Exam 1 Test Bank
Module 3 Homework
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What area plates would a 1.0 F parallel plate capacitor have, with a plate separation of 0.10 mm and a dielectric of constant 10?
1.1 × 106 m2
A 1.56-V battery has an internal resistance of 0.120 Ω. What is the maximum current that can be drawn from this battery?
13.0 A
A 2.50 A current is carried by a copper wire of radius 1.0 mm. If the density of conduction electrons is 8.0 × 1028 m−3, what is the drift velocity of the conduction electrons?
6.2 × 10−5 m/s
A pair of electric charges has a positive potential energy. This implies that
the charges have the same sign.
A 1.65 nC charge experiences an acceleration of 6.33 × 107 m/s2 in an electric field. What is the magnitude of the electric field?
there isn't enough information in the problem to solve this
Electric fields that arise from changing magnetic fields have all the properties below except
they terminate on electric charges.
Some household appliances have plugs with two prongs while others have three prongs. The additional prong is
to connect to ground.
What is the resistance of a 40.0-W, 120-V incandescent lightbulb?
360 Ω R = V^2/P: (120)^2/40
A 50-turn coil with a radius of 11.3 cm is mounted so the coil's axis can be oriented in any horizontal direction. Initially the axis is oriented so the magnetic flux from Earth's field is maximized. If the coil's axis is rotated through 90.0° in 0.080 s, an average emf of 0.957 mV is induced in the coil. What is the magnitude of the horizontal component of Earth's magnetic field at this location?
38.2 μT (0.957×10^−3 V)(0.080 s) / 50π(0.113 m)^2
Doubling both charges changes the potential energy for a pair of point charges by a factor of
4
The arrangement shown is composed of four 6.0 mF capacitors. What is the capacitance of the combination?
4.5 mF
Chelsea touches the terminals of a battery with an emf of 127.4 V that can supply a maximum power of 7.10 W. If the resistance between the points where she contacts the batteries is 1.00 kΩ, how much current passes through her? Assume the internal resistance of the battery is negligible.
55.7 mA 7.1 W / 127.4 V
Two carbon cylinders have radii 2r and r, and the first has length 2L, while the second has length L. What is the resistance of the first if the resistance of the second is 12 Ω?
6 Ω
The magnetic field inside a solenoid having 100 turns per cm and a current of 5.0 A is
6.3 × 10−2 T.
Module 1 Check Your Understanding: Electric Forces and Fields
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Module 2 Check Your Understanding
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Module 3 Check Your Understanding
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Module 4 Check Your Understanding: Magnetic Forces and Fields
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Module 4 Homework: Magnetic Forces and Fields
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Module 5 Check Your Understanding: Electromagnetic Induction
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Module 5 Homework: Electromagnetic Induction
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A pair of parallel conducting plates have potentials of −17 V and 55 V, respectively. An electron is ejected from the plate at potential −17 V and travels to the plate at 55 V. What is the change in the electron's potential energy as it makes this journey?
-1.2 × 10−17J
A thin spherical shell of radius 20.0 cm has 5.0 µC of charge uniformly distributed over its surface. What is the electric field 10.0 cm from the center of the sphere?
0
Point P is midway between two long, straight, parallel wires that run north-south in a horizontal plane. The distance between the wires is 2.90 cm. Each wire carries a current of 3.30 A toward the north. Find the magnetic field at point P.
0
Three point charges, q1 = 2.0 μC, q2 = 2.0 μC, and q3 = −1.0 μC, are located at the vertices of an equilateral triangle of side length 30 cm. What is the potential energy of this arrangement?
0
In an electric motor, a coil with 119 turns of radius 2.60 cm can rotate between the poles of a magnet. The magnetic field magnitude is 0.200 T. When the current through the coil is 51.8 mA, what is the maximum torque that the motor can deliver?
0.00262 N·m 119(0.0518 A)π(0.0260 cm)^2(0.200 T)
Each atom in a sample of lithium (Z=3, atomic mass 6.941u) has one electron removed. If a charge of magnitude 1.0 mC was collected in this way, what is the mass of the lithium sample?
0.072 µ
A 22 μF capacitor is charged to 100 V. What is the energy stored in the capacitor?
0.11 J
A 6.0 Ω resistor and a 3.0 Ω resistor are connected in series to a 1.5 V battery of negligible internal resistance. What is the current in the 3.0 Ω resistor?
0.17 A
A wire bearing current of 1.25 A crosses a region in which there is a uniform B field of magnitude 1.0 T in the +y direction. The wire is inclined at an angle of 75 degrees above the +x direction, in the xy-plane. What is the magnitude of the force on the wire, if the magnetic field region spans 15 cm in the x direction?
0.19 N
In a circuit, three pieces of wire labeled A, B and C are joined at a common point D. If wire B carries 1.5 mA in a direction away from D, and wire C carries current 1.3 mA toward D, what does wire A carry?
0.2 mA toward D
A 300-turn coil of area 25 cm2 is placed in an 80 mT magnetic field. If the coil carries a current of 3.3 A, what is the magnitude of the maximum magnetic torque it could experience?
0.20 N·m
The magnetic field in a cyclotron is 0.50 T. What is the radius of the vacuum chamber for a maximum proton velocity of 1.0 × 107 m/s?
0.21 m
What is the current in a 25.0-W light bulb when connected to a 117-V emf?
0.214 A 25.0 W / 117 V
A copper wire of cross-sectional area 1.50 mm2 has a current of 6.20 A flowing along its length. What is the drift speed of the conduction electrons? Assume 1.30 conduction electrons per copper atom. The mass density of copper is 9.00 g/cm3 and its molar mass is 64.0 g/mol.
0.234 mm/s (6.20 A )(64.0 g/mol) / 1.30(9.00×106 g/m3)(6.022×1023 mol−1)(1.602×10−19 C)(1.50×10−6 m2)
The ions entering the mass spectrometer have the same charges. After being accelerated through a potential difference of 6.90 kV, a singly charged 12C+ ion moves in a circle of radius 17.4 cm in the magnetic field of a mass spectrometer. What is the magnitude of the field? Use these atomic mass values: 12C, 12.0 u; 14C, 14.0 u; 16O, 15.99 u. The conversion between atomic mass units and kilograms is 1 u = 1.66 × 10−27 kg.
0.238 T 1 / 0.174 m x SQRT(2(12.0 u)(1.66×10−27 kg/u)(6.90×103 V) / 1.602×10−19 C)
A current I = 40.0 A flows through a strip of metal. An electromagnet is switched on so that there is a uniform magnetic field. If the width of the strip is 1.60 cm, the magnetic field is 0.750 T, and the Hall voltage is measured to be 3.00 μV, what is the drift velocity of the carriers in the strip?
0.250 mm/s 3.00 ×10−6 V / (0.0160 m)(0.750 T)
A 12.0 V battery is connected across a 4.00-Ω resistor. If the current through the resistor is 2.80 A, what is the internal resistance of the battery?
0.286 Ω
What is the inductance of a coil that has an emf of 0.82 V induced in it while the current through it is changing at a rate of 2.0 A/s?
0.41 H
Crocodiles are thought to be able to detect changes in the flux due to Earth's magnetic field as they move their heads. Suppose a crocodile is initially facing north. The horizontal component of Earth's magnetic field is 42.0 μT. Consider a vertical, circular loop of neurons inside the crocodile's head with radius 11.7 cm. The loop is initially perpendicular to the horizontal component of Earth's magnetic field. The crocodile rotates its head 90.0° until it is facing east in a time interval of 4.30 s. What is the average emf induced around this loop of neurons?
0.420 μV (42.0×10^−6 T)π(0.117 m)^2 / 4.30 s
Some digital thermometers measure the current through a semiconductor to determine a patient's temperature. If a thermometer uses a germanium wire that has a resistance of R at 37.0°C (normal body temperature), what is its resistance at 46.4°C? The temperature coefficient for germanium is α = −0.0500 ª C.
0.530R 1/1+(−50.0×10−3°C−1)(46.4°C−37.0°C)
The magnetic field in a cyclotron used to produce radioactive tracers is 0.740 T. What must be the minimum radius of the dees if the maximum proton speed desired is 4.60 × 107 m/s? The mass of a proton is 1.673 × 10−27 kg.
0.649 m (1.673×10−27 kg)(4.60×107 m/s) / (1.602×10−19 C)(0.740 T)
How much energy due to Earth's magnetic field is present in 1.20 m3 of space near Earth's surface at a place where the field has magnitude 0.0420 mT?
0.842 mJ (0.0420×10^−3 T)^2(1.20 m3) / 2(4π×10^−7 T·m/A)
An ideal step-down transformer has a turns ratio of 1/108. An ac voltage of amplitude 170 V is applied to the primary. If the primary current amplitude is 8.60 mA, what is the secondary current amplitude?
0.929 A 108(8.60×10^−3 A)
After the switch is closed in a series LR circuit, what is the current when a time equal to four time constants has elapsed?
0.98 Imax
If R1 = 6 Ω, R2 = 8 Ω, R3 = 2 Ω, ε1 = 4 V, and ε2 = 14 V, what is the current in R2?
1 A up
A 20 turn coil of area 10 cm2 is placed in a magnetic field so that the normal to the coil's area is in the same direction as the field. If the magnitude of the field increases from 0.25 T to 0.35 T in 2.0 s, what is the average emf induced in the coil?
1.0 mV
A solenoid of radius 1.1 cm, carrying a current of 2.2 A, produces a magnetic field at its center of 0.28 T. How many turns per unit length does the solenoid have?
1.0 × 105 m−1
A 1.00 nC charge is placed on the x-axis at x = −1.00 m. A second 1.00 nC charge is placed on the x-axis at x = 1.00 m. A third charge of 1.00 nC is placed on the y-axis at y = −1.00 m. A fourth charge is place on the y-axis at y = 1.00 m. What is the fourth charge if the electric field at the origin is zero?
1.00 nC
What is the ratio of the electric energy that can be stored in a capacitor to the magnetic energy that can be stored in an inductor of the same size (i.e., the same volume). For the capacitor, assume that air is between the plates; the maximum electric field is then the breakdown strength of air, about 3.00 MV/m. The maximum magnetic field attainable in an ordinary solenoid with an air core is on the order of 10 T.
1.00×10−6 (4π×10−7 T·m/A)(8.854×10−12 C2/N·m2) x (3.00×10^6 V/m10 T)^2
An electron is fired through the space between two oppositely charged, parallel plates. The plates form a 2.00 cm long region with an electric field of 4000 N/C perpendicular to the electron's initial velocity. What is the change in velocity of the electron after it passes through the plates?
1.4 × 106 m/s
Find the force (magnitude and direction) exerted on an electron moving vertically upward at a speed of 2.0 × 107 m/s by a horizontal magnetic field of 0.50 T directed north.
1.6 × 10−12 N east
If electrons are accelerated from rest in an electron gun by sending them through a potential difference of 11.0 kV, what is the resulting kinetic energy of each electron?
1.76 × 10−15 J
A parallel plate capacitor, filled with air, has circular plates with a separation gap of 1.5 mm. If it is desired to store 12 mJ in this capacitor, what must the plate area be for a voltage of 1.5 kV?
1.8 m2
A square loop of wire with side 0.600 m carries a current of 4.20 A as shown in the side-view diagram. When there is no applied magnetic field, the plane of the loop is horizontal and the nonconducting, nonmagnetic spring (k = 550.0 N/m) is unstretched. A horizontal magnetic field of magnitude 1.10 T is now applied. At what angle θ is the wire loop's new equilibrium position? Assume the spring remains vertical because θ is small.
1.92° tan−1 x 4(4.20 A)(1.10 T) / 550.0 N/m
An ideal transformer supplies 100 kW of power to a 120 V circuit. If the input voltage is 10,000 V, what is the input current?
10 A
Two capacitors of values 6.00 mF and 9.00 mF are connected in series to a 30.0 V power supply. What is the resulting charge on the 6.00 mF capacitor?
108 mC
A coffee maker can be modeled as a heating element (resistance R) connected to the outlet voltage of 120.0 V (assumed to be dc). The heating element boils small amounts of water at a time as it brews the coffee. When bubbles of water vapor form, they carry liquid water up through the tubing. Because of this, the coffee maker boils 3.90% of the water that passes through it; the rest is heated to 100°C but remains liquid. Starting with water at 10.0°C, the coffee maker can brew 1.00 L of coffee in 6.10 min. Find the resistance R. The latent heat of vaporization of water is 2,256,000 J/kg and the specific heat of water is 4186 J/ (kg·K).
11.3 Ω (120.0 V)^2(366 s) / (1.00 kg)(4186 J/(kg·K))(90.0 K)+0.0390(1.00 kg)(2,256,000 J/kg)
A transformer with a primary coil of 1000 turns is used to step up the standard 193-V amplitude line voltage to a 227-V amplitude. How many turns are required in the secondary coil?
1176 (227.0 / 193.0) x 1000
In the circuit, switch S is opened at t = 0 after having been closed for a long time. At what time is energy stored in the inductor 0.100 times its initial value? Here, A = 8.30, B = 17.6, C = 0.340, and D = 13.2.
12.7 ms −0.340 H / 2(30.8 Ω) x ln 0.100
A length L0 of wire has a resistance of 32.0 Ω. The wire is uniformly stretched (i.e., the total volume of the wire is unchanged during the stretching) to four times its original length, or 4 L0. If a length L0 is now cut from the stretched wire, what is its resistance?
128 Ω
A series LR circuit includes a 9.0 V battery, a resistance of 0.50 Ω, and an inductance of 0.80 H. What is the current 2.0 s after the switch is closed?
13 A
An electromagnetic flowmeter is to be used to measure blood speed. A magnetic field of 0.175 T is applied across an artery of inner diameter 3.80 mm. The Hall voltage is measured to be 87.3 μV. What is the average speed of the blood flowing in the artery?
13.1 cm/s 87.3×10−6 V / (3.80×10−3 m)(0.175 T)
A mass spectrometer splits a beam of 10B and 11B singly charged ions having the same velocity by passing the beam through a uniform magnetic field. If the radius of the path for the 10B ions is 12.0 cm, what will be the radius for the 11B ions?
13.2 cm
A solenoid of length 5.20 cm and diameter 0.770 cm is wound with 353 turns per centimeter. If the current in the solenoid is decreasing at a rate of 34.7 A/s, what is the induced emf in the ENTIRE solenoid?
131.6 mV (353 cm)(5.20 cm)(7.17×10^−5 V)
A sample containing 12C, 16O, and an unknown isotope is analyzed in a mass spectrometer. As in the figure, the ions move around a semicircle before striking a photographic plate. The 12C+ and 16O+ ions are separated by 7.520 cm on the plate, and the unknown isotope strikes the plate 5.460 cm from the 12C+ ions. What is the mass of the unknown element?
14.8 u (1 + 5.460 / 48.6)^2 (12.0 u )
If 64 coulombs flow along a wire in 4.0 seconds, what is the average current?
16 A
A gold wire of 0.500 mm diameter has 7.30 × 1028 conduction electrons per cubic meter. If the drift speed is 7.10 μm/s, what is the current in the wire?
16.3 mA π/4(7.30×10^28 m−3)(1.602×10^−19 C)(0.000500 m)^2(7.10×10^−6 m/s)
A parallel plate capacitor has a paper dielectric having dielectric strength 8.0 kV/mm and dielectric constant 3.0. The plate area is 3000 cm2 and the plate separation is 0.50 mm. What is the capacitance?
16nF
A 1.7 H inductor has a current of 6.6 A flowing through it. The current reduces to 3.3 A over a period of 1.6 s. What is the average power the inductor supplies to the circuit as the current reduces?
17 W
Copper has 8.5 × 1028 current-carrying electrons per m3. A copper wire of radius 0.15 mm carries a current of 17 mA. What is the average drift velocity for the electrons?
18 × 10−6 m/s
A 2.00 nC charge is placed on the x-axis at x = −3.00 cm, another 2.00 nC charge is placed on the x-axis at x = 3.00 cm, and a third 2.00 nC charge is placed on the y-axis at y = 3.00 cm. What is the potential at the origin?
1800V
An external magnetic field is parallel to the central axis of a 41.0-turn coil of radius 5.70 cm. During an interval of 148 ms, the field changes from 0.190 T in one direction to 0.270 T in the opposite direction. The resistance of the coil is 68.0 Ω. What is the average induced current in the coil during this interval?
19.1 mA 41.0(0.270 T −(−0.190 T))(0.0570 m)^2 / (68.0 Ω)(0.148 s)
Two circuits are constructed using identical, ideal batteries (emf = ε) and identical incandescent lightbulbs (resistance = R). If each bulb in circuit 1 dissipates 4.90 W of power, how much power does each bulb in circuit 2 dissipate? Ignore changes in the resistance of the bulbs due to temperature changes.
19.6 W 4(4.90 W)
A 2.0 Ω resistor is connected across a 6.0 V power supply. An ammeter with internal resistance of 1.0 Ω is used to measure the current in this circuit. What is the ammeter reading?
2.0 A
A flat coil has a maximum flux of 4.0 × 10-3 T·m2 through it, with its area perpendicular to a uniform magnetic field. When the coil is rotated 60° (so that its normal makes a 60° angle with the field), what is the flux through it?
2.0 × 10-3 T·m2
Three charges are located along a horizontal straight line. The charge on the left has a force of 6.00 N on it to the left. The charge in the middle has a force on it of 4.00 N to the right. What is the force on the charge on the right?
2.00 N to the right
In the circuit shown, assume the battery emf is 21.9 V, R = 1.00 MΩ, and C = 1.80 μF. The switch is closed at t = 0. If the capacitor is initially discharged, then at what time t will the voltage across the capacitor be 15.0 V?
2.08 s −(1.00 MΩ)(1.80 μF)ln(1 − 15.0 / 21.9)
The current in a 0.0800-H solenoid increases from 20.2 mA to 160.6 mA in 5.20 s. Find the average emf in the solenoid during that time interval.
2.16 mV (0.0800 H) x (160.6−20.2)×10−3 / 5.20 s
A charged particle enters a region of uniform magnetic field at a speed of 2.8 × 104 m/s, at an angle of 37 degrees relative to the magnetic field direction. What will be the magnitude of the component of the particle's velocity that is parallel to the magnetic field while it is in this region?
2.2 × 104 m/s
A 3.7 pC charge experiences a force of 8.1 × 10-7 N in an electric field. What is the magnitude of the electric field?
2.2 × 105 N/C
The armature of an ac generator is a circular coil with 50 turns and radius 3.90 cm. When the armature rotates at 350.0 rev/min, the amplitude of the emf in the coil is 20.0 V. What is the magnitude of the magnetic field (assumed to be uniform)?
2.28 T 20.0 V / (350.0 rev/min)(2π rad/rev)(1/60 min/s)(50)π(0.0390 m)^2
The electron orbiting the proton in the hydrogen atom is at a distance of 5.3 × 10-9 m. What is the ratio of the electric force to the gravitational force between these particles? (The mass of the proton is 1.67 × 10-27 kg and the mass of the electron is 9.11 × 10-31 kg.)
2.3 × 1039
What is the total electric flux through a closed surface containing a 2.0 µC charge?
2.3 × 105 N·m2/C
A 15.3-Ω resistor has a potential difference of 36.7 V across it. What current flows through the resistor?
2.40 A 36.7 V / 15.3 Ω
Find the magnetic force exerted on a proton moving east at a speed of 4.40 × 106 m/s by a horizontal magnetic field of 3.50 T directed north. If the force is upward, enter a positive value.
2.47×10−12 N up (1.602×10^−19 C)((4.40×10^6 m/s east)×3.50 T north)
Two copper wires, one 1.60 times the diameter of the other, have the same current flowing through them. If the thinner wire has a drift speed v1 and the thicker wire has a drift speed v2, what is the relationship between the drift speeds?
2.56v2 (1.60 / 1) ^2
If 50.0 m of nichrome wire is to have a resistance of 10.0 Ω at 20°C, what diameter wire should be used?
2.62 mm 2 x (SQRT(108×10−8 Ω·m)(50.0 m) / π(10.0 Ω))
A uniform magnetic field points vertically upward; its magnitude is 0.470 T. An electron with kinetic energy 6.80 × 10−18 J is moving horizontally eastward in this field. What is the magnetic force acting on it?
2.91×10−13 N north −(1.602×10−19 C) (SQRT(2(6.80×10^−18 J / 9.109×10^−31) x (0.470 T up)
Two point charges are on the x-axis. One charge, q1 = 10.0 nC, is located at the origin, and the other charge, q2 = 18.0 nC, is located at x = 9.00 m. What is the force on q2?
20.0 nN in the positive x-direction
A 3.6 μC charge is moved from a position where its electric potential energy is 7.2 mJ to a position where its potential energy is 1.8 mJ. What is the potential at the first position?
2000V
A conducting sphere of radius 20 cm is charged to a potential of 1.0 × 106 volts. What is the charge on its surface?
22 μC
An electron moves with speed 2.00 × 105 m/s in a 1.90-T uniform magnetic field. At one instant, the electron is moving due west and experiences an upward magnetic force of 3.30 × 10−14 N. Which of the following is the correct direction of magnetic field? (If there is more than one possible answer, find all the possibilities.)
23.0° N of E 23.0° S of W 32.8° S of W
Suppose you wanted to use Earth's magnetic field to make an ac generator at a location where the magnitude of the field is 0.05000 mT. Your coil has 1002 turns and a radius of 5.400 cm. At what angular velocity would you have to rotate it in order to generate an emf of amplitude 1.100 V?
2397 rad/s 1.100 V / 1002(0.05000×10^−3 T)π (0.05400 m)^2
The primary coil of a transformer has 419 turns; the secondary coil has 1000 turns. An alternating current is sent through the primary coil. The emf in the primary is of amplitude 10.7 V. What is the emf amplitude in the secondary?
25.5 V 1000 / 419(10.7 V)
Three resistors, R1 = 9.0 Ω, R2 = 3.0 Ω, and R3 = 1.0 Ω, are connected in parallel to a 9.0 V battery. What is the power dissipated by R2?
27 W
An air-filled 3.0 nF capacitor is charged to 8.0 V. If the plate separation is 100 μm, what is the energy density in the electric field between the plates?
28 mJ/m3
The intrinsic magnetic dipole moment of the electron has magnitude 9.30 × 10−24 A⋅m2. What is the maximum torque on an electron due to its intrinsic dipole moment in a 0.340-T magnetic field?
3.16 × 10−24 N·m 1(9.30× 10^−24 A·m2)(0.340 T)
A sodium ion (Na+) moves along with the blood in an artery of diameter 1.00 cm. The ion has mass 22.99 u and charge +e. The maximum blood speed in the artery is 5.95 m/s. Earth's magnetic field in the location of the patient has magnitude 33.6 μT. What is the greatest possible magnetic force on the sodium ion due to Earth's field?
3.20×10−23 N (1.602×10^−19 C)(5.95 m/s)(33.6×10^−6 T)
A solenoid is made of 279 turns of wire, wrapped around a hollow cylinder of radius 0.70 cm and length 4.50 cm. What is the self-inductance of the solenoid?
3.35×10−4 H (4π×10^−7H/m)(279)^2π(0.00700 m)^2 / 0.0450 m
A horizontally projected beam of electrons travels at 55 km/s into the space between two horizontal, parallel plates. The plates are separated by 7.4 cm, and they are 12 cm long. The uniform electric field between the plates is 7.2 mV/m upward. If the beam enters the region at a height of 3.7 cm above the lower plate, at what height above the lower plate does the beam exit the region? The electron mass is 9.11 × 10-31 kg.
3.4 cm
Several electrons move at speed 7.10 × 105 m/s in a uniform magnetic field with magnitude B = 0.300 T directed downward.
3.41×10−14 N out of the page −(1.602×10^−19 C)((7.10×10^5 m/s right)×(0.300 T down))
A point charge of 3.0 µC is located on the y-axis at y = 4.0 m, and another point charge of 6.0 µC is located on the x-axis at x = 5.0 m. What is the magnitude of the electric field at the position (5.0 m, 4.0 m)?
3.5 × 103 N/C
Kieran measures the magnetic field of an electron beam. The beam strength is such that 2.80 × 1011 electrons pass a point every 1.30 μs. What magnetic field does Kieran measure at a distance of 1.90 cm from the beam center?
3.63×10−7 T (4×10−7 T·m/A)(2.80×10^11)(1.602×10^−19 C) / 2π (0.0190 m)(1.30×10^−6 s)
A solenoid of length 0.266 m and radius 2.00 cm has 244 turns of wire. What is the magnitude of the magnetic field well inside the solenoid when there is a current of 3.20 A in the wire?
3.69 mT (4π×10−7 T·m/A)(244)(3.20 A) / 0.266 m
If a 91.9-V emf is connected to the terminals A and B and the current in the 4.00-Ω resistor is 17.0 A, what is the value of the unknown resistor R?
3.73 Ω (1 / 1.4059 Ω − 1 / 2.00 Ω)^−1 − 1.00 Ω
A charged particle having electric charge Q = 4.0e enters a region of magnetic field 1.2 T at an angle of θ relative to the magnetic field direction. If the speed of the particle upon entering the region is 2.8 × 104 m/s, and the magnitude of the force on it is 1.3 × 10-14 N, which of the following could be the angle θ?
37o
The electric potential at a distance d from a point charge is V. At a distance d', the potential is 2V. What is the ratio of the electric field at d' to that at d?
4
In an ion accelerator, 1.25×1013 helium-4 nuclei (charge +2e) per second strike a target. What is the magnitude of the beam current?
4.00 μA 2(1.602×10−19 C)(1.25×1013 s−1)
A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-tenth its maximum value?
4.61 s
Two immersion heaters, A and B, are both connected to a 120.0-V supply. Heater A can raise the temperature of 1.00 L of water from 20.0°C to 90.0°C in 5.80 min, whereas heater B can raise the temperature of 4.20 L of water from 20.0°C to 90.0°C in 5.00 min. What is the ratio of the resistance of heater A to the resistance of heater B?
4.87 (5.80)(4.20) / (5.00)(1.00)
An LR circuit is prepared for an experiment, initially with its switch open. The time constant is that time after switch closure at which the energy stored in the inductor reaches approximately what percentage of its final value?
40%
An electromagnet is made by inserting a soft iron core into a solenoid. The solenoid has 1800 turns, radius 2.00 cm, and length 20.9 cm. When 2.00 A of current flows through the solenoid, the magnetic field inside the iron core has magnitude 0.890 T. What is the relative permeability κB of the iron core?
41.1 (0.890 T)(0.209 m) / (4π×10^−7 T·m/A)(1800)(2.00 A)
If a chandelier has a label stating 120 V, 3.70 A, what is its power rating?
444 W (3.70 A)(120 V)
Find the maximum current that a fully charged D-cell can supply—if only briefly—such that its terminal voltage is at least 1.30 V. Assume an emf of 1.80 V and an internal resistance of 0.100 Ω.
5.00 A 1.80 V−1.30 V / 0.100 Ω
Reducing the magnetic field to 71% of its previous value changes the magnetic energy density in the field to _______% of its original value.
50
How much work are the batteries in the circuit doing in every 10.0-s time interval?
51.2 J (3.20 V)^2(10.0 s) / 2.00 Ω
A solenoid has 5270 turns per meter and radius 3.30 cm. The magnetic field inside has magnitude 0.340 T. What is the current in the solenoid?
51.3 A 0.340 T / (4π×10^−7 T·m/A)(5270 m−1)
A cyclotron with a magnetic field of 1.2 T is used to accelerate protons. How long does it take for the protons to make one complete trip around the cyclotron at a radius of 25 cm?
55 ns
How much charge is on a conducting sphere of diameter 20 μm if its surface potential is 50 mV?
56 × 10−18 C
Many home heating systems operate by pumping hot water through radiator pipes. The flow of the water to different "zones" in the house is controlled by zone valves that open in response to thermostats. The opening and closing of a zone valve is commonly performed by a wax actuator, as shown in the diagram. When the thermostat signals the valve to open, a dc voltage of 28.2 V is applied across a heating element (resistance R = 201 Ω) in the actuator. As the wax melts, it expands and pushes a cylindrical rod (radius 2.00 mm) out a distance 1.00 cm to open the zone switch. The actuator contains 3.60 mL of solid wax of density 0.900 g/cm3 at room temperature (20.0°C). The specific heat of the wax is 0.800 J/(g·°C), its latent heat of fusion is 60.0 J/g, and its melting point is 90.0°C. When the wax melts its volume expands by 15.0%. How long does it take until the valve is fully open?
57.3 s (227 J)(201 Ω) / (28.2 V) ^2
Several electrons move at speed 6.10 × 105 m/s in a uniform magnetic field with magnitude B = 0.730 T directed downward. Find the magnetic force on the electron at point c. Enter a positive value if the direction of magnetic force is out of the page and enter a negative value if the direction of magnetic force is in to the page.
6.18×10−14 N (1.602×10−19 C)(6.10×105 m/s)(0.730 T)sin 120.0°
A uniform magnetic field points north; its magnitude is 1.90 T. A proton with kinetic energy 3.80 × 10−13 J is moving vertically downward in this field. What is the magnetic force acting on it? If the force is toward east, enter a positive value.
6.49×10−12 N east (1.602×10−19 C)(SQRT(2(3.80×10−13 J) / 1.673×10−27)×(1.90 T north))
A thin metallic spherical shell of radius 50 cm has a total charge of 4.0 µC placed on it. At the center of the shell is placed a point charge of 2.00 µC. What is the electric field at a distance of 90 cm from the center of the spherical shell?
6.7 × 104 N/C outward
A battery charger delivers a current of 4.80 A for 3.90 h to a 12.0-V storage battery. What is the total charge that passes through the battery in that time?
6.74×10^4 C (4.80 A)(3.90 h)(3600 s/h)=6.74×104 C.
The resistance of a wire is 18.4 Ω at 15.0°C and 27.2 Ω at 85.0°C. What is the temperature coefficient of resistance of the material?
6.83×10−3°C−1 (1 / 85.0°C−15.0°C) (27.2 Ω / 18.4 Ω - 1)
A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. What is the magnetic flux swept through per second by the rod?
60 mT·m2
The magnetic field between the poles of an electromagnet is 3.10 T. A coil of wire is placed in this region so that the field is parallel to the axis of the coil. The coil has electrical resistance 21.3 Ω and radius 1.80 cm. When the current supply to the electromagnet is shut off, the total charge that flows through the coil is 9.00 mC. How many turns are there in the coil?
61 (21.3 Ω)(9.00×10^−3 C) / (3.10 T)π(0.0180 m)^2
A person can be killed if a current as small as 55.9 mA passes near the heart. An electrician is working on a humid day with hands damp from perspiration. Suppose his resistance from one hand to the other is 1.10 kΩ and he is touching two wires, one with each hand. What potential difference between the two wires would cause a 55.9-mA current from one hand to the other?
61.5 V (55.9 mA)(1.10 kΩ)
A current of 10.0 A is carried by a copper wire of diameter 1.60 mm. If the density of the conduction electrons is 8.47 × 1028 m−3, how long does it take for a conduction electron to move 1.50 m along the wire?
68.2 min (π(8.47×1028 m−3)(1.602×10−19 C)(0.00160m/2)2 (1.50m) / 10.0 A)(1min / 60sec)
A circular conducting loop with radius 4.20 cm is placed in a uniform magnetic field of 0.650 T with the plane of the coil perpendicular to the magnetic field as shown. The magnetic field decreases to 0.300 T in a time interval of 28.0 ms. What is the average induced emf in the loop during this interval?
69.3 mV - (0.300−0.650) T π(0.0420 m)^2 / 0.0280 s
A solenoid of length 5.20 cm and diameter 0.770 cm is wound with 353 turns per centimeter. If the current in the solenoid is decreasing at a rate of 34.7 A/s, what is the induced emf in ONE of the windings?
7.17×10−5 V −1/4(4π×10^−7 H/m)π(353 cm−1)(10^2 cm/m)(0.00770 m)^2(−34.7 A/s)
The magnetic field between the poles of a magnet has magnitude 0.510 T. A circular loop of wire with radius 3.50 cm is placed between the poles so the field makes an angle of 22.0° with the plane of the loop. What is the magnetic flux through the loop?
7.35×10−4 Wb (0.510 T)π(0.0350 m)^2cos 68.0°
A coil of 150 turns of wire is in the form of a circle, carries a current of 63 mA, and sits in the center of a region of uniform magnetic field of strength 1.5 T. The torque on the coil has a maximum value of 0.25 N·m. What is the radius of the coils?
7.5 cm
A potential difference is applied between the electrodes in a gas discharge tube. In 1.00 s, 2.45 × 1016 electrons and 2.35 × 1016 singly charged positive ions move in opposite directions through a surface perpendicular to the length of the tube. What is the magnitude of the current in the tube?
7.69 mA (2.45×1016+2.35×1016)(1.602×10−19 C) / 1.00s
A strip of doped silicon 260.0 μm wide contains 8.80 × 1022 conduction electrons per cubic meter and an insignificant number of holes. When the strip carries a current of 116 μA, the drift speed of the electrons is 42.1 cm/s. What is the thickness of the strip?
75.2 μm 116×10−6 A / (8.80×1022 m−3)(1.602×10−19 C)(260.0×10−6 m)(0.421 m/s)
The armature of an ac generator is a rectangular coil 2.00 cm by 6.00 cm with 80 turns. It is immersed in a uniform magnetic field of magnitude 0.650 T. If the amplitude of the emf in the coil is 49.0 V, at what angular speed is the armature rotating?
785 rad/s 49.0 V / (80)(0.650 T)(0.0200 m)(0.0600 m)
A series LR circuit consists of a battery, resistor, inductor and a switch. When the switch is closed the circuit has a time constant of 8.0 s. If the resistance and inductance of the circuit are both doubled, what is the resulting time constant?
8.0 s
The magnetic field in a hospital's cyclotron is 0.110 T. Find the magnitude of the magnetic force on a proton with speed 4.70 × 107 m/s moving in a plane perpendicular to the field.
8.28×10−13 N (1.602×10^−19 C)(4.70×10^7 m/s)(0.110 T)
An infinitely long wire with a uniform linear charge distribution has a charge per unit length of 2.3 × 10-6 C/m. What is the magnitude of the electric field at a perpendicular distance of 0.50 m from the wire?
8.3 × 104 N/C
A current balance is a device to measure magnetic forces. It is constructed from two parallel coils, each with an average radius of 12.5 cm. The lower coil rests on a balance; it has 20 turns and carries a constant current of 3.90 A. The upper coil, suspended 0.314 cm above the lower coil, has 50 turns and a current that can be varied. The reading of the balance changes as the magnetic force on the lower coil changes. What current is needed in the upper coil to exert a force of 1.70 N on the bottom coil?
8.71A 2π(0.314 cm)(1.70 N) / (4π×10^−7 T·m/A)(3.90 A)(500π cm)
The word electric comes from the Greek word for
Amber
If the magnetic field from a long, straight, current-carrying wire has a magnitude B0 at a distance d, what is the magnitude of the field at a distance 2d?
B0/2
Consider a point charge and an imaginary spherical surface surrounding it. Which of the following situations would bring about a change in the electrical flux through the surface?
Bringing a second point charge nearby, and within the surface
A hollow copper pipe is held vertically, and a magnet is dropped down the pipe. The magnet is oriented with its north pole down. What direction do the eddy currents flow as viewed from above the pipe? If copper bar of approximately the same size and weight as the magnet is dropped down the tube instead, will it fall faster or slower than the magnet?
CW above the magnet and CCW below the magnet; copper bar will fall slower
Which of the following correctly indicates the direction and relative magnitude of the magnetic field at each of the points A-F?
Choice A F points to the right C, arrow to right, arrow to right
The temperature at which ferromagnetic materials transform into paramagnetic materials is called the
Curie temperature.
When the voltage across a resistor is decreased by 50%, what happens to the power dissipated?
It decreases by 75%.
If the rotation rate of a generator coil is doubled, what happens to the peak emf?
It doubles.
When measuring the Hall voltage, what happens to the reading when the current is increased 20%?
It increases 20%.
A metal rod of length L moves with velocity v, perpendicular to its length, in a magnetic field B, which is perpendicular to both the rod and its velocity. If the length of the rod is doubled, what happens to the electric field in the rod?
It stays the same.
Two wire loops are side by side, as shown. The current I1 in loop 1 is supplied by an external source (not shown) and is clockwise as viewed from the right. While I1 is constant, in which direction does the current flow in loop 2 as viewed from the right?
No current is induced in loop 2
A coiled loop of wire is in the field region between the poles of an electromagnet, with the axis of the coil aligned with the magnetic field. Which of the following things would NOT result in an induced EMF in the coil?
None of these choices will work.
Which of the following correctly represents the magnetic field lines for two identical bar magnets in the given configuration?
Option B Lines run through magnets Inside lines point right
A bar magnet is initially far from a circular loop of wire. The magnet is moved at constant speed along the axis of the loop. It moves toward the loop, proceeds to pass through it, and then continues until it is far away on the right side of the loop. Which of the following is the correct graph for the current in the loop as a function of the position of the bar magnet. Take the current to be positive when it is counterclockwise as viewed from the left.
Option B down, then up at 2
In the given figure, a square metal loop of side 4.00 cm and resistance 5.00 Ω moves to the right (+x-direction) into, through, and out of a 6.00-cm-wide region of uniform magnetic field perpendicular to the plane of the loop. The magnetic field in the region is 0.250 T. At t = 0, the loop just begins to enter the region of magnetic field. The loop moves at a constant 1.00 cm/s. Which of the following correctly plots the graph of the external force applied to the loop (to keep it moving at constant velocity) as a function of time?
Option C 2 squares at 200
Which of the following correctly represents the magnetic field lines for two identical bar magnets in the given configuration?
Option D Circular arrows move to the right Inside arrows point left Lines through magnet
In the given figure, a square metal loop of side 4.00 cm and resistance 5.00 Ω moves to the right (+x-direction) into, through, and out of a 6.00-cm-wide region of uniform magnetic field perpendicular to the plane of the loop. The magnetic field in the region is 0.250 T. At t = 0, the loop just begins to enter the region of magnetic field. The loop moves at a constant 10.0 cm/s. Which of the following correctly plots the graph of the current in the loop as a function of time? Take counterclockwise current to be positive.
Option D lines 200, 0, -200, 0
Two wire loops are side by side, as shown. The current I1I1 in loop 1 is supplied by an external source (not shown) and is clockwise as viewed from the right. While I1I1 is increasing, what is the direction of the magnetic force exerted on loop 2?
To the right
The SI unit for electric potential energy is equivalent to
VC
The SI unit H (the henry) is equal to a
V·s/A.
In a velocity selector for ions, when the electric field is increased by 50%, what change in the magnetic field is necessary to select the same speed as before?
a 50% increase
The south end of a bar magnet is pushed downward toward a wire loop in the plane of the paper. In which direction is the induced current, and which way is the induced magnetic field?
clockwise, into the paper
The strings of an electric guitar are made of ferromagnetic metal. The pickup consists of two components. A magnet causes the part of the string near it to be magnetized. The vibrations of the string near the pickup coil produce an induced emf in the coil. The electrical signal in the coil is then amplified and used to drive the speakers. In the figure, the string is moving away from the coil. What is the direction of the induced current in the coil?
counterclockwise as viewed from the left
A conducting rod is free to slide on horizontal metal rails without friction. At a particular time, it is sliding with velocity v to the right, as shown. A uniform magnetic field B is directed into the page, the separation of the rails is L, and the resistance of the circuit is R. In what direction in the diagram is the current flowing in the resistor at this time?
down
A negative ion is moving east near the equator where the Earth's magnetic field is horizontal to the north. The direction of the magnetic force on the ion is
down
A proton and electron, each travelling with the same velocity, enter a region of uniform magnetic field. They experience
forces equal in magnitude, but opposite in direction.
In order to protect a delicate electronic component in a circuit from large currents, a fuse should be placed
in series with the component.
An air-filled parallel plate capacitor is attached to a voltage source and charged. The voltage source is removed, and then the plates are separated to double their previous distance. What happens to the electric field between the plates when the plates are separated?
it stays the same
In ancient times permanent magnets were known to the Greeks. These magnets were chunks of iron ore now called magnetite. What is the older name for this material?
lodestone
If the number of turns on a transformer input is greater than the number on the output, then the transformer
outputs less voltage than at the input.
Four point charges are located at the corners of a square, 1.00 m by 1.00 m. On each of two diagonally opposite corners are 1.00 µC charges. On each of the other two corners are −1.00 µC charges. What is the direction of the force on each charge?
positive and negative charges both toward the center of the square
Two large equipotential surfaces are flat and parallel, and they are separated by a relatively small distance compared to their size. One surface is at 25 V and the other is at 33 V. The surfaces are 1.25 cm apart. Assuming the electric field is uniform between the surfaces, what is the direction of the electric field midway between them?
the field is perpendicular to the surfaces and points toward the 25 V surface
If helium nuclei and protons are each accelerated from rest through the same potential difference V, which gets the greatest kinetic energy and by what factor is it greater?
the helium nuclei get twice as much kinetic energy.
In diagrams of magnetic fields, the symbol "×" is used to represent
the magnetic field going into the paper.
The capacitance of a parallel plate capacitor changes when a dielectric is inserted between the plates. This is mainly due to
the polarizability of the material, which sets up an electric field opposite to the applied field, thus reducing the electric field strength in the region.
A capacitor in an RC circuit is charged, storing 1.25 mJ of energy. What is the time required to discharge this capacitor (say, to 1% of its initial charge), as compared to the time required to discharge (to 1%) an identical capacitor in an identical RC circuit which has stored 2.5 mJ of energy instead?
the same time
A 3.0 cm section of a horizontal wire, carrying a 6.7 A current from east to west, is placed in a horizontal north-to-south 0.42 T uniform magnetic field in the lab. In what direction is the magnetic force on the 3.0 cm section?
up
An ohm is equivalent to which of the following?
volt/ampere
The symbols ρ, λ, and σ are used to represent, respectively, the charge density per unit
volume, length, and area.
When an object is polarized, it
will have a separation of positive and negative charge.
The potential differences around a loop ABCA in a circuit (starting at A and going around the loop back to A) are VAB = 10 V, VBC = 6.0 V, and VCA. What is VCA?
−16 V
