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physics
electricity and magnetism
Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions
The (United States) National Electric Code, which sets maximum safe currents for insulated copper wires of various diameters, is given (in part) in the table. Plot the safe current density as a function of diameter. Which wire gauge has the maximum safe current density? ("Gauge" is a way of
A beam contains 2.0 x 108 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.0 x 105 m/s. What are the(a) Magnitude and(b) Direction of the current density J?(c) What additional quantity do you need to calculate the total current i in this ion beam?
A certain cylindrical wire carries current. We draw a circle of radius r around its central axis in Figure (a) to determine the current i within the circle. Figure (b) shows current i as a function of r2. The vertical scale is set by is = 4.0 mA, and the horizontal scale is set by r2s = 4.0
How long does it take electrons to get from a car battery to the starting motor? Assume the current is 300 A and the electrons travel through a copper wire with cross-sectional area 0.21 cm2 and length 0.85 m. The number of charge carriers per unit volume is 8.49 x 1028 m-3.
Near Earth, the density of protons in the solar wind (a stream of particles from the Sun) is 8.70 cm-3, and their speed is 470 km/s.(a) Find the current density of these protons.(b) If Earth's magnetic field did not deflect the protons, what total current would Earth receive?
The magnitude J(r) of the current density in a certain cylindrical wire is given as a function of radial distance from the center of the wire's cross section as J(r) = Br, where r is in meters, J is in amperes per square meter, and B = 2.00 x 105 A/m3. This function applies out to the wire's radius
The magnitude J of the current density in a certain wire with a circular cross section of radius R = 2.00 mm is given by J = (3.00 x 108) r2, with J in amperes per square meter and radial distance r in meters. What is the current through the outer section bounded by r = 0.900R and r = R?
What is the current in a wire of radius R = 3.40A mm if the magnitude of the current density is given by(a) J a = J0r and(b) J b = J0 (1 – r/R), in which r is the radial distance and J0 = 5.50 x 10 4 A/m2?(c) Which function maximizes the current density near the wire's surface?
Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 60.0 A. The resistance per unit length is to be 0.150Ω/km. The densities of copper and aluminum are 8960 and 2600 kg/m3, respectively. Compute(a) The magnitude J of the current density
A wire of Nichrome (a nickel-chromium-iron alloy commonly used in heating elements) is 1.0 m long and 1.0 mm2 in cross-sectional area. It carries a current of 4.0 A when a 2.0 V potential difference is applied between its ends. Calculate the conductivity σ of Nichrome.
A wire 4.00m long and 6.00mm in diameter has a resistance of 15.0mΩ. A potential difference of 23.0 V is applied between the ends.(a) What is the current in the wire?(b) What is the magnitude of the current density?(c) Calculate the resistivity of the wire material.(d) Using Table 26-1, identify
What is the resistivity of a wire of 1.0 mm diameter, 2.0 m length, and 50mΩ resistance?
A certain wire has a resistance R. What is the resistance of a second wire, made of the same material, that is half as long and has half the diameter?
A coil is formed by winding 250 turns of insulated 16- gauge copper wire (diameter = 1.3 mm) in a single layer on a cylindrical form of radius 17 cm. What is the resistance of the coil? Neglect the thickness of the insulation. (Use Table 26-1)
A human being can be electrocuted if a current as small as 50 mA passes near the heart. An electrician working with sweaty hands makes good contact with the two conductors he is holding, one in each hand. If his resistance is 2000Ω, what might the fatal voltage be?
A wire with a resistance of 6.0Ω is drawn out through a die so that its new length is three times its original length. Find the resistance of the longer wire, assuming that the resistivity and density of the material are unchanged.
Figure a gives the magnitude E(x) of the electric fields that have been set up by a battery along a resistive rod of length 9.00 mm (Figure b). The vertical scale is set by Es = 4.00 x 103V/m. The rod consists of three sections of the same material but with different radii. (The schematic diagram
Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1.0 mm. Conductor B is a hollow tube of outside diameter 2.0 mm and inside diameter 1.0 mm. What is the resistance ratio RA/RB measured between their ends?
Figure gives the electric potential V(x) along a copper wire carrying uniform current, from a point of higher potential Vs = 12.0μV at x = 0 to a point of zero potential at xs = 3.00 m. The wire has a radius of 2.00 mm. What is the current in the wire?
A common flashlight bulb is rated at 0.30 A and 2.9 V (the values of the current and voltage under operating conditions). If the resistance of the tungsten bulb filament at room temperature (20°C) is 1.1Ω, what is the temperature of the filament when the bulb is on?
Kiting during a storm the legend that Benjamin Franklin flew a kite as a storm approached is only a legend he was neither stupid nor suicidal. Suppose a kite string of radius 2.00 mm extends directly upward by 0.800 km and is coated with a 0.500 mm layer of water having resistivity l50Ω ∙ m. If
A potential difference of 3.00nV is set up across a 2.00 cm length of copper wire that has a radius of 2.00 mm. How much charge drifts through a cross section in 3.00 ms?
In Figure a, a 9.00 V battery is connected to a resistive strip that consists of three sections with the same cross sectional areas but different conductivities. Figure b gives the electric potential V(x) versus position x along the strip. The horizontal scale is set by x = 8.00 mm. Section 3 has
When 115 V is applied across a wire that is 10 m long and has a 0.30 mm radius, the magnitude of the current density is 1.4 x 104 A/m2. Find the resistivity of the wire.
Earth's lower atmosphere contains negative and positive ions that are produced by radioactive elements in the soil and cosmic rays from space. In a certain region, the atmospheric electric field strength is 120 Y lm and the field is directed vertically down. This field causes singly charged
A block in the shape of a rectangular solid has a cross sectional area of 3.50 cm2 across its width, a front-to-rear length of 15.8 cm, and a resistance of 935 Ω. The block's material contains 5.33 x 1022 conduction electrons/m3. A potential difference of 35.8 V is maintained between its front
If the gauge number of a wire is increased by 6, the diameter is halved; if a gauge number is increased by 1, the diameter decreases by the factor 21/6 (see the table in Problem 6). Knowing this, and knowing that 1000ft of 10-gauge copper wire has a resistance of approximately 1.00Ω, estimates
An electrical cable consists of 125 strands of fine wire, each having 2.65μΩ resistance. The same potential difference is applied between the ends of all the strands and results in a total current of 0.750 A.(a) What is the current in each strand?(b) What is the applied potential difference?(c)
Swimming during a storm figure shows a swimmer at distance D = 35.0 m from a lightning strike to the water, with current I = 78 kA. The water has resistivity 30 ?? ?? m, the width of the swimmer along a radial line from the strike is 0.70 m, and his resistance across that width is 4.00??O. Assume
In Figure current is set up through a truncated right circular cone of resistivity 731 ?? ?? m, left radius a = 2.00 mm, right radius b = 230 mm, and length L = 1.94 cm. Assume that the current density is uniform across any cross section taken perpendicular the length. What is the resistance of the
Figure shows wire section 1 of diameter D1 = 4.00R and wire section 2 of diameter D2 = 2.00R, connected by u tapered section. The wire is copper and carries a current. Assume that the current is uniformly distributed across any cross-sectional area through the wire's width. The electric potential
Show that, according to the free-electron model of electrical conduction in metals and classical physics, the resistivity of metals should be proportional to √T, where T is the temperature in Kelvin’s (See Eq. 19-31)
A student kept his 9.0 V 7.0 W radio turned on at full volume from 9:00 P.M. until 2:00 A.M. How much charge went through it?
A 120 Y potential difference is applied to a space heater whose resistance is 14 Ω when hot.(a) At what rate is electrical energy transferred to thermal energy?(b) What is the cost for 5.0 h at US$0.05/kW ∙ h?
In Figure a battery of potential difference V = 12V is connected to a resistive strip of resistance R = 6.0 ??. When an electron moves through the strip from one end to the other, (a) In which direction in the figure does the electron move? (b) How much work is done on the electron by the electric
An unknown resistor is connected between the terminals of a 3.00 V battery. Energy is dissipated in the resistor at the rate of 0.540 W. The same resistor is then connected between the terminals of a 1.50 V battery. At what rate is energy now dissipated?
Thermal energy is produced in a resistor at a rate of 100 W when the current is 3.00 A. What is the resistance?
A 1250 W radiant heater is constructed to operate at 115 V.(a) What is the current in the heater when the unit is operating?(b) What is the resistance of the heating coil?(c) How much thermal energy is produced in 1.0 h?
In Figure a, a 20?? resistor is connected to a battery. Figure b shows the increase of thermal energy Eth in the resistor as a function of time t. The vertical scale is set by Eth = 2.50mJ, and the horizontal scale is set by rs = 4.0 s. What is the electric potential across the battery?
A certain brand of hotdog cooker works by applying a potential difference of 120 V across opposite ends of a hot dog and allowing it to cook by means of the thermal energy produced. The current is 10.0 A, and the energy required to cook one hot dog is 60.0 kJ. If the rate at which energy is
Exploding shoes the rain-soaked shoes of a person may explode if ground current from nearby lightning vaporizes the water. The sudden conversion of water to water vapor causes a dramatic expansion that can rip apart shoes. Water has density 1000 kg/m3 and requires 333kJ/kg to be vaporized. If
A 120V potential difference is applied to a space heater that dissipates 500 W during operation. (a) What is its resistance during operation?(b) At what rate do electrons flow through any cross section of the heater element?
The current through the battery and resistors 1 and 2 in Figure (a) is 2.00 A. Energy is transferred from the current to thermal energy Eth in both resistors. Curves I and 2 in Figure (b) give that thermal energy Eth for resistors 1 and 2, respectively, as a function of time t. The vertical scale
A heating element is made by maintaining a potential difference of 75 .0 V across the length of a Ni chrome wire that has a 2.60 x 10-6 m2 cross section. Ni chrome has a resistivity of 5.00 x 10-7 Ω ∙ m.(a) If the element dissipates 5000 W what is its length?(b) If 100 V is used to obtain the
The current-density magnitude in a certain circular wire is J = (2.75 x 1010 A/m4) r2, where r is the radial distance out to the wire's radius of 3.00 mm. The potential applied to the wire (end to end) is 60.0 V. How much energy is converted to thermal energy in 1.00 h?
A 100 W lightbulb is plugged into a standard 120V outlet. (a) How much does it cost per 31 day month to leave the light turned on continuously? Assume electrical energy costs US$0.06/kW ∙ h.(b) What is the resistance of the bulb?(c) What is the current in the bulb?
A copper wire of cross-sectional area 2.00 x 10-6 m2 and length 4.00 m has a current of 2.00 A uniformly distributed across that area.(a) What is the magnitude of the electric field along the wire?(b) How much electrical energy is transferred to thermal energy in 30 min?
Wire C and wire D are made from different materials and have length Lc = LD = 1.0 m. The resistivity and diameter of wire C are 2.0 x 10-6 ?? ?? m and 1.00 mm, and those of wire D are 1.0 x 10-6 ?? ?? m and 0.50 mm. The wires are joined as shown in Figure and a current of 2.0 A is set up in them.
Figure shows a rod resistive material. The resistance per unit length of the rod increases in the positive direction of the x axis. At any position x along the rod, the resistance d R of a narrow (differential) section of width dx is given by d R = 5.00x dx, where d R is in ohms and x is in meters.
A steady beam of alpha particles (q = +2e) traveling with constant kinetic energy 20 MeV carries a current of 0.25μA.(a) If the beam is directed perpendicular to a flat surface, how many alpha particles strike the surface in 3.0 s?(b) At any instant, how many alpha particles are there in a given
The chocolate crumb mystery this story begins with Problem 56 in Chapter 23 and continues through Chapters 24 and 25. The chocolate crumb powder moved to the silo through a pipe of radius R with uniform speed v and uniform charge density p.(a) Find an expression for the current i (the rate at which
A 500 W heating unit is designed to operate with an applied potential difference of 115 V.(a) By what percentage will its heat output drop if the applied potential difference drops to 110 V? Assume no change in resistance.(b) If you took the variation of resistance with temperature into account,
A potential difference of 1.20 V will be applied to a 33.0 m length of 18-gauge copper wire (diameter = 0.0400 in.). Calculate(a) The current,(b) The magnitude of the current density,(c) The magnitude of the electric field within the wire, and(d) The rate at which thermal energy will appear in the
A Nichrome heater dissipates 500 W when the applied potential difference is 110 V and the wire temperature is 800°C. What would be the dissipation rate if the wire temperature were held at 200°C by immersing the wire in a bath of cooling oil? The applied potential difference remains the same, and
An aluminum rod with a square cross section is l.3 m long and 5.2 mm on edge.(a) What is the resistance between its ends?(b) What must be the diameter of a cylindrical copper rod of length 1.3 m if its resistance is to be the same as that of the aluminum rod?
A cylindrical metal rod is 1.60 m long and 5.50 mm in diameter. The resistance between its two ends (at 20°C) is 1.09 x 10-3 Ω(a) What is the material?(b) A round disk, 2.00 cm in diameter and 1.00 mm thick, is formed of the same material. What is the resistance between the round faces, assuming
A cylindrical resistor of radius 5.0 mm and length 2.0 cm is made of material that has a resistivity of 3.5 x 10-5 Ω ∙ m. What are?(a) The magnitude of the current density and(b) The potential difference when the energy dissipation rate in the resistor is 1.0 W?
A potential difference V is applied to a wire of cross-sectional area A, length L, and resistivity p. You want to change the applied potential difference and stretch the wire so that the energy dissipation rate is multiplied by 30.0 and the current is multiplied by 4.00. Assuming the wire's density
The headlights of a moving car require about 10 A from the l2 V alternator, which is driven by the engine. Assume the alternator is 80% efficient (its output electrical power is 80% of its input mechanical power), and calculate the horsepower the engine must supply to run the lights.
An 18.0 W device has 9.00 V across it. How much charge goes through the device in 4.00 h?
The current density in a wire is uniform and has magnitude 2.0 x 106 A/m2, the wire's length is 5.0 m, and the density of conduction electrons is 8.49 x 1028 m-3. How long does an electron take (on the average) to travel the length of the wire?
How much energy is consumed in 2.00 h by an electrical resistance of 400 O when the potential applied across it is 90.0 V?
A resistor with a potential difference of 200 V across it transfers electrical energy to thermal energy at the rate of 3000 W. What is the resistance of the resistor?
A coil of current-carrying Nichrome wire is immersed in a liquid. (Ni chrome is a nickel chromium-iron alloy commonly used in heating elements.) When the potential difference across the coil is 12 V and the current through the coil is 5.2 A, the liquid evaporates at the steady rate of 21, mg/s.
A current is established in a gas discharge tube when a sufficiently high potential difference is applied across the two electrodes in the tube. The gas ionizes; electrons move toward the positive terminal and singly charged positive ions toward the negative terminal.(a) What is the current in a
A 2.0 kW heater element from a dryer has a length of 80 cm. If a 10 cm section is removed, what power is used by the now shortened element at 120 V?
The copper windings of a motor have a resistance of 50Ω at 20°C when the motor is idle. After the motor has run for several hours, the resistance rises to 58Ω. What is the temperature of the windings now? Ignore changes in the dimensions of the windings. (Use Table 26-1)
A certain x-ray tube operates at a current of 7.00 mA and a potential difference of 80.0 kV. What is its power in watts?
A caterpillar of length 4.0 cm crawls in the direction of electron drift along a 5.2-mm-diameter bare copper wire that carries a uniform current of 12 A.(a) What is the potential difference between the two ends of the caterpillar?(b) Is its tail positive or negative relative to its head?(c) How
(a) At what temperature would the resistance of a copper conductor be double its resistance at 20.0°C? (Use 20.0°C as the reference point in Eq.26-17; compare your answer with Figure)(b) Does this same "doubling temperature" hold for all copper conductors, regardless of shape or size?
A steel trolley-car rail has a cross-sectional area of 56.0 cm2. What is the resistance of 10.0 km of rail? The resistivity of the steel is 3.00 x 10-7 Ω ∙ m
What must be the distance between point charge q1 = 26.0μC and point charge q2 = – 47.0μC for the electrostatic force between them to have a magnitude of 5.70 N?
Two equally charged particles are held 3.2 x 10-3 m apart and then released from rest. The initial acceleration of the first particle is observed to be 7.0 m/s2 and that of the second to be 9.0m/s2. If the mass of the first particle is 6.3 x l0-7 kg, what are?(a) The mass of the second particle
A particle of charge + 3.00 x 10-6 C is 12.0 cm distant from a second particle of charge – 1.50 x 10-6 g. Calculate the magnitude of the electrostatic force between the particles.
Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (Figure a). The electrostatic force acting on sphere 2 due to sphere 1 is F. Suppose now that a third identical sphere 3, having an insulating handle and
Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated as particles. For what value of q/Q will the electrostatic force between the two spheres be maximized?
In the return stroke of a typical lightning bolt, a current of 2.5 x 104 A exists for 20μs. How much charge is transferred in this event?
Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.108 N when their center-to-center separation is 50.0 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force
In Figure four particles form a square. The charges are q1 = q4 = Q and q2 = q3 = q. (a) What is Q/q if the net electrostatic force on particles 1 and 4 is zero? (b) Is there any value of q that makes the net electrostatic force on teach of the four particles zero?Explain.
In Figure the particles have charges q1 = ?? q2 = 100nC and q3 = ?? q4 = 200nC, and distance a = 5.0cm. What are the(a) x and(b) y components of the net electrostatic force onparticle?
Three particles are fixed on an x axis. Particle 1 of charge q1 is at x = – a, and particle 2 of charge q2 is at x = + a. If their net electrostatic force on particle 3 of charge + Q is to be zero, what must be the ratio q1/q2 when particle 3 is at?(a) x = + 0.500a and(b) x = + 1.50a?
In Figure three charged particles lie on an x axis. Particles 1 and 2 are fixed in place. Particle 3 is free to move, but the net electrostatic force on it from particles 1 and 2 happens to be zero. If L23 = L12, what is the ratioq1/q2?
Figure shows four identical conducting spheres that are actually well separated from one another. Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial charge of ?? 32e) and then they are separated.
In Figure a, particles 1 and 2have charge 20.0?C each and are held at separation distance d = 1.50 m.(a) What is the magnitude of the electrostatic force on particle 1 due to particle 2? In Figure b, particle 3 of charge 20.0?C is positioned so as to complete an equilateral triangle.(b) What is the
In Figure a, particle 1 (of charge q1) and particle 2 (of charge q2) are fixed in place on an x axis, 8.00 cm apart. Particle 3 (of charge q3 = +8.00 x 10-19 C) is to be placed on the line between particles 1 and 2 so that they produce a net electrostatic force F3,net on it. Figure b gives the x
In Figure particle 1, of charge + 1.0μC and particle 2 of charge ?? 3.0μC are held at separation L = 10.0 cm on an x axis. If particle 3 of unknown charges q3 is to be located such that the net electrostatic force on it from particles 1 and 2 ts zero, what must be the (a) X and (b) Y coordinates
In Figure a, three positively charged particles are fixed on an x axis. Particles B and C are so close to each other that they can be considered to be at the same distance from particle A. The net force on particle A due to particles B and C is 2.014 x 10 -23 N in the negative direction of the x
The charges and coordinates of two charged particles held fixed in an xy plane are q1 = + 3.0μC, x1 = 3.5 cm, y1 = 0.50 cm, and q2 = – 4.0μC, x2 = – 2.0 cm, y2 = 1.5 cm. Find the(a) Magnitude and(b) Direction of the electrostatic force on particle 2 due to particle 1.At what(c) x and(d) y
Two particles are fixed on an x axis. Particle 1 of charge 40μC is located at x = – 2.0 cm; particle 2 of charge O is located at x = 3.0 cm. Particle 3 of charge magnitude 20μC is released from rest on the y axis at y = 2.0 cm. What is the value of Q if the initial acceleration of
In Figure particle 1 of charge + q and particle 2 of charge + 4.00q are held at separation L = 9.00 cm on an x axis. If particle 3 of charge q3 rs to be located such that the three particles remain in place when released, what must be the (a) X and (b) Y coordinates of particle 3, and (c) The
Figure shows an arrangement of four charged particles, with angle ? = 30.0o and distance d = 2.00 cm. Particle 2 has charge q2 = + 8.00 x 10-19 Ct particles 3 and 4 have charges q3 = q4 = ?? 1.60 x 10-19C.(a) What is distance D between the origin and particle 2 1f the net electrostatic force on
In Figure particles 1 and 2 of charge q1 = q2 = +3.20 x 10-19 C are on a y axis at distance d = 17.0 cm from the origin. Particle 3 of charge q3 = + 6.40 x 10-19 C is moved gradually along the x axis from x = 0 to x = + 5.0 m. At what values of x will the magnitude of the electrostatic force on the
Figure a shows an arrangement of three charged particles separated by distance d. Particles A and C are fixed on the x axis, but particle B can be moved along a circle centered on particle A. During the movement, a radial line between A and B makes an angle 0 relative to the positive direction of
A non conducting spherical shell, with an inner radius of 4.0 cm and an outer radius of 6.0 cm, has charge spread non-uniformly through its volume between its inner and outer surfaces. The volume charge density p is the charge per unit volume, with the unit coulomb per cubic meter. For this shell p
What is the magnitude of the electrostatic force between a singly charged sodium ion (Na+, of charge + e) and an adjacent singly charged chlorine ion (Cl–, of charge – e) rn a salt crystal if their separation is 2.82 x 10 -10 m?
The magnitude of the electrostatic force between two identical ions that are separated by u distance of 5.0 x 10–10 m is 3.7 x 10–9 N. (a) What is the charge of each ion? (b) How many electrons are "missing" from each ion (thus giving the ion its charge imbalance)?
A current of 0.300 A through your chest can send your heart into fibrillation, ruining the normal rhythm of heartbeat and disrupting the flow of blood (and thus oxygen) to your brain. If that current persists for 2.00 min, how many conduction electrons pass through your chest?
How many electrons would have to be removed from a coin to leave it with a charge of + 1.0 x 10-7 C?
Two tiny, spherical water drops, with identical charges of – 1.00 x 10-16 C, have a center-to-center separation of 1.00 cm. (a) What is the magnitude of the electrostatic force acting between them? (b) How many excess electrons are on each drop, giving it its charge imbalance?
Earth's atmosphere is constantly bombarded by cosmic ray protons that originate somewhere in space. If the protons all passed through the atmosphere, each square meter of Earth's surface would intercept protons at the average rate of 1500 protons per second. What would be the electric current
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