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2015-2016 Bahar Fiz102 Bee's Physics HW 1 P21.43 Identical point charges Q are placed at each of the four corners of a rectangle measuring 1.63 m by 4.29 m. If Q = 12.3 μC, what is the magnitude of the electrostatic force on any one of the charges? 0.551 N P050.problem A +2.07 mC charge is fixed in position on the x-axis at x = 0 and a –6.45 mC charge is fixed in position on the xaxis at x = 4.11 m. a) Where on the x-axis could a +8.43 mC charge be placed so that the net force on it is zero? -5.37 m b) Where on the x-axis could a -8.43 mC charge be placed so that the net force on it is zero? -5.37 m P22.31 A small metal ball with a mass of 5.61 g and a charge of 6.33 mC is located at a distance of 0.67 m above the ground in an electric field of 17.9 N/C directed to the east. The ball is then released from rest. What is the speed of the ball after it has moved downward a vertical distance of 0.27 m? 5.268 m/s P22.53 A -4.55 nC point charge is located at the center of a conducting spherical shell. The shell has an inner radius of 2 m, an outer radius of 4 m, and a charge of 7.05 nC. a) What is the magnitude of the electric field at r = 1 m? -4.090×101 N/C b) What is the magnitude of the electric field at r = 3 m? 0.000 N/C c) What is the magnitude of the electric field at r = 5 m? 8.990×10-1 N/C d) What is the surface charge density, σ, on the outside surface of the shell? 1.243×10-11 C/m^2 P082.problem A proton enters the gap between a pair of metal plates (an electrostatic separator) that produces a uniform, vertical electric field between them. Ignore the effect of gravity on the proton. a) Assuming that the length of the plates is 23.7 cm, and that the proton will approach the plates at a speed of 24.1 km/s, what electric field strength should the plates be designed to provide, if the proton must be deflected vertically by 1.33·10–3 rad? 3.398×10-2 N/C b) What speed does the proton have after exiting the electric field? 2.410×104 m/s c) Suppose the proton is one in a beam of protons that has been contaminated with positively charged kaons, particles whose mass is 494 MeV/c2 (8.81·10–28 kg), compared to the mass of the proton, which is 938 MeV/c2 (1.67·10–27 kg). The kaons have +1e charge, just like the protons. If the electrostatic separator is designed to give the protons a deflection of 2.81·10 –3 rad, what deflection will kaons with the same momentum as the protons experience? 1.482×10-3 rad E= www.beesphyiscs.com 2015-2016 Bahar Fiz102 Bee's Physics HW 2 P027.problem A proton gun fires a proton from midway between two plates, A and B, which are separated by a distance of 10.1 cm; the proton initially moves at a speed of 123 km/s toward plate B. Plate A is kept at zero potential, and plate B at a potential of 633 V. With what speed will it hit plate A? 2.754×105 m/s P23.41 An electric field varies in space according to this equation E(x) = a x e-bx, where a = 2.249 N(Cm)1 and b = 0.209 m-1. a) For what value of x, xmax, does the electric field have its largest value? 4.785 m b) What is the potential difference between the points at x = 0 and x = xmax? -13.605 V -a P22.48 An infinite non-conducting plane has a uniform charge distribution of 5.41 nC/m2 and is located in the yz-plane at x = 0. A point charge of 11.3 nC is located at x = 2.45 m. At what position(s) on the xaxis is the electric potential a minimum? 1.873 m P22.65 A Van de Graaff generator has a spherical conductor with a radius of 26.1 cm. It can produce a maximum electric field of 4.65·106 V/m. a) What is the maximum potential difference it can generate? 1213.7 kV b) What is the maximum charge that it can hold? 3.524×10-5 C P22.75 A total charge of Q = 6.7·10–6 C is placed on a conducting sphere (sphere 1) of radius R = 30.1 cm. a) What is the electric potential, V1, at the surface of sphere 1 assuming that the potential infinitely far away from it is zero? (Hint: What is the change in potential if a charge is brought from infinitely far away, where V(∞) = 0, to the surface of the sphere?) 2.001×105 V b) A second conducting sphere (sphere 2) of radius r = 7.5 cm with an initial net charge of zero (q = 0) is connected to sphere 1 using a long thin metal wire. How much charge flows from sphere 1 to sphere 2 to bring them into equilibrium? 1.336×10-6 C c) After the spheres are connected, what is the absolute value of the electric field on the surface of sphere 1? 5.322×105 V/m d) After the spheres are connected, what is the absolute value of the electric field on the surface of sphere 2?2.136×106 V/m www.beesphyiscs.com 2015-2016 Bahar Fiz102 Bee's Physics HW 3 P038.problem A potential difference of V = 11.0 V is applied across a circuit with capacitances C1 = 3.9 nF, C2 = 1.5 nF, and C3= 3.9 nF, as shown in the figure. a) What is the magnitude and sign of q3l, the charge on the left plate of C3 (marked by point A)? -2.491×10-8 C b) What is the electric potential difference, V3, across C3? 6.4 V c) What is the magnitude and sign of the charge q2r, on the right plate of C2 (marked by point B)? -6.919×10-9 C P046.problem A 4520.-nF parallel plate capacitor is connected to a 14.2-V battery and charged. a) What is the charge Q on the positive plate of the capacitor? 6.418×10-5 C b) What is the electric potential energy stored in the capacitor? 4.557×10-4 J The 4520.-nF capacitor is then disconnected from the 14.2-V battery and used to charge three uncharged capacitors, a 135.-nF capacitor, a 250.-nF capacitor, and a 310.-nF capacitor, connected in series. c) After charging, what is the potential difference across each of the four capacitors? [Enter the potential differences across the 4520.-nF capacitor, the135.-nF capacitor, the 250.-nF capacitor, and the 310.-nF capacitor, separated by commas, in units of volts. Example: if you think that the potential difference across the 4520.-nF capacitor is 7 V and across each of the others is 9 V, then you should enter 7,9,9,9]. 13.9890, 7.0810, 3.8240, 3.0840 d) How much of the electrical energy stored in the 4520.-nF capacitor was transferred to the other three capacitors? 6.686×10-6 J P066.problem A 3.3-pF parallel plate capacitor has a potential difference of 28.0 V across it. The plates are 3.1 mm apart, and the space between them contains air. a) What is the charge on the capacitor? 9.240×10-11 C b) How much energy is stored in the capacitor? 1.294×10-9 J c) What is the area of the plates? 1.156×10-3 m^2 d) What would the capacitance of this capacitor be if the space between the plates were filled with polystyrene (κ = 2.6)? 8.58 pF P078.problem A typical AAA battery has stored energy of about 3400 J. (Battery capacity is typically listed as 625 mA h, meaning that much charge can be delivered at approximately 1.5 V.) Suppose you want to build a parallel plate capacitor to store this amount of energy, using a plate separation of 1.79 mm and with air filling the space between the plates. a) Assuming that the potential difference across the capacitor is 1.5 V, what must the area of each plate be? 6.113×1011 m*m b) Assuming that the potential difference across the capacitor is the maximum that can be applied without dielectric breakdown occurring, what must the area of each plate be? 7.542×104 m*m www.beesphyiscs.com 2015-2016 Bahar Fiz102 Bee's Physics HW 4 P064.problem A circuit consists of a gold wire of length 13.7 m and radius 1.51 mm connected to a 12.7 V battery. A tantalum wire of length 4.55 m is connected to the same battery and dissipates the same amount of power. What is the radius of the tantalum wire? (See Table 25.1.) 2.009×10-3 m P068.problem A 220.0 V, 1.66 kW heater has a 2.97 m long steel heating element. (See Table 25.1.) a) What is the conductance of the heating element? 3.430×10-2 ohm^-1 b) What is the radius of the heating element? 5.972×10-5 m P080.problem Before bendable tungsten filaments were developed, Thomas Edison used carbon filaments in his light bulbs. Though carbon has a very high melting temperature (3599 °C), its sublimation rate is high at high temperatures. So carbon filament bulbs were kept at lower temperatures, thereby rendering them dimmer than later tungsten-based bulbs. A typical carbon-filament bulb requires an average power of 43.1 W, when 110.7 volts is applied across it, and has a filament temperature of 1847 °C. Carbon, unlike copper, has a negative temperature coefficient of resistivity: α = –5.00·10-4 °C–1. Calculate the resistance at room temperature (20.0 °C) of this carbon filament. 3.287×103 ohm P032.problem A Wheatstone bridge is constructed using a 1.00-m-long Nichrome wire (the purple line in the figure) with a conducting contact that can slide along the wire. A resistor, R1 = 121 Ω, is placed on one side of the bridge, and another resistor, R, of unknown resistance, is placed on the other side. The contact is moved along the Nichrome wire, and it is found that the ammeter reading is zero for L = 21.6 cm. Knowing that the wire has a uniform cross section throughout its length, determine the unknown resistance. 439.2 Ohm P038.problem You want to make an ohmmeter to measure the resistance of unknown resistors. You have a battery with voltage Vemf = 18.0 V, a variable resistor, R, and an ammeter that measures current on a linear scale from 0 to 20.0 mA. a) What resistance should the variable resistor have so that the ammeter gives its full-scale (maximum) reading when the ohmmeter is shorted? 900 Ohm b) Using the resistance from part (a), what is the unknown resistance if the ammeter reads 1/3 of its full scale? 1800 Ohm www.beesphyiscs.com 2015-2016 Bahar Fiz102 Bee's Physics HW 5 P046.problem Two parallel plate capacitors, C1 and C2, are connected in series with a 45.0-V battery and a 310-kΩ resistor, as shown in the figure. Both capacitors have plates with an area of 1.51 cm2 and a separation of 0.210 mm. Capacitor C1 has air between its plates, and capacitor C2 has the gap filled with porcelain (dielectric constant of 7 and dielectric strength of 5.70 kV/mm). The switch is closed, and a long time passes. a) What is the charge on capacitor C1? 2.507×10-10 C b) What is the charge on capacitor C2? 2.507×10-10 C c) What is the total energy stored in the two capacitors? 5.640×10-9 J d) What is the electric field inside capacitor C2? 2.679×104 V/m , d) P050.problem The circuit in the figure has a capacitor, C = 4.50 mF, connected to a V = 15.0-V battery, two switches, and three resistors (R1 = 330 Ω, R2 = 210 Ω, and R3 = 110 Ω. Initially, the capacitor is uncharged and both of the switches are open. a) Switch S1 is closed. What is the current flowing out of the battery immediately after switch S 1 is closed? 3.409×10-2 A b) After 10.0 min, switch S2 is closed. What is the current flowing out of the battery immediately after switch S2 has been closed? 3.730×10-2 A c) What is the current flowing out of the battery 10.0 min after switch S 2 has been closed? 3.409×10-2 A d) After another 10.0 min, switch S1 is opened. How long will it take until the current in the R2 = 210-Ω resistor is below 1.00 mA? 3.544 s P054.problem In the circuit in the figure, the capacitors are completely uncharged. The switch is then closed for a long time. As shown, R1 = 6.10 Ω, R2 = 8.30 Ω, and V = 11.5 V. a) Calculate the current through the 4.00 Ω-resistor. 0 b) Find the potential difference across the 4.00 Ω-resistor. 0 c) Find the potential difference across the R1 = 6.10 Ω-resistor. 4.872 V d) Find the potential difference across the R2 = 8.30 Ω-resistor. 6.628 V e) Find the potential difference across the 1.00 μF-capacitor 6.628 V (a) If the switch is closed for a long time, the capacitor is fully charged and there is no current through that branch. Therefore, the current throught the 4.00 Ω resistor is i = 0 A. (b) With no current through R2, the potential drop acros it is ΔV2=0V. The two resistors R1 and R3 are in series with each other, so the current through them is The potential drop across the R1 resistor is P058.problem An ammeter with an internal resistance of 52.0 Ω measures a current of 5.75 mA in a circuit containing a battery and a total resistance of 1390 Ω. The insertion of the ammeter alters the resistance of the circuit, and thus the measurement does not give the actual value of the current in the circuit without the ammeter. Determine the actual value of the current. 5.965 mA P062.problem As shown in the figure, C1 = 1.95-μF, C2 = 2.60-μF, and V = 14.5 V. a) For the circuit shown in the figure, determine the charge on capacitor C 1 when switch S has been closed for a long time. 9.425×10-6 C b) Determine the charge on capacitor C2 when switch S has been closed for a long time. 2.513×10-5 C c) Determine the charge on capacitor C1 when switch S has been open for a long time. 1.616×10-5 C d) Determine the charge on capacitor C2 when switch S has been open for a long time. 1.616×10-5 C www.beesphyiscs.com 2015-2016 Bahar Fiz102 Bee's Physics HW 6 P036.problem The most common material used for sandpaper, silicon carbide, is also widely used in electrical applications. One common device is a tubular resistor made of a special grade of silicon carbide called carborundum. A particular carborundum resistor (see the figure) consists of a thick-walled cylindrical shell (a pipe) of inner radius a = 1.95 cm, outer radius b = 2.95 cm, and length L = 45.7 cm. The resistance of this carborundum resistor at 20 °C is 1.097 Ω. a) Calculate the resistivity of carborundum at room temperature. 3.695×10-3 Ohm*m b) Carborundum has a high temperature coefficient of resistivity: α = 2.14·10-3 K–1. If, in a particular application, the carborundum resistor heats up to 316.0 °C, what is the percentage change in its resistance between room temperature (20.0 °C) and this operating temperature? 6.334×101 P074.problem In the circuit shown in the figure, R1 = 3.57 Ω, R2 = 6.57 Ω, R3 = 24.7 Ω, and V = 11.9 V. a) Determine a value for the equivalent resistance. 1.466×101 ohm b) Calculate the magnitude of the current flowing through R3 on the top branch of the circuit (marked with a vertical arrow). 4.058×10-1 A P078.problem A piece of silver wire is used to form a circular loop of radius 10.1 cm. The wire has a cross-sectional area of 19.7 mm2. Points A and B are 90.0° apart, as shown in the figure. Find the resistance between points A and B. (See Table 25.1.) 9.785×10-5 ohm P047.problem What is the equivalent resistance of the five resistors in the circuit in the figure, if R1 = 23 Ω? 61.28 Ohm www.beesphyiscs.com 2015-2016 Bahar Fiz102 Bee's Physics HW 7 P023.problem A particle with a charge of 18.1 μC moves along the x-axis with a speed of 48.5 m/s. It enters a magnetic field given by = 0.311 + 0.715 , in teslas. a) Determine the magnitude of the magnetic force on the particle. 6.845×10-4 N b) Determine the direction of the magnetic force on the particle. 23.51 deg P038.problem A copper wire (density ρ = 8960 kg/m3) of radius 0.515 mm is carrying a current at the Earth's Equator. Assuming that the magnetic field of the Earth has magnitude 0.445 G at the Equator and is parallel to the surface of the Earth and that the current in the wire flows toward the east, what current is required to allow the wire to levitate? 1645.82 A P020.problem A proton moving with a speed of 3.81·105 m/s in the positive y-direction enters a uniform magnetic field of 0.371 T pointing in the positive x-direction. Calculate the magnitude of the force on the proton. 2.264×10-14 N P044.problem A rectangular coil with 20 windings carries a current of 2.17 mA flowing in the counterclockwise direction. It has two sides that are parallel to the y-axis and have length 8.17 cm and two sides that are parallel to the x-axis and have length 6.45 cm. A uniform magnetic field of 49.5 μT acts in the positive x-direction. What torque must be applied to the loop to hold it steady? 1.132×10-8 N*m P054.problem A cyclotron in a magnetic field of 8.23 T is used to accelerate protons to 47.7 % of the speed of light. a) What is the cyclotron frequency of these protons? 1.257×108 Hz b) What is the radius of their trajectory in the cyclotron? 0.181 m c) What is the cyclotron frequency of the same protons in the Earth's magnetic field? Assume that the Earth's magnetic field is about 0.451 G. 6.886×102 Hz d) What is the trajectory radius of the same protons in the Earth's magnetic field? Assume that the Earth's magnetic field is about 0.451 G. 3.305×104 m m=1.67.10-27 kg, q=1.602.10-19C www.beesphyiscs.com 2015-2016 Bahar Fiz102 Bee's Physics HW 8 P028.problem Find the magnetic field in the center of a wire semicircle like that shown in the figure, with radius R = 16.7 cm, if the current is i = 12.7 A.2.389×10-5 T P28.36 A long, straight wire has a 10.1 A current flowing in the positive x-direction, as shown in the figure. Close to the wire is a square loop of copper wire that carries a 1.07 A current in the direction shown. The near side of the loop is d = 58.3 cm away from the wire. The length of each side of the square is a = 1.61 m. Find the net force between the two current-carrying objects. 4.382×10-6 N P068.problem Two long, straight parallel wires are separated by a distance of 20.9 cm. Each wire carries a current of 15.1 A in the same direction. What is the magnitude of the resulting magnetic field at apoint that is 13.7 cm from each wire? 2.851×10-5 T P072.problem Two wires, each 26.9 cm long, are connected to two separate 9.00 V batteries as shown in the figure. The resistance of the first wire is 5.00 Ω, and that of the other wire is unknown (R). If the separation between the wires is 3.81 mm, what value of R will produce a force of magnitude 2.17·10–5 N between them? 1.054×101 ohm P080.problem A circular wire of radius 4.67 cm has a current of 2.13 A flowing in it. The wire is placed in a uniform magnetic field of 4.93 mT. a) Determine the maximum torque on the wire. 7.195×10-5 N*m b) Determine the range of the magnetic potential energy of the wire. 1.439×10-4 J max min 180 0 www.beesphyiscs.com 2015-2016 Bahar Fiz102 Bee's Physics HW 9 P032.problem An elastic circular conducting loop expands at a constant rate over time such that its radius is given by r(t) = r0 + vt, where r0 = 0.110 m and v = 0.0210 m/s. The loop has a constant resistance of R = 18.5 Ω and is placed in a uniform magnetic field of magnitude B0 = 1.73 T, perpendicular to the plane of the loop, as shown in the figure. Calculate the direction and the magnitude of the induced current, i, at t = 4.67 s. (Use positive numbers for a clockwise current and negative numbers for a counterclockwise current.) 2.57×10-3 A P036.problem The long, straight wire in the figure has a current i = 2.21 A flowing in it. A square loop with 10-cm sides and a resistance of 0.0389 Ω is positioned 10 cm away from the wire. The loop is then moved in the positive x-direction with speed v = 17.43 cm/s. a) Find the direction of the induced current in the loop. (Enter -1 for clockwise, +1 for counterclockwise). -1 By the right-hand rule, the flux is into the page. Since the square is moving away from the wire, the flux is decreasing. Lenz’s law states that the current is moving clockwise. b) Identify the directions of the magnetic forces acting on all sides of the square loop. (You can enter x, -x, y, -y, z, -z, for each of the 4 sides. The first answer is for the top part of the loop, the next for the right side, then the bottom, and finally the left side. Separate the answers for each side by commas. Use no spaces. Example: If you think that the force vectors on the top and bottom point in the negative z-direction [=into the page], and the force vectors on the left and right point in the positive y-direction, then enter: "-z,y,-z,y".) y,x,-y,-x c) Calculate the magnitude of the net force acting on the loop at the instant it starts to move. 2.188×10-13 N P044.problem In the circuit in the figure, R = 122.0 Ω, L = 2.39 H, and Vemf = 31.0 V. After the switch is closed, how long will it take the current in the inductor to reach 127.0 mA? 0.0136 s P052.problem An emf of 20.0 V is applied to a coil with an inductance of 48.0 mH and a resistance of 0.85 Ω. a) Determine the energy stored in the magnetic field when the current reaches one fourth of its maximum value. 0.830 J b) How long does it take for the current to reach this value? 0.0162 s P062.problem A wedding ring (of diameter 1.79 cm) is tossed into the air and given a spin, resulting in an angular velocity of 13 rotations per second. The rotation axis is a diameter of the ring. Taking the magnitude of the Earth’s magnetic field to be 3.47·10–5 T, what is the maximum induced potential difference in the ring? 7.133×10-7 V www.beesphyiscs.com 2015-2016 Bahar Fiz102 Bee's Physics HW 10 P020.problem An electric field of magnitude 210 V/m is directed perpendicular to a circular planar surface with radius 5.91 cm. If the electric field increases at a rate of 14.3 V/ms, determine the magnitude of the magnetic field at a radial distance 11.5 cm away from the center of the circular area. 2.42×10-18 T P022.problem The current flowing in a solenoid that is 20.1 cm long and has a radius of 2.60 cm and 542 turns decreases from 3.31 A to 1.45 A in 0.160 s. Determine the magnitude of the induced electric field inside the solenoid 1.30 cm from its center. 2.56×10-4 V/m P026.problem The amplitude of the electric field of an electromagnetic wave is 241 V/m. What is the amplitude of the magnetic field of the electromagnetic wave? 8.03×10-7 T P31.24 A parallel plate capacitor has circular plates of radius 10.5 cm that are separated by a distance of 5.30 mm. The potential across the capacitor is increased at a constant rate of 1170 V/s. Determine the magnitude of the magnetic field between the plates at a distance r = 3.40 cm from the center. 4.17×10-14 T P032.problem The antenna of a cell phone is a straight rod 3.95 cm long. Calculate the operating frequency of the signal from this phone, assuming that the antenna length is 1/4 of the wavelength of the signal. 1.90×109 Hz www.beesphyiscs.com