PHY 102-112 Practice Problems for Exam 1 PDF

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Practice Problems for Exam 1 (Giancoli Chapters 41, 21, 22, 23, 24, 25) Chapter 41: Nuclear Physics and Radioactivity 1. Rutherfordium-261 has a half-life of 1.08 min. How long will it take for a sample of rutherfordium to lose one-third of its nuclei? Ans: 0.63 min 2. The decay constant of a given nucleus is 3.8×10−5 s-1. What is its half-life (in hours)? Ans: 5.1 hours 3. The radius R of a nucleus of mass number A is given by R = R0 A1/3, where R0 = 1.2 × 10-15 m. (a) Estimate the radius (in fm) of a radon (atomic number Z = 86) nucleus that contains 136 neutrons. (b) What is the approximate radius of a Cd-112 nucleus? Ans: (a) 7.3 fm (b) 5.8 fm

226 Ra decays into an alpha particle (helium nucleus) and which of the following? Explain. 88 222 230 230 226 Rn U Th E) Ac B) C) D) 86 92 90 89

4. A radium nucleus A)

222 Po 84

5. Compared to the electrostatic force, the nuclear force between adjacent protons in a nucleus is A) much weaker. B) only slightly weaker. C) about the same size. D) only slightly larger. E) much larger. Ans: E 6. An aluminum foil 0.10 mm thick has how many aluminum atoms per square cm? (The density of aluminum is 2.7 × 103 kg/ m3 and the atomic mass of aluminum is 27.) Ans: 6 × 1020 7. Uranium-238 decays into thorium-234 plus an alpha particle. How much energy is released in this process? The atomic masses of helium-4, thorium-234 and uranium-238 are 4.002603 u, 234.043583 u and 238.050786 u. Ans: 4.28 MeV 8. Living matter has 1.3 × 10-10 % of its carbon in the form of 14C which has a half-life of 5730 yr. A 300 gram carbon sample from an old mammoth bone is found to have an activity of 20 decays per second. How old is the bone? Ans: 10,900 years. 9. A certain substance has a half-life of 5.0 hours. How many nuclei of the substance are required to give an initial activity of 6.0 μCi? 1 Ci = 3.7 × 1010 Bq. Ans: 5.8 × 109 nuclei 10. In beta minus decay, the number of neutrons in the nucleus A) is decreased by 1. B) is decreased by 2. C) is increased by 1. D) is increased by 2. E) remains unchanged. Ans: A 11. Carbon-14 has a half-life of 5730 years. A sample of wood has been recovered by an archaeologist. The sample is sent to a laboratory, where it is determined that the activity of the sample is 0.144 Bq/g. By comparing this activity with the activity of living organic matter, 0.230 Bq/g, the scientist determines how old the wood sample is, or more precisely, when the tree that the sample came from died. How old is the sample of wood? Ans: 3870 years 12. A carbon-14 nucleus decays to a nitrogen-14 nucleus by beta decay. How much energy (in MeV) is released if carbon-14 has a mass of 14.003242 u and nitrogen-14 has a mass of 14.003074 u? Ans: 0.156 MeV 13. The radioactivity due to carbon-14 measured in a piece of a wooden casket from an ancient burial site was found to produce 20 counts per minute from a given sample, whereas the same amount of carbon from a piece of living wood produced 160 counts per minute. The half-life of carbon-14, a beta emitter, is 5730 years. Thus we would estimate the age of the artifact to be about how many years? Ans: 17,200 years

Chapter 21: Electric Charge and Electric Field 1. A long line of charge with charge per unit length λ1 is located on the x-axis and another long line of charge with charge per unit length λ2 is located on the y-axis with their centers crossing at the origin. In what direction is the electric field at

point z = a on the positive z-axis if λ1 and λ2 are positive? Ans: + z-direction. Find the magnitude of the electric field. 2. Two large, flat, horizontally oriented plates are parallel to each other, a distance d apart. Half way between the two plates the electric field has a magnitude E. If the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates? Ans: E 3. A positive charge +8 nC is held fixed at (x = 0, y = -1 m) and a second positive charge +2 nC is held fixed at (x = -1 m, y = 0). (a) Compute the components (Ex and Ey) of the electric field at the origin. Give proper units. (b) What is the direction of the electric field at the origin? Specify the angle E makes with the +x axis. 4. Three point charges are placed on the x-axis. A charge of +2.0 μC is placed at the origin, -2.0 μC to the right at x = 50 cm, and +4.0 μC at the 100 cm mark. What are the magnitude and direction of the electrostatic force which acts on the charge at the origin? Ans: 0.072 N, toward the right 5. Three 3.0 μC charges are at the three corners of a square of side 0.50 m. The last corner is occupied by a -3.0 μC charge. Find the electric field at the center of the square. Ans: 4.3 × 10 5 N/C 6. An atomic nucleus has a charge of +40e. An electron is 10-9 m from the nucleus. What is the Coulomb force on the electron? Ans: 9.2 nN 7. An electric dipole is held in a uniform electric field oriented along an unknown direction. The torque on the dipole in this position is 0.1 N m. When the dipole is let go, and it reaches equilibrium, its potential energy is equal to -0.2 J. What was the initial angle between the direction of the dipole moment and the direction of the electric field? Ans: 30° 8. A charge Q = 3 μC is located at the origin. Compute the electric field created by this charge at a point P whose of coordinates are (x = 2 m, y = 0 m). Ans: 6.75 × 103 N/C 9. Three point charges each equal to 10 microcoulombs are located at x = 1m, x = 2m, and x = 3m, respectively, on the xaxis. What is the magnitude and direction of the electric field at the origin? Ans: -1.22 × 10 5 N/C i 10. Consider a square with 1 m sides. Charges are placed at the corners of the square as follows: +4.0 μC at (0, 0); +4.0 μC at (1, 1); +3.0 μC at (1, 0); -3.0 μC at (0, 1). (a) What is the magnitude of the electric field at the square's center? Ans: 1.08 × 105 N/C. (b) What angle does the electric field make with the x-axis? 11. A charge Q1 is located at coordinates (x = +a, y = +a). A second charge Q2, identical to Q1, is located in such a way that the net electric field at the origin of the coordinate axis (x = 0, y = 0) is equal to 0. What are the coordinates of Q 2? Ans: x = -a, y = -a 12. A long, thin rod parallel to the y-axis is located at x = - 1 cm and carries a uniform charge density λ = 1 nC/m. A second long, thin rod parallel to the z-axis is located at x = +1 cm and carries a uniform negative charge density λ = - 1 nC/m. What is the electric field at the origin? Ans: (3.6 × 103 N/C) 13. Two large, flat plates are parallel to each other. Plate A, located at y = 1 cm, is along the xz-plane and carries a uniform charge density σA = -1 μC/m2. Plate B is located at y = -1 cm and carries a uniform charge density σ B = +2 μC/ m2. What is the electric field at the point of coordinates (x, y, z) = ( -0.5 cm, 0, 0)? Ans: ( +1.7 x 10 5 N/C) 14. A thin, circular disk of radius R = 30 cm is oriented in the yz-plane with its center as the origin. The disk carries a total charge Q = +3 μC distributed uniformly over its surface. Calculate the magnitude of the electric field due to the disk at the point x = 15 cm along the x-axis. Ans: 3.32 × 105 N/C 15. A metal sphere of radius 2.0 cm carries a charge of 3.0 μC. What is the electric field 6.0 cm from the center of the sphere? Ans: 7.5 × 106 N/C 16. A proton is placed in an electric field of intensity 700 N/C. What is the magnitude and direction of the acceleration of this proton due to this field? Ans: 6.71 × 1010 m/ s2 in the direction of the electric field

17. An electric dipole is made of two charges of equal magnitudes and opposite signs. The positive charge, q = 1 μC, is located at the point (0, 1 cm, 0) while the negative charge is located at the point (0, -1 cm, 0). How much work will be done by an electric field E = (3 × 106 N/C) i to bring the dipole to its stable equilibrium position? Ans: 0.06 J 18. A positive charge Q = +13 nC is distributed uniformly on the surface of an insulating sphere of radius R = 10 cm. Consider two points A and B, located at a distance of 30 cm and 4 cm respectively from the center of the sphere. (a) Compute the magnitude of the electric field at A. (b) Compute the potential at A. (c) Compute the magnitude of the electric field at B. (d) How much work is needed to take a positive charge q0 = +2 nC from A to B? Ans: (a) 1300 N/C (b) 390 V (c) 0 (d) 1.56 *10-6 J Chapter 22: Gauss's Law 1. A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. (a) What is the magnitude of the electric field at a distance R/2 from the center of the sphere? Ans: kQ/2R 2 (b) What is the magnitude of the electric field at a distance 2R from the center of the sphere? Ans: kQ/4R 2 2. Three parallel flat planes of charge are separated by a distance d between each of the planes. The charge density on each of the planes is +σ. Compute the magnitude of the electric field in the regions (a) between the planes, and (b) outside all the planes. Ans: (a) 2kσ (b) 6kσ 3. A uniform electric field of magnitude E = 100 N/C is oriented along the positive y-axis. What is the magnitude of the electric flux through a small square of surface area A = 0.2 m 2, whose normal is oriented at an angle of 42 degrees with respect to the y-axis. Ans: 14.9 N m2/C 4. A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r 1 = R/4 the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r 2 = 2R? Ans: E0 5. A spherical, non-conducting shell of inner radius r1 = 10 cm and outer radius r2 = 15 cm carries a total charge Q = 15 μC distributed uniformly throughout its volume. What is the electric field at a distance r = 12 cm from the center of the shell? Ans: 2.87 × 106 N/C 6. A non-conducting sphere of radius R = 7 cm carries a charge Q = 4 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere does the electric field reach a value equal to half its maximum value? Ans: 3.5 cm and 9.9 cm 7. An infinitely long cylinder of radius R = 2 cm carries a uniform charge density ρ = 18 μC/ m 3. Calculate the electric field at distance r = 1 cm from the axis of the cylinder. Ans: 10.2 × 10 3 N/C

Chapter 23: Electric Potential 1. Three electric charges QA = q, QB = -q, and QC = -2q are located at the points A (x = + a, y = 0), B (x = -a, y = 0), and C (x = 0, y = +2a) respectively. What is the value of the electric potential at the origin? Ans: -kq/a 2. A charge Q distributed uniformly along the edge of a ring of radius R. What is the electric potential due to this charge at a distance x = R from the center the ring along its axis? kQ/2 R 3. Two uniformly distributed rings of charge, one of total charge Q 1 and radius r1 and the other of total charge Q2 and radius r2, have the same center. Compute the potential at the center. Ans: Q 1/4π εo r1 + Q2/4π εo r2. 4. Two equal charges Q are separated by a distance d. One of the charges is released and moves away from the other due

to the force between them. When the moving charge is a distance 3d from the other charge, what is its kinetic energy? Ans: Q2/6π εod 5. At a certain point in space there is a potential of 400 V. What is the potential energy of a +2-μC charge at that point in space? Ans: 8 × 10-4 J 6. An 800 V/m electric field is directed along the +x-axis. If the potential at x = 0 m is 2000 V, what is the potential at x = 2 m? Ans: 400 V 7. A +8-μC charge is situated along the +y-axis at y = 0.4 m. What is the electric potential at the origin because of this charge? Ans: +180 × 103 V 8. Two point charges 4 μC and -4 μC are situated along the x-axis at x1 = 2 m and x2 = -2 m respectively. What is the electric potential at the origin? Ans: 0 9. Two electric charges QA = + 1 μC and QB= - 2 μC are located 0.5 m apart. How much work is needed to move the charges apart and double the distance between them? Ans: 0.054 J 10. A charge of 1.5 μC is located at (0, 0) and a charge of 2.1 μC is located at (4 m, 0). What is the potential at the point (4 m, 3 m)? Ans: 9000 V 11. Four point charges, each of charge 2.5 x 10-5 C, are located on the x- and y-axes, one at each of the locations (0, 2.0 m), (0, -2.0 m), (2.0 m, 0), and (-2.0 m, 0). The potential at the origin is Ans: 4.5 × 10 5 V. 12. Three charges QA = -2.0 μC, QB= 6.0 μC, and QC= -4.0 μC are located along the y-axis at yA= -4.0 cm, yB = 0, and yC = 2.0 cm respectively. Calculate the electric potential at the point x = 6.0 cm on the x-axis. Ans: 0.81 × 10 5 V 13. Two charges QA = +q and QB = - 3q are located on the x-axis at x= 0 and x= d respectively. Where is the electric potential equal to zero? Ans: x = d/4 14. Two charges QA = +2 μC and QB = - 6μC are located at xA= - 1 cm and xB= +2 cm respectively. Where should a third charge, QC = + 3μC, be placed on the positive x-axis so that the potential at the origin is equal to zero? Ans: x =  3 cm 15. Two point charges q1 = 4 μC and q2 = -8 μC are placed along the x-axis at x1 = 0 m and x2 = 0.2 m, respectively. What is the electric potential energy of this system of charges? Ans: -1.44 J 16. Three equal charges of magnitude + 4 μC are placed at the corners of an equilateral triangle of side 2 cm. What is the electric potential energy of this system of charges? Ans: 21.6 J 17. If an electron is accelerated through a potential difference of 500 V between two parallel plates separated by a distance of 2 cm. The change in kinetic energy of the electron during this motion is? Ans: 500 eV 18. A circular area of radius 0.02 m is centered at the origin in a region where there exists a uniform electric field given by E = (320 i + 400 j + 690 k) N/C . (i) What is the electric flux (in N m2/C) through this circular area when the unit normal n to the area points in the +z direction. Ans: 0.87 N m2/C (ii) What is the angle between E and the z-axis (in degrees)? Ans: 36.6° 19. An electric field of 7 104 V/m exists between the plates of a circular parallel-plate capacitor that has a plate separation of 4 mm and a plate radius of 0.3 m. What is the voltage across the capacitor? What is the charge on each capacitor plate? 20. A positive point charge of +8 µC is located at the origin. A negative point charge of -18 µC is located at position z = 1.3 m. Find the position on the z-axis at which a proton would be in equilibrium.

21. An electric dipole consists of charges e and –e separated by a distance of 0.50 nm. It is placed in a uniform electric field with a magnitude of 1.9 105 N/C. (a) What is the electric dipole moment (in C m)? (b) What is the magnitude of the torque on the dipole when it is aligned with the electric field? (c) How much work must be done (in J) to rotate the dipole from an aligned to an anti-aligned position? 22. A thin nonconducting spherical shell of radius R carries a total positive charge +Q that is uniformly distributed on its surface. How much work must you do to bring a proton from infinity to a distance R/3 from the center of the shell? Explain your reasoning. Express your answers in terms of the quantities k, Q, R, and e. 23. Four point charges of equal magnitude are arranged at the corners of a square of side L as shown in the figure below. Express your answer in terms of the quantities k, q, L. (a) Compute the potential at the center of the square. (b) Find the magnitude and direction of the force exerted on the charge in the lower right corner by the other three charges.

Chapter 24: Capacitance 1.A 1 mF, a 2 mF, and a 3 mF capacitor are connected in series, the combination being connected across a 9 volt battery. (a) Which capacitor has the greatest charge? (b) Which capacitor has the greatest voltage? Ans: (a) They all have the same charge. (b) 1 mF 2. If you were a parallel plate capacitor manufacturer, state three ways you might make larger valued capacitors. Ans: Increase plate area, decrease separation, increase the dielectric constant. 3. A parallel-plate capacitor has plates of area 0.40 m2 and plate separation of 0.20 mm. The capacitor is connected to a 9.0 V battery. (a) What is the electric field between the plates? (b) What is the capacitance of the capacitor? (c) What is the charge on the capacitor? Ans: (a) 4.5 × 104 N/C (b) 18 nF (c) 162 nC 4. A parallel plate capacitor with plate separation of 4.0 cm has a plate area of 6.0 × 10 -2 m2. What is the capacitance of this capacitor if a dielectric material with a dielectric constant of 2.4 is placed between the plates? Ans: 32 × 10 -12 F 5. Three capacitors (5 μF, 10 μF, 50 μF) are connected in series across a 12V battery. (a) How much charge is stored in the 5 μF capacitor? (b) What is the potential difference across the 10 μF capacitor? Ans: (a) 37.5 μC (b) 3.75 V 6. Two capacitors of 6 μF and 8 μF are connected in parallel. The combination is then connected in series with a 12 V battery and a 14 μF capacitor. (a) What is the equivalent capacitance? (b) What is the charge on the 6-μF capacitor? (c) What is the voltage across the 6-μF capacitor? Ans: (a) 7 μF (b) 36 μC (c) 6 V 7. A 15-μF capacitor is connected to a 50-V battery and becomes fully charged. The battery is removed and a slab of dielectric that completely fills the space between the plates is inserted. The dielectric has a dielectric constant of 5.0. (a) What is the capacitance of the capacitor after the slab is inserted? (b) What is the voltage across the capacitor's plates after the slab is inserted? Ans: (a) 75 μF (b) 10 V 8. The magnitude of the charge on each plate of a parallel plate capacitor is 4 μC and the potential difference between the

plates is 80 V. What is the capacitance of this capacitor? Ans: 5 × 10-8 F 9. A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20 V power supply. The power supply is then removed and a dielectric of dielectric constant 4 is used to fill the space between the plates. (a) Compute the voltage now across the capacitor. (b) How much energy is stored in the capacitor? Ans: (a) 5 V (b) 500 mJ 10. Three capacitors have capacitances of 2.2 µF, 2.5 µF, 3.9 µF. (a) Find the equivalent capacitance if the capacitors are connected in series. Ans: 0.9 µF (b) Find the equivalent capacitance if the capacitors are in parallel. Ans: 8.6 µF 11. A 12 mF capacitor is connected in series with a 4 mF capacitor, the combination being connected across a 6 V power supply. The charge on the 12 mF capacitor is Ans: 18 mC. 12. A 4-μF capacitor has a potential drop of 20 V between its plates. The electric potential energy stored in this capacitor is: Ans: 800 μJ 13. A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V battery. How much work was done in charging this capacitor? Ans: 12.0 μJ

Chapter 25: Electric Currents and Resistance 1. The resistivity of the material of a wire is 1.76 × 10-8 Ωm. If the diameter of the wire is 2 × 10-3 m and its length is 2 m, what is its resistance? Ans: 0.0112 Ω 2. A light bulb operating at a voltage of 120 V has a resistance of 200 Ω. What is the power? Ans: 72 W 3. A 110 V hair dryer is rated at 1200 W. What current will it draw? Ans: 10.9 A 4. A 1500 W heater is connected to a 120 V line for 2 hours. How much heat energy is produced? Ans: 10.8 MJ 5. A battery is rated at 12 V and 160 A h. How much energy does the battery store? Ans: 6.9 MJ 6. A 100 W driveway light bulb is on 10 hours per day. Assuming the power company charges 10 cents for each kilowatt-hour of electricity used, estimate the annual cost to operate the bulb. Ans: $36.50 7. A certain metal has a resistivity of 1.68 × 10-8 Ω m. You have a long spool of wire made from this metal. If this wire has a diameter of 0.150 mm, how long should you cut a segment so its resistance will be 15.0 Ω? Ans: 15.8 m...