Consider the system shown in Fig. 4-62 with mA = 9.5 kg and mB = 11.5 kg. The angles θA = 59∘ and θB = 32∘, (a) In the absence of friction, what force F→ would be required to pull the masses at a constant velocity up the fixed inclines? (b) The force F→ is now removed. What is the magnitude and direction of the acceleration of the two blocks? (c) In the absence of F→, what is the tension in the string? FIGURE 4-62 Problem 86.
Two 1.50−V batteries-with their positive terminals in the same direction-are inserted in series into the barrel of a flashlight. One battery has an internal resistance of 0.350 Ω, the other an internal resistance of 0.100 Ω. When the switch is closed, a current of 600 mA occurs in the lamp. (a) What is the bulb's resistance? Ω (b) What fraction of the chemical energy transformed appears as internal energy in the batteries? %
You just landed a job as an assistant to an electrician who is working on a building site. He is making use of long single-conductor insulated wire for some of the connections in the complicated "smart building." A new shipment of spools of this wire has been delivered, and the electrician is not happy that it came from a manufacturer that he suspects is producing inferior wire. The electrician asks you to determine the resistance per unit length of the wire (in Ω/m ) and provides you with a battery and a high-quality multimeter. Despite the quality of the meter, he suggests that you not use the ohmmeter to measure resistance, because the value of the resistance is so low that the meter is not likely to measure it accurately. You are puzzled as to how to go about this task. As the electrician runs off to attend to another task, he says, "Cut off a couple of different lengths of wire and use the battery and the multimeter. " You put the multimeter in voltage mode across the terminals of the battery without a wire connected and measure 7.00 V. You then cut off two lengths of wire, one 5.00 m in length, and one 10.0 m in length. Connecting them one at a time to the battery through the multimeter in current mode, you find that there is a current of 5.17 A in the 5.00 m length of wire, and 3.00 A in the 10.0 m length of wire. Ah-ha, now you have enough information! Ω/m
Three 100 Ω resistors are connected as shown in the figure. The maximum power that can safely be delivered to any one resistor is 23.0 W. (a) What is the maximum potential difference that can be applied to the terminals a and b? V (b) For the voltage determined in part (a), what is the power delivered to each resistor? resistor on the left W resistor at the top of the loop W resistor at the bottom of the loop W (c) What is the total power delivered to the combination of resistors? W
In the figure below, show how to add just enough ammeters to measure every different current. Show how to add just enough voltmeters to measure the potential difference across each resistor and across each battery. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet.
A professor created the circuit shown in the figure for her lab. Assuming ε = 9.00 V and R = 5.00 Ω, find the following quantities. (a) the current in the 2.00 Ω resistor (Enter the magnitude in mA.) mA (b) the potential difference (in V ) between points a and b Vb − Va = V
You are working in a lab where RC circuits are used to delay the initiation of a process. One particular experiment involves an RC circuit with a half-life of t1/2 = 3.00 s. Your supervisor is concerned that the initiation of the process is occurring too soon and that the half-life needs to be extended. He asks you to change the resistance of the circuit to make the half-life longer. All you can find in the supply room is a single 52.0 Ω resistor. You look at the RC circuit and see that the resistance is 59.0 Ω. You combine the new resistor with the old to extend the half-life of the circuit. Determine the new half-life (in s). s
Consider a series RC circuit as in the figure below for which R = 9.00 MΩ, C = 8.00 μF, and ε = 25.0 V. (a) Find the time constant of the circuit. s (b) What is the maximum charge on the capacitor after the switch is thrown closed? μC (c) Find the current in the resistor 10.0 s after the switch is closed. μA
A heating element in a stove is designed to receive 2,715 W when connected to 240 V. (a) Assuming the resistance is constant, calculate the current in the heating element if it is connected to 120 V. A (b) Calculate the power it receives at that voltage. W
An electron is accelerated through 1.85×103 V from rest and then enters a uniform 2.60-T magnetic field. (a) What is the maximum magnitude of the magnetic force this particle can experience? N (b) What is the minimum magnitude of the magnetic force this particle can experience? N
A scientist builds an apparatus to measure the charge to mass ratio of ions. An ion is first accelerated to a speed of 4.50×107 m/s. It then passes through a region of magnetic field, with a magnitude of 2.44×10−2 T, perpendicular to the ion's velocity. Because the ion is moving so fast, it is only in the presence of the magnetic field for 2.00×10−7 s. Upon exiting the magnetic field, the scientist measures that the ion was deflected a distance of 3.00 cm in a direction perpendicular to its initial velocity. (a) What is the ratio of the absolute value of the ion's charge to its mass (in C/kg )? Assume the velocity change is small, and that the component of the velocity along the ion's original direction does not change noticeably. |q| m = Cg (b) Suppose the scientist determines the ion is singly charged; that is, the magnitude of its charge is that of a proton. What is the mass of the ion (in kg)? kg
An electron moves in a circular path with a speed of 1.26×107 m/s in the presence of a uniform magnetic field with a magnitude of 1.94 mT. The electron's path is perpendicular to the field. (a) What is the radius (in cm) of the circular path? cm (b) How long (in s) does it take the electron to complete one revolution? s
Cathode ray tubes in old television sets worked by accelerating electrons and then deflecting them with magnetic fields onto a phosphor screen. The magnetic fields were created by coils of wire on either side of the tube carrying large currents. In one such TV set, the phosphor screen is 48.4 cm wide, and is 10.1 cm away from the center of the magnetic deflection coils (that is, the center of the region of magnetic field). The electron beam is first accelerated through a 10,000 V potential difference before it enters the magnetic field region, which is 1.00 cm wide. The field is approximately uniform and perpendicular to the velocity of the electrons. If the field were turned off, the electrons would hit the center of the screen. What magnitude of magnetic field (in mT) is needed to deflect the electrons so that they hit the far edge of the screen? Ignore any relativistic corrections. mT
You are working during the summer at a company that builds theme parks. The company is designing an electromagnetic propulsion system for a new roller coaster. A model of a substructure of the device appears in the figure below. (i) The rod is of length d = 1.00 m and mass m = 0.600 kg. The rod carries a current I = 100 A in the direction shown and rolls along the rails of length L = 20.0 m without slipping. The entire system of rod and rails is immersed in a uniform downward-directed magnetic field with magnitude B = 2.30 T. The electromagnetic force on the rod is parallel to the rails, causing the rod to roll to the right in the figure. When a full-scale device is produced, this rod will represent the axle of wheels on which the car and its passengers ride. The electromagnetic force on the axle will provide the motion of the car at the beginning of the roller-coaster ride. Your supervisor wants to test the substructure in the figure in a flat outdoor area on the grounds of the company. By projecting the rod from the rails in a horizontal direction from a height h = 2.20 m, the projection speed can be determined from how far from the ends of the rails the rod hits the ground. Your supervisor asks you to determine the length of the outdoor area needed to test the device. (Determine the total horizontal distance, in m, from the initial position of the rod on the tracks to the final position of the rod where it lands on the ground.) m
A wire 2.80 m in length carries a current of 6.60 A in a region where a uniform magnetic field has a magnitude of 0.480 T. Calculate the magnitude of the magnetic force on the wire assuming the following angles between the magnetic field and the current. (a) 60.0∘ (b) 90.0∘ N (c) 120∘ N
An eight-turn coil encloses an elliptical area having a major axis of 40.0 cm and a minor axis of 30.0 cm (see figure). The coil lies in the plane of the page and has a 6.20-A current flowing clockwise around it. If the coil is in a uniform magnetic field of 1.98×10−4 T directed toward the left of the page, what is the magnitude of the torque on the coil? Hint: The area of an ellipse is A = πab, where a and b are, respectively, the semimajor and semiminor axes of the ellipse. N⋅m
In an experiment designed to measure the Earth's magnetic field using the Hall effect, a copper bar 0.520 cm thick is positioned along an east-west direction. Assume n = 8.46×1028 electrons /m3 and the plane of the bar is rotated to be perpendicular to the direction of B→. If a current of 8.00 A in the conductor results in a Hall voltage of 4.50×10−12 V, what is the magnitude of the Earth's magnetic field at this location? μT
An ion with a mass m and a magnitude of charge of 1 e is initially at rest when it is accelerated by a potential difference of magnitude ΔV. After exiting the accelerating potential, it enters a region with a uniform magnetic field perpendicular to the ion's velocity. The ion moves in a semicircle of radius R. Next, an ion with a mass m′ and a magnitude of charge of 4e is accelerated by the same potential difference and deflected by the same magnetic field. The radius of its semicircular path is R′ = 3R. Find the ratio of the ion masses, m′/m. m′/m =
(a) A velocity selector consists of electric and magnetic fields described by the expressions E→ = Ek^ and B→ = Bj^, with B = 22.0 mT. Find the value of E (in kV/m) such that a 740 eV electron moving in the negative x-direction is undeflected. kV/m (b) What If? For the value of E found in part (a), what would the kinetic energy of a proton have to be (in MeV) for it to move undeflected in the negative x-direction? MeV
An arbitrarily curved wire that carries a current between two endpoints in the presence of a uniform magnetic field will experience the same net magnetic force as a straight wire carrying the same current between the same endpoints. Essentially, any forces experienced by parts of the wire that curve or twist away from the straight-line path are canceled out by forces on sections that curve back toward the original path. Furthermore, if the wire forms a closed loop in between the endpoints, the net force on the closed loop is zero. Using this result, consider a town where the Earth's magnetic field has a magnitude of 51.3 μT. The magnetic field vector lies in a vertical plane defined by the north-south and up-down axes, and it points 60.0∘ below the northward direction. In this town, a storefront window lies along the north-south vertical plane, and in the window is a neon sign (which is a thin current-carrying discharge tube). The sign carries a 35.1 mA current, starting from the lower south corner of the window, and ending at the opposite corner, which is 1.32 m to the north and 0.850 m upward. The sign spells out the word "BURGERS" between the two points. What is the net vector magnetic force (in μN ) on the neon sign? (Take east to be the +x-axis, up to be the +y-axis, and south to be the +z-axis. Do not include units in your answer.) F→B = μN
A 52.5-turn circular coil of radius 4.70 cm can be oriented in any direction in a uniform magnetic field having a magnitude of 0.465 T. If the coil carries a current of 25.9 mA, find the magnitude of the maximum possible torque exerted on the coil. N⋅m
A Hall-effect probe operates with a 120−mA current. When the probe is placed in a uniform magnetic field of magnitude 0.0760 T, it produces a Hall voltage of 0.720 μV. (a) When it is used to measure an unknown magnetic field, the Hall voltage is 0.380 μV. What is the magnitude of the unknown field? mT (b) The thickness of the probe in the direction of B is 1.40 mm. Find the density of the charge carriers, each of which has charge of magnitude e). m−3
A measurement was made of the magnetic field due to a tornado, and the result was 16.00 nT to the north. The measurement was made at a position 9.10 km west of the tornado. What was the magnitude (in A) and direction of the current in the funnel of the tornado? Assume the vortex was a long, straight wire carrying a current. A (conventional current) flowing ---Direction--the tornado.
In the figure below, the current in the long, straight wire is I1 = 6.00 A and the wire lies in the plane of the rectangular loop, which carries a current I2 = 10.0 A. The dimensions in the figure are c = 0.100 m, a = 0.150 m, and ℓ = 0.680 m. Find the magnitude and direction of the net force exerted on the loop by the magnetic field created by the wire. magnitude μN direction
Two long, parallel, current-carrying wires lie in an xy-plane. The first wire lies on the line y = 0.310 m and carries a current of 26.5 A in the +x direction. The second wire lies along the x-axis. The wires exert attractive forces on each other, and the force per unit length on each wire is 285 μN/m. What is the y-value (in m ) of the line in the xy-plane where the total magnetic field is zero? m
(a) A wire is held horizontally in a vacuum chamber, and carries a current of 1.85 μA. A proton is traveling in a direction parallel to the wire (opposite the current) with a constant speed of 2.90×104 m/s at a distance d above the wire. Ignoring the magnetic field due to the Earth, determine the value of d (in cm). cm (b) What If? At what distance d (in m) would an electron moving with the same speed as the proton move parallel to the wire? m What direction would the electron have to move? In the same direction as the proton. In the opposite direction as the proton. There is too little information to determine the direction.
(a) A student is experimenting with some insulated copper wire and a power supply. She winds a single layer of the wire on a tube with a diameter of dsolenoid = 10.0 cm. The resulting solenoid is ℓ = 65.0 cm long, and the wire has a diameter of dwire = 0.100 cm. Assume the insulation is very thin, and adjacent turns of the wire are in contact. What power (in W) must be delivered to the solenoid if it is to produce a field of 8.60 mT at its center? (The resistivity of copper is 1.70×10−8 Ω⋅m. ) W What If? Assume the maximum current the copper wire can safely carry is 22.0 A. (b) What is the maximum magnetic field (in T) in the solenoid? (Enter the magnitude.) T (c) What is the maximum power (in W) delivered to the solenoid? W
A long solenoid that has 950 turns uniformly distributed over a length of 0.390 m produces a magnetic field of magnitude 1.00×10−4 T at its center. What current is required in the windings for that to occur? mA
You are working for a company that creates special magnetic environments. Your new supervisor has come from the financial side of the organization rather than the technical side. He has promised a client that the company can provide a device that will create a magnetic field inside a cylindrical chamber that is directed along the cylinder axis at all points in the chamber and increases in the axial direction as the square of the value of y, where y is in the axial direction and y = 0 is at the bottom end of the cylinder. Prepare a calculation to show that the field requested by your supervisor and promised to a client is impossible. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet.
Consider the situation when almost all of the magnetic moments of a sample of a particular ferromagnetic metal are aligned. In this case, the magnetic field can be calculated as the permeability constant μ0 multiplied by the magnetic moment per unit volume. In a sample of iron, for example, where the number density of atoms is approximately 8.50×1028 atoms/m3, the magnetic field can reach 1.96 T. If each electron contributes a magnetic moment of 9.27×10−24 A⋅m2 (1 Bohr magneton), how many electrons per atom contribute to the saturated field of iron? electrons/atom