PHYSICS 222 Fall 2009 EXAM 1: October 1, 2009 8:00pm—10:00pm

Name (printed): ______________________________________________ Recitation Instructor: _________________________ Section #_______ INSTRUCTIONS: This exam contains 25 multiple-choice questions, plus two extra-credit questions, each worth 3 points. Choose one answer only for each question. Choose the best answer to each question. Answer all questions. Allowed material: Before turning over this page, put away all materials except for pens, pencils, erasers, rulers and your calculator. There is a formula sheet attached at the end of the exam. Other copies of the formula sheet are not allowed. Calculator: In general, any calculator, including calculators that perform graphing, is permitted. Electronic devices that can store large amounts of text, data or equations (like laptops, palmtops, pocket computers, PDA or e-book readers) are NOT permitted. If you are unsure whether or not your calculator is allowed for the exam, ask your TA. How to fill in the bubble sheet:

Use a number 2 pencil. Do NOT use ink. If you did not bring a pencil, ask for one. Write and fill in the bubbles corresponding to: - Your last name, middle initial, and first name. - Your ID number (the middle 9 digits on your ISU card) - Special codes K to L are your recitation section. (Honors sections: H1 → 10;

H2 → 23). Always use two digits (e.g. 01, 09, 11, 13) Please turn over your bubble sheet when you are not writing on it. If you need to change any entry, you must completely erase your previous entry. Also, circle your answers on this exam. Before handing in your exam, be sure that your answers on your bubble sheet are what you intend them to be. You may also copy down your answers on a piece of paper to take with you and compare with the posted answers. You may use the table at the end of the exam for this. When you are finished with the exam, place all exam materials, including the bubble sheet, and the exam itself, in your folder and return the folder to your recitation instructor. No cell phone calls allowed. Either turn off your cell phone or leave it at home. Anyone answering (or using) a cell phone must hand in their work immediately; their exam is over.

Best of luck, Paul Canfield

1) The apparent weight of a steel sphere immersed in various liquids is measured using a spring scale. The greatest reading is obtained for that liquid: A) having the smallest density B) having the largest density C) subject to the greatest atmospheric pressure D) having the greatest volume E) in which the sphere was submerged the deepest 2) A certain block of wood has a volume of 150 cm3 and floats on water (density = 1000 kg/m3) with 25% of its volume submerged. The downward force that must be applied to hold the block completely under water is about: A) 0.11 N B) 0.37 N C) 1.1 N D) 1.5 N E) 1.1 x 106 N 3) A 8.0 kg solid sphere, made of a metal with a density of 2300 kg/m3, hangs suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is reduced to 23 N. The density of the liquid is closest to: A) 1600 kg/m3 B) 1500 kg/m3 C) 1400 kg/m3 D) 1300 kg/m3 E) 1200 kg/m3 4) A U-tube is partially filled with water. One side of the tube is inside of a box with still air and the other side has a wind blowing across the open end with a velocity of 50 km/h. What is the difference in the height of water between the two sides of the tube? Note: ρ(air) = 1.2 kg/m3, ρ(water) = 1000 kg/m3. A) 0.016 cm B) 0.16 cm C) 1.2 cm D) 12 cm E) 116 cm

5) Bernoulli’s equation can be derived from the conservation of: A) energy B) mass C) angular momentum D) volume E) pressure 6) Kepler’s second law, “A line from the Sun to a given planet sweeps out equal areas in equal times.” can be derived from conservation of: A) energy B) mass C) angular momentum D) volume E) pressure 7) Two uncharged metal spheres, L and M, are in contact. A negatively charged plastic rod is brought close to L, but not touching it, as shown below. The two spheres are then slightly separated and, after this separation, the rod is removed. As a result of these steps:

A) both spheres are neutral B) both spheres are positively charged C) both spheres are negatively charged D) L is negatively and M is positively charged E) L is positively and M is negatively charged

8) What equal, positive charges would have to be placed on the Earth and the Sun so as to balance their gravitational attraction? (Mass of Sun ~ 2 x 1030 kg) A) 9.0 x 109 C B) 8.8 x 1012 C C) 5.7 x 1013 C D) 6.6 x 1015 C E) 3.0 x 1017 C 9) Two particles, X and Y, are 4.0 m apart. X has a charge of 2Q and Y has a charge of Q. The ratio of the magnitude of the electrostatic force on X to that on Y is: A) 4:1 B) 2:1 C) 1:1 D) 1:2 E) 1:4 10) The diagram below shows the electric field lines in a region of space containing two small charged spheres, Y and Z. We can deduce that:

A) Y is positive and Z is negative B) the magnitude of the electric field is the same everywhere C) the electric field is strongest midway between Y and Z D) a small negative charge placed at point X would experience a force to the left E) Y and Z must have the same sign

11) In the figure below, a small 80 g sphere is suspended from point P by an insulating thread that is 50 cm long. The sphere bears an unknown charge, Q. A positive point charge, q = +2.0 μC, is brought to a position directly below P and the sphere is repelled to a new position, 30 cm to the right of q, as shown. The charge Q is closest to:

A) 1.5 μC B) 2.0 μC C) 2.5 μC D) 3.0 μC E) 3.5 μC 12) The diagrams below show four possible orientations of an electric dipole in a uniform electric field (for 2 and 4 the angle with respect to the applied field is 45º and 135º). Rank them according to the magnitude of the torque exerted on the dipole by the field, least to greatest.

A) 1, 2, 3, 4 B) 4, 3, 2, 1 C) 1, 2, 4, 3 D) 3, 2 and 4 tie, then 1 E) 1, 2 and 4 tie, then 3 13) A point charge, +Q is placed 10 cm from an infinite sheet of charge that has σ = +10 μC/m2. If the magnitude of the electric field is zero half way along the line from the sheet to the point charge, what is the size of Q? A) 0.16 μC B) 1.6 μC C) 10 μC D) 16 μC E) 100 μC

14) A hollow conducting sphere has an inner radius of 0.80 m and an outer radius of 1.20 m. The sphere carries a charge of – 500 nC. A point charge of + 300 nC is present at the center of the sphere. The surface charge density on the outer surface is closest to:

A) 0 nC/m2 B) -11 nC/m2 C) -16 nC/m2 D) -28 nC/m2 E) -44 nC/m2 15) The figure below shows four egg-shaped Gaussian surfaces, labeled 1, 2, 3, and 4, enclosing 0, 1, 2, 3 point charges, respectively. The point charges are +Q, +2Q and -5Q. Rank the surfaces in terms of the magnitude of total flux, |Φtotal|, through each, from lowest to highest.

A) 1, 2, 3, 4 B) 4, 3, 2, 1 C) 3, 4, 2, 1 D) 1 and 4 tie, 2, 3 E) 1, 2, 4, 3

16) A solid, insulating sphere of radius R contains a uniform volume distribution of positive charge. Which of the graphs below correctly gives the magnitude, E, of the electric field as a function of r?

17) A long cylindrical insulator (r = 0.8 m) has a cross section as shown. A smaller, cylindrical, hollow space (r = 0.2 m) is drilled parallel to the axis of the larger cylinder, but centered on a point half way between the center and edge of the larger cylinder. If the volume charge density of the insulating material is ρ = 10 mC/m3, what it the magnitude of the electric field at the center of the hollow space? A) 2.3 x 108 N/C B) 4.5 x 108 N/C C) 6. 8 x 108 N/C D) 11 x 108 N/C E) 18 x 108 N/C

18) Two charges Q are fixed at the vertices of an equilateral triangle with sides of length a. Using k = 1/4πε0, the work required to move a third charge, q, from the third vertex to the center of the line joining the two fixed charges is:

A) 0 B) kQq/a C) kQq/a2 D) 2kQq/a E) (√2)kQq/a 19) A ring of charge has a radius of 1 m and a linear charge density of 3 mC/m. If V(∞) = 0, what is the electric potential 2 m from the center of the ring along the axis of symmetry (along the line perpendicular to the ring, going through its center)? A) 1.2 x 107 V B) 3.3 x 107 V C) 7.5 x 107 V D) 8.4 x 107 V E) 17 x 107 V 20) Two identical, small, insulating, m = 10 g, spheres each have + 1 mC of charge uniformly distributed throughout their volumes. They are initially at rest with their centers separated by 1 m. After they are released they are both free to move. Assuming that the only force acting on the spheres is the electrostatic one, what is the magnitude of their final velocities? A) 30 m/s B) 94.7 m/s C) 947 m/s D) 3000 m/s E) 30,000 m/s

21) Suppose one has available: Two sheets of copper A sheet of mica (thickness = 0.1 mm, K = 6) A sheet of glass (thickness = 2.0 mm, K = 7) A slab of paraffin (thickness = 1 cm, K = 2) To obtain the largest capacitance, place the two copper sheets on either side of: A) a 0.05 mm air gap B) the mica C) the glass D) the paraffin E) the mica, glass, and paraffin (a composite slab of thickness = 1.21 cm) 22) The diagram shows six, 6 μF capacitors. The capacitance between points a and b is:

A) 3 μF B) 4 μF C) 6 μF D) 9 μF E) 18 μF 23) A battery is used to charge a parallel-plate capacitor, after which it is disconnected. Then the plates are pulled apart to twice their original separation. This process will double the: A) capacitance B) surface charge density on each plate C) stored energy D) magnitude of the electric field between the two plates E) charge on each plate

24) Three 12 pF capacitors are arranged in series, parallel, and combinations of the two. Which of the following equivalent capacitances is not possible? A) 4 pF B) 8 pF C) 12 pF D) 18 pF E) 36 pF 25) Three capacitors are arranged as shown in the sketch below. What is the ratio of the charge on the plates of C1 = 2 μF, C2 = 4 μF and C3 = 6 μF?

Q1:Q2:Q3 = A) 1 : 4 : 9 B) 1 : 2 : 3 C) 1 : 1 : 1 D) 3 : 2 : 1 E) 9 : 4 : 1

Q

q • X Y • • Z

EXTRA CREDIT 26) Two charges Q1 = 1.0 C and Q2 = 2.0 C are located on the x axis at x1 = 0 and x2 = 2.0 cm. A third charge Q3 is to be placed between them at position x3 such that the whole system is in equilibrium. Find Q3 and x3. A) 0.52 cm, –0.12 C B) 0.83 cm, –0.34 C C) 0.83 cm, +0.12 C D) 0.52 cm, +0.34 C E) It is not possible to achieve this equilibrium. 27) A hollow metal sphere has a net charge Q > 0. A point charge q > 0 is placed next to it. Consider points X, Y (on the inner surface of the sphere) and point Z (on the outer surface). Which of the following is TRUE? A) VX = VY = VZ B) VX = VY > VZ C) VX > VY > VZ D) VX = VY < VZ E) VX < VY < VZ

You may record your answers on this page and take it with you after the exam to compare to the posted solutions.

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