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physics
particle physics
Principles And Practice Of Physics 2nd Global Edition Eric Mazur - Solutions
Given that the induced dipole moment \(\vec{p}_{\text {ind }}\) points from the negative to the positive end of an induced dipole and the electric field \(\vec{E}\) displaces the positive charge center in the direction of the electric field and the negative charge center in the opposite direction,
(a) How does doubling the charge \(q_{\mathrm{A}}\) carried by an object A affect the force exerted by \(\mathrm{A}\) on another charged particle? (b) How does doubling \(q_{\mathrm{A}}\) affect the force exerted by \(\mathrm{A}\) on an induced dipole? (c) Explain why your answers to parts \(a\)
Draw several field lines representing the electric field of an isolated positively charged particle. Repeat for a negatively charged particle.
(a) Is it possible for two electric field lines to cross? What is the direction of the electric field at the point of intersection?) (b) Can two electric field lines touch?
Imagine a hollow sphere enclosing the charged object in Figure 24.5, centered on the object.(a) Given that 26 field lines emanate from the charged object, how many field lines cross the surface of the hollow sphere? (b) If the radius of the hollow sphere is \(R\), what is the number of field line
(a) In Figure 24.6, for what orientation is the number of field lines that cross the surface a minimum? (b) How many field lines cross a plane surface of area \(0.5 \mathrm{~m}^{2}\) placed perpendicular to the field lines in Figure 24.6? (c) Using your answer to part \(b\), what is the number of
Imagine moving the hollow sphere of radius \(R\) of Checkpoint \(24.3 a\) sideways so that the charged object is no longer at the center of the sphere (but still within it).(a) How does the number of field line crossings through the surface of the sphere change as it is moved? (b) How does the
Suppose eight field lines emanate from an object carrying a charge \(+q\). How many field lines pierce the surface of a hollow sphere if the sphere contains (a) a single object carrying a charge \(+2 q\) and (b) two separate objects, each carrying a charge \(+q\) ?(c) If the sphere is pierced by
(a) If more than one field line reenters the donut in Figure 24.9a, what happens to the field line flux? (b) Are there any closed surfaces enclosing a charged particle through which the field line flux is different from that through a simple sphere around that particle? Figure 24.9 The number of
(a) What is the field line flux through the closed spherical surface in Figure \(24.9 b\) due to a charged particle outside the sphere? (b) Does your answer to part \(a\) change if we move the particle around (but keep it outside the volume enclosed by the surface)? Figure 24.9 The number of field
What is the field line flux through the surface of a rectangular box that encloses both ends of an electric dipole?
Consider the two-dimensional field line diagram in Figure 24.11, part of which is hidden from view. (a) If the object in the top left carries a charge of \(+1 \mathrm{C}\), what is the charge enclosed in the region that is hidden? (b) What is the field line flux through a surface that encloses the
There are two reasons the field line flux through a closed surface may be zero: because the field is zero everywhere or because the outward flux is balanced by an equal inward flux. Why can't the latter situation be true for the Gaussian surface in Figure 24.12c? Figure 24.12 Using spherical
Consider a point on the curved part of the Gaussian surface in Figure 24.14. Does the magnitude of the electric field at that point increase, decrease, or stay the same if you (a) change the location of the point on the curved surface or (b) increase the radius of the Gaussian surface?(c) What is
Consider a point on the right surface of the Gaussian surface in Figure 24.15. Does the magnitude of the electric field at that point increase, decrease, or stay the same if you(a) change the location of the point on the right surface, or(b) increase the height \(b\) of the Gaussian surface?(c) Is
Consider a spherical Gaussian surface inside a positively charged conducting object that has reached electrostatic equilibrium. (a) Is the field line flux through the Gaussian surface positive, negative, or zero? (b) What can you conclude from your answer to part \(a\) about the charge enclosed by
Suppose the charged conducting object in Figure 24.17 contains an empty cavity. Does any surplus charge reside on the inner surface of the cavity? Figure 24.17 Because the electric field inside a conducting object in electrostatic equilibrium is zero, we conclude that there cannot be any surplus
In Example 24.4, is the electric field inside the cavity zero?Data from Example 24.4An electrically neutral, conducting sphere contains an irregularly shaped cavity. Inside the cavity is a particle carrying a positive charge \(+q\). What are the sign and magnitude of the charge on the sphere's
(a) Consider the front surface of the trapezoidal box in Figure 24.22a, detached from the rest of the trapezoidal box. Does the field line flux through that surface increase, decrease, or stay the same if any of the following quantities is increased: (i) the area of the front surface, (ii) the
Let the area of the back surface of the trapezoidal box in Figure 24.22 be \(1.0 \mathrm{~m}^{2}\), the magnitude of the electric field be \(1.0 \mathrm{~N} / \mathrm{C}\), and \(\theta=30^{\circ}\) for the front surface.(a) What are the magnitudes of the area vectors for the front and back
Consider a spherical Gaussian surface of radius \(r\) with a particle that carries a charge \(+q\) at its center.(a) On the Gaussian surface, what is the magnitude of the electric field due to the particle? (b) What is the electric flux through the sphere due to the charged particle?(c) Combining
Suppose Coulomb's law showed a \(1 / r^{2.00001}\) dependence instead of a \(1 / r^{2}\) dependence.(a) Calculate the electric flux through a spherical Gaussian surface of radius \(R\) centered on a particle carrying a charge \(+q\).(b) Substitute your result in Eq. 24.8. What do you notice? : =
Suppose \(q\) is outside the irregularly shaped surface in Figure 24.26. Show that the electric flux due to \(q\) through the closed surface is zero. (Draw a small wedge from \(q\) through the surface and determine the electric flux through the two intersections between the wedge and the surface.)
What is the electric field outside a solid sphere carrying a charge +q uniformly distributed throughout its volume?
The direct integration procedure also yields an expression for a rod of finite length (see Example 23.4). Can you use Gauss's law to derive this expression as well? Why or why not?Data from Example 23.4A thin rod of length \(\ell\) carries a uniformly distributed charge \(q\). What is the electric
(a) A very large metal plate of surface area \(A\) carries a positive charge \(q\). What is the surface charge density of the plate? What is the magnitude of the field created by the plate? (b) A very large, thin nonconducting sheet of surface area \(A\) carries a fixed, uniformly distributed
(a) What are the SI units of \(Q\) ?(b) For the process depicted in Figure 20.2a, make an energy diagram for each of these systems: (i) water, pot, and flame; (ii) pot and flame; (iii) pot. Figure 20.2 When a pot of water is heated, the energy diagram for a system comprising only the water is
Make an energy diagram for gas B in Figure 20.4. Figure 20.4 When gases of different temperatures are placed in thermal contact, energy is transferred thermally from the hotter to the cooler gas until the temperatures of the two gases are the same. (a) Gases at different temperatures are placed in
Suppose you were to play the two film clips shown in Figure 20.7 backward. Would the resulting processes be possible? Figure 20.7 Quasistatic versus non-quasistatic expansion of a cylin- der containing a gas. (a) Quasistatic expansion: piston rises gradually 1 2 3 piston 4 5 6 At all instants, gas
Which of the following systems undergo a quasistatic process? (a) A gas-containing balloon is popped inside a vacuum container. System: container, gas, and balloon. (b) A cup of coffee cools down. System: coffee. (c) A sample of compressed gas in a cylinder fitted with a heavy piston is allowed to
(a) During a certain day the outdoor temperature ranges between \(60^{\circ} \mathrm{F}\) and \(80^{\circ} \mathrm{F}\). What is the corresponding range in degrees Celsius and in kelvins?(b) The filament temperature of an incandescent light bulb is about \(2800 \mathrm{~K}\). What is the
Which is greater in each pair: (a) the thermal energy of a pool of water or that of a glass of water at the same temperature, (b) the heat capacity of a pool of water or that of a glass of water at the same temperature, (c) the thermal energy of a cold glass of water or that of an equal amount
Consider the four-atom ammonia molecule illustrated in Figure 20.14.(a) Which of the three rotational degrees of freedom can store thermal energy?(b) Based on your answer to part \(a\), what is the thermal energy per molecule? (c) What is the heat capacity per molecule? (d) Does your prediction
Two identical volumes of gases-one monatomic and the other diatomic-are at the same pressure at room temperature. The temperature of each is raised by the same amount by thermally transferring energy to each of them. Is the energy transferred to the monatomic gas smaller than, equal to, or greater
Consider the equilibrium states represented by points 1 and 2 in Figure 20.20a. Compare these quantities for an ideal gas in these two states: pressure \(P\), volume \(V\), temperature \(T\), entropy \(S\), and thermal energy \(E_{\text {th }}\). Figure 20.20 Isotherms and isentropes in a PV
(a) For which of the two quasistatic processes shown in Figure 20.22, if either, is the change in entropy greater? (b) Is the energy transferred thermally to the gas the same along both paths? Figure 20.22 Two quasistatic processes that transform a gas from an initial state i to a final state f. P
For each process in Figure 20.25, determine whether the following quantities are positive, negative, or zero: \(W, Q, \Delta E_{\mathrm{th}}, \Delta S\). Figure 20.25 Four types of constrained quasistatic processes. P isobaric process (P fixed) isentropic process (S fixed) isochoric process
What is the thermal energy associated with a gas sample that contains \(N\) hydrogen molecules at temperature \(T=300 \mathrm{~K}\) ?
Which quasistatic process from the initial state \(i\) to the final state \(f\) in Figure 20.28 requires more work done on the gas? Figure 20.28 Checkpoint 20.13 and Example 20.5. P P P process B V V process A V
Consider the three processes shown in Figure 20.29. Process B is isothermal. (a) For which of the three processes is the energy transferred thermally greatest? (b) For which of the three processes is the energy transferred thermally smallest? Figure 20.29 Checkpoint 20.14. P process B process C f
Is Eq. 20.15 valid for an isothermal process \((\Delta T=0)\) ? AEth NCAT (any ideal gas process). (20.15)
Is the product \(P V\) in the final state in Figure \(20.33 c\) greater than, equal to, or smaller than the product \(P V\) in the initial state?Figure 20.33c (c) PV diagram showing the isentropic process P V Q=0 W 0 V Solid shading: work done on gas is positive. V
Suppose the isobaric process in Figure \(20.34 c\) begins and ends on the same isotherms as the isochoric process in Figure 20.30c. Which process requires a greater amount \(Q\) of energy transferred thermally?Figure 20.34cFigure 20.30c (c) PV diagram showing the isobaric process P P = P - T. Solid
Consider an ideal gas undergoing the two processes depicted in Figure \(\mathbf{2 0 . 3 7}\) between the same initial and final states that lie on an isotherm. In process \(A\) the gas is taken via an isochoric process to an intermediate state 1 and then via an isobaric process to the final state.
Can you use Eq. 20.36 to calculate the change in entropy for an isochoric process? AS = Q kBT (isothermal process). (20.36)
Suppose two different combinations of constrained quasistatic processes take two identical ideal gases from the same initial equilibrium state to the same final equilibrium state. Is the change in entropy the same or different in the two cases?
For a quasistatic ideal gas process that ends on a higher isentrope, are \(W, Q, \Delta E_{\text {th }}\), and \(\Delta S\) positive, negative, or zero when the gas is(a) expanded(b) compressed?
An amount of water with a mass of \(0.010 \mathrm{~kg}\) at a temperature of \(20^{\circ} \mathrm{C}\) is placed in a freezer and turns into an ice cube at \(0.0^{\circ} \mathrm{C}\). What is the corresponding entropy change? Ignore any volume changes.
A steady heat engine, in contact with its environment, absorbs energy of magnitude \(Q_{\mathrm{H}}\) as heat from a hightemperature reservoir, while \(120 \mathrm{~J}\) of work is done on it. Without specifying anything about the way the entropy of the engine, source, or environment responds to
A \(1500-\mathrm{kg}\) car constantly moving at \(90 \mathrm{kmph}\) accidentally crashes into a concrete wall. The impact produces \(750 \mathrm{~J}\) of sound energy. The car gains \(3.8 \mathrm{~kJ}\) of thermal energy from the impact, and \(15 \mathrm{~kJ}\) of thermal energy escapes after the
Find the temperature in Kelvin and degree Celsius of a thermal reservoir with an entropy gradient value of \(1.985 \times 10^{20} \mathrm{~J}^{-1}\).
The entropy of a thermal reservoir of unknown temperature is defined by the function \(S=a E^{3} / 3 b^{2}\). (a) Derive an expression for the entropy gradient \(d S / d E\). (b) Calculate the entropy gradient of the reservoir if the ratio \(E / b\) is \(3.00 \mathrm{~J}^{-1}\) and \(a=1.00
A reversible heat engine transfers energy from a \(426-\mathrm{K}\) reservoir to second reservoir. What must be the temperature of the second reservoir if the engine has a maximum efficiency of 0.350 ?
What is the coefficient of performance of heating of a heat engine that takes in \(6.45 \mathrm{~kJ}\) and expels \(7.30 \mathrm{~kJ}\) of thermal energy?
A heat pump with a coefficient of performance of heating of 14 supplies thermal energy to a house to maintain a comfortable temperature for the occupants. Calculate the daily thermal energy supplied to the house if \(6.8 \mathrm{~kW}\) of power is needed to drive the heat pump.
What is the maximum efficiency of a Carnot heat engine that operates between \(485 \mathrm{~K}\) and \(625 \mathrm{~K}\) ?
Two Carnot heat engines have the following values for the temperatures \(T_{\text {in }}\) and \(T_{\text {out }}\) of the reservoirs:Engine 1: \(T_{\text {in }}=450 \mathrm{~K}\) and \(T_{\text {out }}=350 \mathrm{~K}\)Engine 2: \(T_{\text {in }}=550 \mathrm{~K}\) and \(T_{\text {out }}=450
For each system, identify the complementary changes of state and associated energies, and determine whether or not the entropy of the system increases. (a) A puck slides to a stop on a surface. System: puck and surface. (b) A compressed spring is released and accelerates a cart on a low-friction
(a) For the situation illustrated in Figure 21.5, draw an energy input-output diagram for the gas. (b) Do the energy and entropy of the gas change? Ignore any friction in the piston and any energy transferred thermally out of the gas. Figure 21.5 When a volume of gas is heated at constant pressure
Suppose we slowly push the piston back to its original position in Figure 21.6, all the while maintaining a constant temperature in the gas. (a) Over the time interval that includes the expansion and the compression of the gas, has any energy been converted? (b) Does the entropy of the gas
What are the signs of \(\Delta E_{\mathrm{R}}, \Delta S_{\mathrm{R}}\), and \(\Delta S_{\mathrm{R}} / \Delta E_{\mathrm{R}}\) for a thermal transfer of energy \((a)\) to and \((b)\) from a thermal reservoir?
For a steady device that has a single input of energy and a single output of energy, does the quality of the energy increase, decrease, or stay the same when the entropy change in the environment is \((a)\) positive and \((b)\) zero?
In an entropy diagram, which of these statements are true?(a) The quality of the energy is proportional to the entropy gradient.(b) The quality of the energy is inversely proportional to the entropy gradient.(c) High-temperature energy is of high quality.(d) High-temperature energy is of low
Draw an entropy diagram for the refrigerator in Figure \(21.2 b\). Figure 21.2 Examples of energy input-output diagrams. (a) Energy input-output diagram for car engine thermal input from fuel combustion Qin car engine Wou mechanical output to turn wheels Lout thermal output via exhaust and engine
Why must the degrade rectangle in Figure \(21.22 a\) have a greater height than the upgrade rectangle? Figure 21.22 For a steady device, the entropy change in the environment must be greater than or equal to zero. (a) Reversible process: = entropy change 0. (b) Irreversible process: entropy change
Suppose you keep \(W\) and \(T_{\text {out }}\) in the reversible process of Figure 21.24a fixed but increase \(T_{\mathrm{in}}\). Do the magnitudes of these quantities increase, decrease, or stay the same: (a) \(\Delta S\) associated with the upgrade, (b) \(\Delta S\) associated with the
When the temperature of the output reservoir in Example 21.3 is lowered, does the efficiency increase, remain the same, or decrease?Data from Example 21.3 A reversible heat engine converts energy taken from a thermal reservoir at temperature \(T_{\text {in }}\) by doing work on the environment and
Estimate these quantities for the heat pump in Figure 21.26: (a) coefficient of performance of cooling and (b) coefficient of performance of heating. Figure 21.26 A heat pump can serve as an air-conditioner in summer by removing energy from inside the house and as a heater in winter by transferring
If you begin at state 1 again but this time go through the cycle in Figure 21.28 clockwise rather than counterclockwise, what are the magnitude and sign of \((a)\) the work done on the system and \((b)\) the work done on the environment? Figure 21.28 The work done on a system during a thermodynamic
Why doesn't the transfer of energy from the interior of the refrigerator to the room violate the entropy law?
What is the change in the energy of the environment in a device for which Eqs. 21.1-21.5 hold?Eqs. AE 0 (steady device, complete cycle). (21.1)
Suppose the bar in Example 21.5 is disconnected from the hightemperature reservoir and allowed to thermally equilibrate with the lowtemperature reservoir.(a) Are the changes in the energy and entropy of the bar during this process positive, negative, or zero? (b) Is there any change in the entropy
(a) Draw an entropy diagram for a steady device that converts thermal energy from a thermal reservoir to mechanical energy. (b) From the diagram, compute the entropy change that occurs during the process and show that such a device is impossible.
Is it possible to reduce the amount of thermally discarded energy to zero by bringing \(T_{\text {out }}\) down to absolute zero?
A hurricane thermally takes in energy from ocean water at \(26^{\circ} \mathrm{C}\), discards some of it to the upper atmosphere at \(-52^{\circ} \mathrm{C}\), and converts the remainder to mechanical energy in the form of wind. (a) What is the maximum possible efficiency for the
What is the coefficient of performance of heating for the electric blanket in Figure 21.39? Figure 21.39 A setup that converts mechani- cal energy (from the motor) to thermal energy. (a) motor (b) generator electric blanket out W >0 Lout 1 height-out 0 1 1 length kyTou 1 kT out kgT
(a) If the heat pump from the refrigerator in Example 21.7 is used during the winter to heat a room to \(20^{\circ} \mathrm{C}\) when it's \(4{ }^{\circ} \mathrm{C}\) outside, what is \(\mathrm{COP}_{\text {heating }}\) ?(b) At what rate must work be done on the heat pump if you want to heat the
What is the change in entropy during each of the four legs of the cycle in Example 21.8?Data from Example 21.8In a reversible heat engine, \(6.02 \times 10^{23}\) molecules of nitrogen gas are used as the working substance. The gas undergoes a Carnot cycle as illustrated in Figure 21.43. The volume
(a) What is the efficiency of the jet engine in Example 21.9?(b) If the jet engine were to operate on a Carnot cycle between the same highest and lowest temperatures, what would its efficiency be?Data from Example 21.9Consider a jet engine operating on the Brayton cycle. The working substance is
In an airplane, the body of the aircraft gets charged if friction occurs between it and the air, which contains dust particles. As there is no possibility of grounding through a copper wire on the ground, the aircraft contains sharp wicks. Explain their role in protecting the aircraft from damage
A metal sphere is grounded and an electrically charged rod is held close to it. The sphere acquires a charge \(q\). The grounding wire is removed, and the sphere is brought in contact with another uncharged identical metal sphere.(a) What is the charge on each sphere after they are separated?(b)
If you rub a balloon with hair and bring it close to a stream of water in a wash basin, the water gets attracted toward the balloon. Can you predict the charge on the stream of water?
By rubbing object \(A\) against \(B\), if 10 electrons get transferred from \(A\) to \(B\), calculate the electric force between the two objects if separated \(10 \mathrm{~cm}\) apart.
Two particles carrying charges \(q_{1}\) and \(q_{2}\) are separated by a distance \(r\) and exert an electric force of magnitude \(F^{\mathrm{E}}\) on each other. If \(q_{1}\) is doubled and \(q_{2}\) is halved, what distance between them can keep the magnitude \(F^{\mathrm{E}}\) constant?
Two identical metal spheres, one carrying a \(12.0 \mu \mathrm{C}\) charge and the other carrying a \(-32.0 \mu \mathrm{C}\) charge, are initially \(50 \mathrm{~mm}\) apart. They are brought in contact with each other and then moved back to their original positions. What is the numerical value of
In the Bohr model, a hydrogen atom consists of an electron orbiting a one-proton nucleus. Furthermore, the angular momentum of the electron is quantized, i.e., it equals \(n \hbar\), where \(n\) is an integer and \(\hbar\) a fundamental constant. Derive an algebraic expression for the relationship
You scrunch up three same-size sheets of aluminum foil to form three balls 1,2, and 3, and stick each one onto the end of a wooden stake (which allows you to transport the balls without touching them). You place the stakes holding balls 1 and 2 an arm's length apart and then give each ball charge
Sphere A carries \(6.0 \mathrm{nC}\) of charge. It is placed \(100 \mathrm{~mm}\) from sphere B, which carries \(3.0 \mathrm{nC}\) of charge. Assume the spheres are much smaller than their separation distance.(a) What is the magnitude of the electric force exerted on A?(b) Draw a figure showing the
A charged particle of \(40-\mathrm{nC}\) is located at the origin of the coordinate system. A second charged particle of \(50 \mathrm{nC}\) is located at \((x, y)=(0,2 m)\) and another charged particle of \(50 \mathrm{nC}\) is located at \((\mathrm{x}, \mathrm{y})=(2 \mathrm{~m}, 2 \mathrm{~m})\).
Two particles with identical positive charges separated by \(2.5 \mathrm{~cm}\) are released from rest on a nonconducting, lowfriction track. Immediately after release, one particle, which has a mass of \(10 \mathrm{mg}\), has an acceleration of magnitude \(5.0 \mathrm{~m} / \mathrm{s}^{2}\), while
Two identical metal spheres carrying the same charge hang by insulating strings from the same point. The balls repel each other so that they hang in the air some distance apart. If you touch one of the spheres and let it go, what will the new equilibrium distance between the spheres be?
Two charges of equal magnitude, \(2 \mu \mathrm{C}\), are separated by a \(2 \mathrm{~cm}\) distance. Compare the electric force if the separation is increased to \(6 \mathrm{~cm}\).
Two particles carrying charges \(q_{1}=-4 \mu \mathrm{C}\) and \(q_{2}=\) \(12 \mu \mathrm{C}\) are located \(5 \mathrm{~m}\) apart. Choose a coordinate system where the first particle is at the origin, and the second is at \(x=5 \mathrm{~m}\). In this coordinate system, an electron sits at \((2
Particle 1 , carrying charge \(q\), particle 2 , carrying charge \(2 q\), and particle 3 , carrying charge \(-q\), are located at the vertices of an equilateral triangle of side \(\ell\) in the \(x y\) plane. Particle 1 is located at \((-\ell / 2,0)\), particle 2 is located at \((\ell / 2,0)\), and
Four charged particles are located at the vertices of a square of side length \(1 \mathrm{~m}\) in the \(x y\)-plane. Particles 1,2 , and 3 \((q 1=5.00 \mu \mathrm{C}, q 2=-4.00 \mu \mathrm{C}\), and \(q 3=-3.00 \mu \mathrm{C})\) are located, respectively, at \((0,0),(1 \mathrm{~m}, 0)\) and \((0,1
Two identical charged dice having \(+5 \mu \mathrm{C}\) of charge, each having mass \(3 \mathrm{~g}\), stay in static equilibrium on the surface of a table with a separation of \(12 \mathrm{~m}\) among them. Calculate the coefficient of static friction.
Two particles 1 and 2 , each carrying \(3.0 \mathrm{nC}\) of charge, are located \(6 \mathrm{~cm}\) apart. Where along the symmetry axis between particles 1 and 2 should a particle 3 carrying a charge of \(+2.0 \mathrm{nC}\) be located if it experiences an upward electric force of \(1.2 \times
Compare the ratio of electric force to gravitational force among two electrons and two protons, respectively, separated by \(1 \mathrm{~nm}\) apart. Comment on the obtained different rations. \(\cdot\)
How many Coulombs of charge are contained due to the electrons present in \(1 \mathrm{~kg}\) of liquid ammonia?
A \(10 \mu \mathrm{C}\) negatively charged balloon having a total mass of \(5 \mathrm{~g}\) that remains floated on top of a charged plastic board above \(15 \mathrm{~cm}\). Estimate the charge on the plastic board.
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