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Unformatted text preview: Print your name here: ________________________________________ Scores: Section 1 ___________ Section 2 ___________ Section 3 ___________ Section 4 ___________ Physics 126 Total ____________ Exam #1 Gary Morris and Gordon Mutchler Chapters 19 – 21 Tuesday, February 12, 2002 Do not open this exam until you are instructed to do so. Carefully read all the instructions listed below. • • • • • • • Look at the seat to your left. Look at the seat to your right. If they are not BOTH unoccupied, you must change seats until the seats on either side of you contain no persons. Clear your desktop of all items except a pencil/pen, a (scientific) calculator, and a single 3” X 5” note card (hand-written). You may not use your book or any additional notes during this exam. You must staple your note card to this exam before turning in the exam. You will have 70 minutes to complete the exam. When you are instructed to stop working on the exam, you must put down your pencil/pen immediately. We will notify you when there are 30 minutes, 15 minutes, and 5 minutes remaining in the exam period. Read through the entire exam before you start. The last page contains useful constants and mathematical formulas. Generous partial credit is provided. However, you must show your work to receive credit. Do not simply write down the answers. No partial credit will be given on the multiple-choice section. Everyone must work the multiple choice section. You need only work 2 out of the 3 non-multiple-choice sections on this exam. NOTE: you must circle the numbers corresponding to the two sections you would like us to grade. Please sign the following statement: On my honor, I have not given, received, or tolerated the use of any unauthorized aid during this examination. _____________________________________ “What happens is not as important as how you react to what happens.” – people would “If God lived on earth,Thaddeus Golas break his windows.” – Yiddish Proverb “It seldom pays to be rude. It never pays to be only half rude.” – Douglas Section 1 Multiple Choice – Required for EVERYONE Each question in this section is worth 5 points. Please record your answers in the blanks on this page. There will be NO partial credit on this section of the test. In each case, choose the BEST possible answer from the choices given. 1) ________ 2) ________ 3) ________ 4) ________ 5) ________ 6) ________ 7) ________ 8) ________ 9) ________ 10) ________ 1) A uniform electric field of 2000 N/C points in the +x-direction. A point charge Q = +3e, held initially at rest at the origin, is released. Determine the magnitude of the potential difference through which the charge passes as it moves from x = 0 to x = 4.0 m? a) b) c) d) e) 48 mJ 48 mV 0 8000 J 8000 V 2) A copper wire of cross-sectional area 2 × 10-6 m2 carries a current of 20 A. How much charge passes through the end of the wire in 5 minutes? a) b) c) d) e) 6C 12 C 100 C 6000 C Impossible to determine from the information given. 3) The ratio of the electrostatic potential at point A due to charge +Q in the left picture below to the electrostatic potential at point B due to charge +Q in the right picture below is a) b) c) d) e) 1:4 1:2 1:1 2:1 4:1 “Medicine is the only profession that labors the body treats “The human mind treats a new idea the same way incessantly to a destroy the reason for its existence.” – Bryce strange protein; it rejects it.” – P. B. Medawar 4) A charge of q = +6.0 nC sits at the origin (x = 0, y = 0). What is the ratio of the y-component of the electric field to the x-component of the electric field (that is, Ey / Ex) at the point (x = 0.4 m, y = 0.3 m)? a) b) c) d) e) 0.56 0.60 0.75 1.33 1.78 5) A spherical conducting shell of radius R is alone in the universe and has a charge q distributed uniformly on its surface. The electrical potential difference between a point on its surface and a point located r = R / 2 from its center is a) 0 b) kq / R c) 2kq / R d) kq 2 / R e) 2kq / R 2 6) Three capacitors, each of identical capacitance C, are combined in a variety of ways using copper wires. What is the minimum value of the effective capacitance that can be found in a combination that uses all three capacitors? a) b) c) d) e) C/6 C/3 C/2 C 3C/2 7) A capacitor is first charged by connecting it, by means of wires and a switch, to a battery with a potential difference between its terminals of 120 V. After the capacitor is fully charged, the switch is opened. A second metal wire is now inserted between the charged plates to connect the surfaces of the two plates. What happens? a) b) c) d) e) The positive and negative plates are reversed. The electric field between the plates is reversed. The electrostatic potential energy of the system is increased. The electrostatic potential difference between the plates becomes zero. None of the above. “Procrastination is the grave in which opportunity is buried.” “It seldom pays to be rude. It never pays to be only half rude.” – Douglas – Author Unknown 8) An ammeter A is connected between points a and b as shown. All four resistors in this circuit are identical. The current through the ammeter is a) b) c) d) e) I/4 I/2 I 0 –I 9) Three pithballs are suspended from threads. Up to 3 of the pithballs are then charged by contact with other charged objects. It is found that pithballs 1 and 2 attract each other and that pithballs 2 and 3 repel each other. From this we can conclude with certainty that f) g) h) i) j) pithballs 1 and 3 carry charges of opposite sign. pithballs 1 and 3 carry charges of the same sign. all three pithballs carry charges of the same sign. one of the pithballs carries no charge. we need more data to reach a conclusion with certainty. 10) A charge +Q is located at the geometrical center of a tetrahedron, as pictured below. Each edge of the tetrahedron has length a. What is the total electric flux through the surface of the tetrahedron? a) 0 b) Q / ε 0 Q c) 3a 2ε 0 12Q d) 2a 3ε 0 e) None of the above. Q “We know the truth not only by reason, but also by the heart.” “Medicine is the only profession that labors incessantly to destroy the – Blaise Pascal, Thoughts – Bryce reason for its existence.” Section 2 j A uniform external electric field of E = −E0 ˆ is created in the region near the origin of our coordinate system by distant charges. A positive charge of +q is then held in place by a non-electric force at the origin, as shown at right. a) [ 9 points ] Compute the total electric field at point A (x = a, y = 0). b) [ 14 points ] Compute the potential difference between point B (x = 0, y = –2a) and point A (x = a, y = 0), i.e., (VB – VA). In the presence of the same external field and while the positive charge is held in place by the non-electric force at the origin, a negative charge of –q is now held in place at point A (x = a, y = 0) by a second non-electric force. c) [ 9 points ] Draw a free-body diagram for the negative charge. Identify all forces. Identify the 3rd Law Pair forces of all the forces in your free-body diagram. d) [ 10 points ] Determine the non-electric force on the negative charge required to hold the negative charge at point A (x = a, y = 0). The negative charge is now moved from its initial position at point A (x = a, y = 0) to point B (x = 0, y = –2a). NOT TO SCALE y a +q + A x 2a B y a +q + – –q A x 2a B y a +q + e) [ 8 points] Compute the amount of work done by an external force in moving the negative charge from point A (where it begins at rest) to point B (where it ends at rest). A x 2a B – –q “We can’t all be heroes because somebody has to sit on the curb “It seldom pays to be rude. It never pays to be only half rude.” – Douglas and clap as they go by.” – Will Rogers Section 3 b A solid, insulating sphere of radius a has a total charge Q distributed uniformly throughout its volume. Concentric with this sphere is a conducting spherical shell whose inner and outer radii are b and c, respectively, as shown, and whose net charge is zero. a c a) [ 5 points ] Determine an expression for the volume charge density in the inner sphere of radius a. b) [ 5 points ] Determine an expression for the surface charge density on the inner surface of the conducting spherical shell (i.e., at r = b ). c) [ 25 points ] Determine an expression for the radial component of the electric field as a function of r (the distance from the center of the insulating sphere of radius a) in each of the following regions: r < a, a < r < b, b < r < c, and c < r. Then sketch a graph of the radial component of the electric field for 0 < r < ∞ . Be sure to label points r = a, r = b, and r = c on your graph and label both axes clearly. d) [ 15 points ] Determine an expression for the electrostatic potential as a function of r (the distance from the center of the insulating sphere of radius a) in each of the following regions: c < r and b < r < c. Then sketch a graph of the electrostatic potential for b < r < ∞ . Be sure to label points r = b, and r = c on your graph and label both axes clearly. Use V = 0 for r = ∞ . ““Tell me what you eat, and I will tell labors incessantly to Medicine is the only profession that you what you are.” destroy the reason forPhysiology of Taste – Brillat-Savarin, its existence.” – Bryce 25.0 V Section 4 For the circuit pictured at right, calculate the following quantities: a) [ 21 points ] The current through the battery. b) [ 7 points ] The power supplied by the battery. c) [ 7 points ] The potential difference between points A and B (VB – VA). A d) [ 7 points ] The current through the 7.5 Ω resistor. e) [ 8 points ] The current through the 7.5 Ω 10.0 Ω resistor. – + 5.0 Ω 10.0 Ω B 15.0 Ω “Try not. Do. Or do not. There is no try.” “It seldom pays to be rude. Yoda, Return to be only half rude.” – Douglas – It never pays of the Jedi 22.5 Ω Useful Formulas and Constants Nm 2 k = 8.99 ×10 a single charge: C2 1 C2 ε0 = = 8.85 ×10−12 4π k Nm 2 1 e = 1.6 × 10−19 C 9 1 eV = 16 × 10−19 J . ω=2πf τ = Iα F = ma 1 amu = 167 × 10−27 kg . dW = F ⋅ dx = Fdx cos θ e = 2.718… the exponential function W = -∆U 1 kW hr = 3.6 × 106 J P = dW/dt µ 0 = 4π × 10−7 Tm / A . mass of proton = 167 × 10−27 kg x +y 2 mass of electron = 9.1 × 10−31 kg sin θ = 2 y cosθ = θ x y x + y2 2 x x + y2 2 The surface area of a sphere of radius r is 4πr2. The volume of a sphere of radius r if 4πr3/3. The surface area of the sides of a cylinder of length L and radius r is 2πrL. The surface area of a circle of radius r is πr2. The volume of a cylinder of length L and radius r is πr2L. The surface area of a tetrahedron with sides of length L is 3L2 . The volume of a tetrahedron with sides of length L is 23 L. 12 “Medicine is the only profession that labors incessantly to destroy the reason for its existence.” – Bryce ...
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This note was uploaded on 11/03/2010 for the course PHYSICS 303 taught by Professor Shih during the Spring '10 term at University of Texas at Austin.

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