PHYS-115(3) (Kaldon-16406) Name ______________________________________WMU - Winter 2001Exam 1 - 100,000 points Book Title __________________________________________Section: 3a 3b 3c 3d Sample Exam A to F G to M N to S T to Z Rev. 1/31/01State Any Assumptions You Need To Make -- Show All Work -- Circle Any Final AnswersUse Your Time Wisely - Work on What You Can - Be Sure to Write Down EquationsBOLDFACE Variables Are Vectors - Feel Free to Ask Any Questions“You Can’t Imagine the Power of the Dark Side of the Coulomb Force!” (25,000 points)1.) (a) In class Dr. Phil commented that it is very important the charge of the electron (-e) and the proton (+e)are exactly the same magnitude. Suppose this is not true. Suppose that the charge on the electron was slightlydifferent than that on the proton. List three things that would be different in our universe.(b) In the dark cold of space, Darth Vader’s Death Star silently approaches a rebel planet. At 100,000 kmabove the center of the planet, the Death Star fires a beam of “something” at the unsuspecting planet. Whatcould the evil Empire be using as a weapon? How about charge? (I know, it’s a stretch considering the materialin Physics 106.) Suppose they transferred 1.576 × 1044 electrons (Q = -2.536 × 1025 C) from the Death Star(mass = 2.68 × 1017 kg) to the planet. Find the acceleration of the Death Startoward the planet. Physics 115 / Sample Exam 1 Winter 2001 Page 2“You’re Our Only Hope, Obi-Wan Kenobi...” (continued)(c) As evil as they are, the Imperial scientists are not idiots. Suppose that the Death Star beam works tosomehow “turn off” the charge on all the electrons. For every gram of matter, there would be one mole (6.02 x1023 ) of these electron charges suddenly made to go to a charge of zero. If the mass of the planet is5.55 × 1024 kg, find the total number, N, of these planetary electrons; the total charge onthe planet, Q; and the charge density, r. (Rplanet = 6.16 × 106 m; Vsphere = 4/3 p r3 ). (d) Use Gauss’ Law to find the E-field on the surface of the planet, using the new charge density r.(e) Find the acceleration of a proton (mp = 1.67 × 10-27 kg) that ison the planet’s surface.Physics 115 / Sample Exam 1 Winter 2001 Page 3Just Pull Out Your Credit Card and Say, “Charge It, Please!” (25,000 points)2.) (a) Two charged plates are separated by a distance of d = 1.00 mm = 0.00100 m. In the diagram below,sketch in relevant electric field lines (use solid lines) and equipotential lines (use dashed lines).(b) If the two plates are separated by air, what is the maximum potential difference, VMAX , between the plates?What is the maximum magnitude of the electric field, E?(c) Use Gauss’ Law to find the surface charge, s, on the plates.(d) First an electron (me = 9.11 × 10-31 kg) and then a proton (mp = 1.67 × 10-27 kg) are shot right between theplates, at a speed of v = 1000 m/s. On the diagram below, sketch an approximate path of the electron (use solidlines) and the proton (use dashed lines).(e) If the plates are 1.000 m long, how far is the electron deflected from its original path? How far is the protondeflected?Physics 115 / Sample Exam 1 Winter 2001 Page 4Batman Returns Forever (25,000 points)3.) In the movie Batman Returns from a couple of years ago, Michelle Pfeiffer’s character gets into troublebecause she saw the plans for a building her evil boss was constructing to “steal all thepower from Gotham City” and determined that these plans were for “a giant capacitor”.Consider a parallel plate capacitor that is building sized: length = 100 m, width = 50.0m, plate separation = 30.0 m. Find (a) the capacitance, C, and charge Q on the plates ifthe voltage difference is V = 125,000 volts, and the capacitor is filled with glass (k = 4.7 ; dielectric strength =14 × 106 V/m ) acting as a dielectric between the plates.(b) Rather than making just one big capacitor to fill a building, suppose we stack a two identical capacitors inthe building. Find the capacitance of just one of these capacitors. Use the length and width of the building fromabove. (c) Determine whether this arrangement is parallel or series, then find Q´ and V´ for each capacitor, andCeq for the pair of capacitors.(d) On the other hand, suppose we set two identical capacitors side by side in the building. Find the capacitanceof just one of these capacitors. Use the length and width of the building from above. (e) Determine whetherthis arrangement is parallel or series, then find Q´´ and V´´ for each capacitor, and Ceq for the pair of capacitors.Physics 115 / Sample Exam 1 Winter 2001 Page 5 The Atoms Family (25,000 points)4.) A helium ion, He+, consists of two protons and two neutrons in the nucleus, and a single electron orbitingaround outside. (a) Find the electric field, E, at a point 1.00 m from this ion.The two protons are about 1 fermi apart. This is 1 femtometer or 1.00 × 10-15 m. (b) Find the electric forcebetween the two protons, and (c) find the initial acceleration of one of the protons assuming that there was nostrong nuclear force from the neutrons holding the nucleus together.(d) If we take a classical view of the atom, then the electron in orbit (r = 1 Å = 1.00 × 10-10 m) is in UniformCircular Motion: ac = v2/ r. Find the centripetal force on the electron.(e) Find the speed of the electron.Physics 115 / Sample Exam 1 Winter 2001 Page 6Star Trek Science (40,000 points)5.) As pointed out in class, not everything in science fiction is scientifically accurate. Take Star Trek, forexample. The USS Enterprise (right) can apply a tractor beam on the Klingon warship (left), which applies anattractive force. We can actually make something like a tractor beam, if the Enterprise transfers some electronsto the Klingon. (a) If both ships started out as charge neutral, each has a mass of 20,000 metric tons (20 x 106kg) and are one kilometer (1000 m) apart, find the acceleration between them after -5.00 C of electrons aretransferred.(b) The electrons are accelerated through a potential difference of 2.20 x 106 V. Find the speed of the electrons,using K = ½ mv2. Determine if the final speed of the electrons is relativistic (more than 42% the speed of light).“We Hold These Truths To Be Self-Evident, That All Q’s Are Created Equal” (25,000 points)6.) If C1 = 125 pF, C2 = 175 pF, C3 = 225 pF, then (a) find the equivalent