Version: A. Earth s gravitational field g = 9.81 N/kg Mass of a Proton m p = kg

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1 PHYS 2212 G & J Quiz and Exam Formulæ & Constants Fall 2017 Fundamental Charge e = C Mass of an Electron m e = kg Earth s gravitational field g = 9.81 N/kg Mass of a Proton m p = kg Coulomb constant K = N m 2 /C 2 Vacuum Permittivity ϵ 0 = C 2 /N m 2 Speed of Light c = m/s Vacuum Permeability µ 0 = 4π 10 7 T m/a Unless otherwise directed, friction, drag, and gravity should be neglected, and all batteries and wires are ideal. All derivatives and integrals in free-response problems must be evaluated. k = 1 4πϵ 0 V = E d s V = k q r U = q V I = dq/dt P = I V R = V I Series : 1 = 1 C eq C i R eq = R i Parallel : 1 R eq = 1 R i C eq = C i ϵ 0 E = k q r 2 ˆr F = k q 1q 2 r 2 ˆr F = q E p = q d τ = p E U = p E E p r 3 Φ E = E da E d A = q enclosed E d l = dφ B dt C = Q V A C = ϵ 0 d U = 1 2C [ V ]2 R = ρ l A τ C = RC u E = 1 2 ϵ 0E 2 B = µ 0q 4π db = µ 0I 4π F = q v B F = I l B µ = NI A τ = µ B v ˆr r 2 d l ˆr r 2 U = µ B Φ B = B da B d A = 0 B d l = µ 0 (I c + I d ) L = Φ B I L = µ 0 N 2 A l U = 1 2 LI2 B = µ 0 ni τ L = L/R u B = 1 2µ 0 B 2 q = q max (1 e t/τ C q = q 0 e t/τ C I = I max (1 e t/τ L I = I 0 e t/τ L I = J da J = σ E E = N dφ B dt I d = ϵ 0 dφ E dt E = L di dt c = fλ = E B S = 1 µ 0 E B ) ) Please remove this sheet from your Quiz or Exam Version: A

2 YOUR form number is 225 Recitation Sections

3 Version Quiz #2 Form #225 Name: A Physics 2212 G&J Fall 2017 Recitation Section: Print your name, quiz form number (3 digits at the top of this form), and student number (9 digit Georgia Tech ID number) in the section of the answer card labeled Student Identification. Bubble the Quiz Form Number in columns 1 3, skip column 4, then bubble your Student Number in columns Free-response questions are numbered I III. For each, make no marks and leave no space on your card. Show all your work clearly, including all steps and logic. Box your answer. Multiple-choice questions are numbered 1 7. For each, select the answer most nearly correct, circle this answer on your quiz, and bubble it on your answer card. Do not put any extra marks on the card. Turn in your quiz and answer card as you leave. Your score will be posted when your quiz has been graded. Quiz grades become final when the next quiz is given. You may use a calculator that cannot store letters, but no other aids or electronic devices. I. (16 points) An electron (mass m e, charge e) is at rest on the surface of a fixed uniform insulating sphere with positive charge Q and radius R. The electron is then given a speed v 0 away from the sphere. What maximum distance from the center of the sphere will the electron reach? Express your answer in terms of the parameters defined in the problem, and physical or mathematical constants. Form #225 Page 1 of 6

4 II. (16 points) A radially symmetric insulating sphere of charge has a radius R and a non-uniform volume charge density ρ that depends on distance r from the center according to ρ = ρ 0 ( r R where ρ 0 is a positive constant. What is the magnitude of the electric field at a distance 2R/3 from the center? Express your answer in terms of the parameters defined in the problem, and physical or mathematical constants. ) 2 1. (6 points) The sphere in the problem above is shown at the right. What is the direction of the electric field at the point indicated with an asterisk, a distance 2R/3 from the center? (a) Away from the center. (b) Toward the center. (c) Up the page. (d) Out of the page. (e) Down the page. Form #225 Page 2 of 6

5 III. (16 points) A positively charged insulating cylinder with radius R/2 has the uniform volume charge density ρ 0. The cylinder is placed at the center of a negatively charged insulating hollow cylinder with inner radius R, outer radius 3R, and volume charge density ρ 0 /4. Calculate the magnitude of electric field at a distance 2R from the center of the cylinders. Express your answer in terms of the parameters defined in the problem, and physical or mathematical constants. 2. (6 points) In the problem above, the charge per unit length of the hollow insulating cylinder is λ HC = 8λ IC, where λ IC is the charge per unit length on the inner insulating cylinder. Consider two cylindrical Gaussian surfaces with the same length. Gaussian surface A has radius R/2 < r A < R, and Gaussian surface B has radius r B = 4R. What is the relationship between the electric fluxes Φ A and Φ B measured through the surfaces A and B, respectively? (a) Φ B = +9Φ A (b) Φ B = 7Φ A (c) Φ B = +7Φ A (d) Φ B = Φ A (e) Φ B = 8Φ A Form #225 Page 3 of 6

6 3. (8 points) An infinite insulating slab has thickness 2t. It extends to ± in the x and y directions, and is centered on the z axis, extending to ±t. It has a non-uniform volume charge density ρ that depends on position z according to ρ = ρ 0 ( z t where ρ 0 is a constant. If it can be determined, what is the magnitude of the electric field at the origin? ) 2 (a) The magnitude cannot be determined because the sign of ρ 0 is not specified. (b) The magnitude cannot be determined because the slab is infinite. (c) Kρ 0 /t 2 (d) Kρ 0 /z 2 (e) Zero. 4. (8 points) Three particles with charges +2Q, 2Q, and Q are located at the vertices of an equilateral triangle with sides of length s. What is the electric potential energy of this system, with respect to zero at infinity? (a) KQ/s (b) 5KQ2/s (c) KQ 2 /s 2 (d) 4KQ 2 /s (e) 4KQ 2 /s Form #225 Page 4 of 6

7 5. (8 points) A negatively charged sphere is moved from some initial point to the final point in the direction of a uniform electric field. Considering a system consisting of the sphere and the source of the uniform field, during this displacement: (a) the potential energy of the system decreases. (b) the potential energy of the system increases if the speed of the sphere increases and the potential energy of the system decreases if the speed decreases. (c) the potential energy of the system does not change. (d) the potential energy of the system decreases if the speed of the sphere increases and the potential energy of the system increases if the speed decreases. (e) the potential energy of the system increases. 6. (8 points) A conductor with a hollow cavity has a total charge Q tot placed upon it. A small point charge q is then placed within the cavity, through a negligibly small hole in the conductor. What will be the resulting residual charge Q out on the outer surface of the conductor, after equilibrium is reached? (a) Q out = Qtot q (b) Q out = Qtot q (c) Q out = Qtot + q (d) Q out = Qtot (e) Q out = Qtot + q Form #225 Page 5 of 6

8 7. (8 points) Two parallel conducting plates are separated by 7.5 cm and one of them is taken to be at zero volts. What is the potential difference between the plates if the electric potential 5.0 cm from the zero volt plate (and 2.5 cm away from the other plate) is +300 Volts? (a) +150 Volts (b) +900 Volts (c) -150 Volts (d) +450 Volts (e) +600 Volts Form #225 Page 6 of 6