius R and charge Q. A point charge Q of mass M is initially at rest at the center of the ring. When it is displaced slightly, the point charge accelerates from the center along the x axis to infinity. (a) (8) Show that the electric potential at a point on the axis of the ring at a position x from the center is given by V=keQ/(x2+R2)1/2. (b) (4) Find the potential energy at the particle at the initial and final positions. v . R Q Q x . x Score:________ Check if solution is continued on the back. 6 (c) (7)Show that the ultimate speed of the point charge is 12 2 2        MR k Q v e (d) (5) Determine the three components of the electric field at distance x from the ring center. Score:________ Check if solution is continued on the back. 7 1. (20%) In 1911 Rutherford, Geiger and Marsden conducted an experiment in which they had an alpha particle, having charge +2e and mass 6.64 × 10–27 kg hits a gold sheet (+79e). a) (7) An electric field E = 1 V/m is applied on the alpha particle. How long must E be applied so that, starting from rest, the alpha particle reaches a velocity of v=107 m/s. b) (7) Determine the analytical expression of the minimum distance the alpha particle can get to the gold. c) (6) Use the numerical values in order compare d it to the radius of an atom which is about 10-9 m. What is d? Score:________ Check if solution is continued on the back. 8 SCRATCH PAPER Nothing on this page will be graded