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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

Two point charges 2.0 cm apart have an electric potential energy -180 μJ. The total charge is 30 nC. What are the two charges?
A 5.0-cm-diameter metal ball has a surface charge density of 10 μC/m2. How much work is required to remove one electron from this ball?
The two halves of the rod in FIGURE EX25.35 are uniformly charged to ±Q. What is the electric potential at the point indicated by the dot? ++++++++ FIGURE EX25.35
Two point charges qaand qbare located on the x-axis at x = a and x = b. FIGURE EX25.34 is a graph of V, the electric potential. a. What are the signs of qa and qb?b. What is the ratio |qa/qb|?c.
A -2.0 nC charge and a +2.0 nC charge are located on the x-axis at x = -1.0 cm and x = +1.0 cm, respectively.a. Other than at infinity, is there a position or positions on the x-axis where the
The electric potential at the dot in FIGURE EX25.32 is 3140 V.What is charge q? -5.0 nC 2.0 cm 4.0 cmi 5.0 nC FIGURE EX25.32
What is the electric potential at the point indicated with the dot in FIGURE EX25.31? 1.0 nC 3.0 cm,' 3.0 cm 3.0 cm -2.0 nC -2.0 nC FIGURE EX25.31
What is the electric potential at the point indicated with the dot in FIGURE EX25.30? 2.0 nC -1.0 nC 3.0 cm 14.0 cm +, 2.0 nC FIGURE EX25.30
In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm.a. What is the electric potential of the proton at the position of the electron?b. What is the
A 1.0-mm-diameter ball bearing has 2.0 × 109 excess electrons.What is the ball bearing’s potential?
a. What is the electric potential at points A, B, and C in FIGURE EX25.27?b. What are the potential differences Î”VAB= VB- VAand Î”VCB= VB- VC? 2,0 cm, 1.0 cm в +, 2.0 nC
In FIGURE EX25.26, a proton is fired with a speed of 200,000 m/s from the midpoint of the capacitor toward the positive plate. a. Show that this is insufficient speed to reach the positive plate.b.
Two 2.0-cm-diameter disks spaced 2.0 mm apart form a parallel-plate capacitor. The electric field between the disks is 5.0 × 105 V/m.a. What is the voltage across the capacitor?b. An electron is
Two 2.00 cm × 2.00 cm plates that form a parallel-plate capacitor are charged to ±0.708 nC. What are the electric field strength inside and the potential difference across the capacitor if the
A 3.0-cm-diameter parallel-plate capacitor has a 2.0 mm spacing. The electric field strength inside the capacitor is 1.0 × 105 V/m.a. What is the potential difference across the capacitor?b. How
a. What is the potential of an ordinary AA or AAA battery?b. An AA battery is connected to a parallel-plate capacitor having 4.0 cm × 4.0 cm plates spaced 1.0 mm apart. How much charge does the
Show that 1 V/m = 1 N/C.
Physicists often use a different unit of energy, the electron volt, when dealing with energies at the atomic level. One electron volt, abbreviated eV, is defined as the amount of kinetic energy
A student wants to make a very small particle accelerator using a 9.0 V battery. What speed will(a) A proton(b) An electron have after being accelerated from rest through the 9.0 V potential
In proton-beam therapy, a high-energy beam of protons is fired at a tumor. As the protons stop in the tumor, their kinetic energy breaks apart the tumor’s DNA, thus killing the tumor cells. For one
Through what potential difference must a proton be accelerated to reach the speed it would have by falling 100 m in vacuum?
An electron with an initial speed of 500,000 m/s is brought to rest by an electric field.a. Did the electron move into a region of higher potential or lower potential?b. What was the potential
A proton with an initial speed of 800,000 m/s is brought to rest by an electric field.a. Did the proton move into a region of higher potential or lower potential?b. What was the potential difference
What potential difference is needed to accelerate a He+ ion (charge +e, mass 4 u) from rest to a speed of 2.0 × 106 m/s?
What potential difference is needed to accelerate an electron from rest to a speed of 2.0 × 106 m/s?
What is the speed of an electron that has been accelerated from rest through a potential difference of 1000 V?
Reproduce FIGURE Q25.12 on your paper. Then draw a dot (or dots) on the figure to show the position (or positions) at which the electric potential is zero. | FIGURE Q25.12
What is the speed of a proton that has been accelerated from rest through a potential difference of -1000 V?
FIGURE Q25.11 shows three points near two point charges. The charges have equal magnitudes. For each part, rank in order, from most positive to most negative, the potentials Vato Vc.a.b. +, +) b a
FIGURE EX25.10 shows the potential energy of an electric dipole. Consider a dipole that oscillates between ?60?. a. What is the dipole??s mechanical energy?b. What is the dipole??s kinetic energy
FIGURE Q25.10 shows two points near a positive point charge.a. What is the ratio V2/V1of the electric potentials? Explain.b. What is the ratio E2/E1of the electric field strengths? 1 mm 2 3 mm
A water molecule perpendicular to an electric field has 1.0 × 10-21 J more potential energy than a water molecule aligned with the field. The dipole moment of a water molecule is 6.2 × 10-30 C m.
FIGURE Q25.9 shows two points inside a capacitor. Let V = 0 V at the negative plate.a. What is the ratio V2/V1of the electric potentials? Explain.b. What is the ratio E2/E1of the electric field
Two positive point charges are 5.0 cm apart. If the electric potential energy is 72 μJ, what is the magnitude of the force between the two charges?
Rank in order, from largest to smallest, the electric potentials Vato Veat points a to e in FIGURE Q25.8. Explain. a • b. + ++ + + + + + + + + + + +++ FIGURE Q25.8
What is the electric potential energy of the group of charges in FIGURE EX25.7? -4.0 nC 3.0 nC + 3.0 cm 14.0 cm 3.0 nC FIGURE EX25.7
A capacitor with plates separated by distance d is charged to a potential difference ΔVC. All wires and batteries are disconnected, then the two plates are pulled apart (with insulated handles) to a
What is the electric potential energy of the group of charges in FIGURE EX25.6? 1.0 nC 3.0 cm \ 3.0 cm 3.0 сm -2.0 nC -2.0 nC FIGURE EX25.6 +
FIGURE Q25.6 shows the electric potential along the x-axis. a. Draw a graph of the potential energy of a 0.1 C charged particle. Provide a numerical scale for both axes.b. If the charged particle is
What is the potential energy of the electron-proton interactions in FIGURE EX25.5? The electrons are fixed and cannot move. Proton 0.50 nm Electrons - 2.0 nm 0.50 nm FIGURE EX25.5
Rank in order, from most positive to most negative, the potential energies Uato Ufof the six electric dipoles in the uniform electric field of FIGURE Q25.5. Explain. a d. e
A proton is released from rest at the positive plate of a parallelplate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. The experiment is repeated with
Two protons are launched with the same speed from point 1 inside the parallel-plate capacitor of FIGURE Q25.4. Points 2 and 3 are the same distance from the negative plate. a. Is ΔU1??2, the change
A proton is released from rest at the positive plate of a parallelplate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. What will be the final speed of
An electron moves along the trajectory of FIGURE Q25.3 from i to f. a. Does the electric potential energy increase, decrease, or stay the same? Explain.b. Is the electron??s speed at f greater than,
The electric field strength is 50,000 N/C inside a parallel plate capacitor with a 2.0 mm spacing. A proton is released from rest at the positive plate. What is the proton’s speed when it reaches
FIGURE Q25.2 shows the potential energy of a proton (q = +e) and a lead nucleus (q = +82e). The horizontal scale is in units of femtometers, where 1 fm = 10-15m. a. A proton is fired toward a lead
The electric field strength is 20,000 N/C inside a parallel plate capacitor with a 1.0 mm spacing. An electron is released from rest at the negative plate. What is the electron’s speed when it
a. Charge q1 is distance r from a positive point charge Q. Charge q2 = q1/3 is distance 2r from Q. What is the ratio U1/U2 of their potential energies due to their interactions with Q?b. Charge q1 is
A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r ≤ R) is E(r) = r4Emax/R4.a. What is Emax in terms of Q and R?b. Find an expression for the
sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere isThis charge density decreases linearly from Ï0 at the center to zero at the edge of the
A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r) = C/r2, where C is a constant to be determined.a. The charge within a small volume dV is dq = ρ
An infinite cylinder of radius R has a linear charge density λ.The volume charge density (C/m3) within the cylinder (r ≤ R) is ρ(r) = rρ0/R, where ρ0 is a constant to be determined.a. Draw a
All examples of Gauss€™s law have used highly symmetric surfaces where the flux integral is either zero or EA. Yet we€™ve claimed that the net Î¦e=
Newton’s law of gravity and Coulomb’s law are both inverse square laws. Consequently, there should be a “Gauss’s law for gravity.”a. The electric field was defined as E = F on q/q, and we
An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nucleus) at the center of a sphere of radius R with uniformly
A spherical shell has inner radius Rin and outer radius Rout. The shell contains total charge Q, uniformly distributed. The interior of the shell is empty of charge and matter.a. Find the electric
A long cylinder with radius b and volume charge density ρ has a spherical hole with radius a < b centered on the axis of the cylinder. What is the electric field strength inside the hole at
The electric field must be zero inside a conductor in electrostatic equilibrium, but not inside an insulator. It turns out that we can still apply Gauss’s law to a Gaussian surface that is entirely
The electric field must be zero inside a conductor in electrostatic equilibrium, but not inside an insulator. It turns out that we can still apply Gauss’s law to a Gaussian surface that is entirely
A very long, uniformly charged cylinder has radius R and linear charge density λ. Find the cylinder’s electric field strength(a) Outside the cylinder, r ≥ R,(b) Inside the cylinder, r ≤ R.(c)
A long, thin straight wire with linear charge density λ runs down the center of a thin, hollow metal cylinder of radius R.The cylinder has a net linear charge density 2λ. Assume λ is positive.
FIGURE P24.48 shows two very large slabs of metal that are parallel and distance l apart. The top and bottom of each slab has surface area A. The thickness of each slab is so small in comparison to
FIGURE P24.47 shows an infinitely wide conductor parallel to and distance d from an infinitely wide plane of charge with surface charge density Î·. What are the electric fields E1to E4in
An infinite slab of charge of thickness 2z0 lies in the xy plane between z = -z0 and z = +z0. The volume charge density ρ (C/m3) is a constant.a. Use Gauss’s law to find an expression for the
The three parallel planes of charge shown in FIGURE P24.45 have surface charge densities -1/2Î·, Î·, and -1/2Î·. Find the electric fields E1to E4in regions 1 to
A uniformly charged ball of radius a and charge -Q is at the center of a hollow metal shell with inner radius b and outer radius c. The hollow sphere has net charge +2Q. Determine the electric field
Part A Find the electric field inside a hollow plastic ball of radius R that has charge Q uniformly distributed on its outer surface. Give your answer as a multiple of Q/ε0. Part B Find the electric
A positive point charge q sits at the center of a hollow spherical shell. The shell, with radius R and negligible thickness, has net charge -2q. Find an expression for the electric field strength(a)
A hollow metal sphere has 6 cm and 10 cm inner and outer radii, respectively. The surface charge density on the inside surface is -100 nC/m2. The surface charge density on the exterior surface is
Figure 24.32b showed a conducting box inside a parallel plate capacitor. The electric field inside the box is E = 0. Suppose the surface charge on the exterior of the box could be frozen. Draw a
The earth has a vertical electric field at the surface, pointing down, that averages 100 N/C. This field is maintained by various atmospheric processes, including lightning. What is the
FIGURE P24.38 shows a solid metal sphere at the center of a hollow metal sphere. What is the total charge on (a) The exterior of the inner sphere,(b) The inside surface of the hollow sphere,(c) The
A 20-cm-radius ball is uniformly charged to 80 nC.a. What is the ball’s volume charge density (C/m3)?b. How much charge is enclosed by spheres of radii 5, 10, and 20 cm?c. What is the
A hollow metal sphere has inner radius a and outer radius b.The hollow sphere has charge + 2Q. A point charge + Q sits at thecenter of the hollow sphere.a. Determine the electric fields in the three
A neutral conductor contains a hollow cavity in which there is a +100 nC point charge. A charged rod then transfers -50 nC to the conductor. Afterward, what is the charge(a) On the inner wall of the
A spherically symmetric charge distribution produces the electric field E = (5000r2)r̂ N/C, where r is in m.a. What is the electric field strength at r = 20 cm?b. What is the electric flux through a
A 10 nC charge is at the center of a 2.0 m × 2.0 m × 2.0 m cube. What is the electric flux through the top surface of the cube?
Charges q1 = -4Q and q2 = +2Q are located at x = -a and x = +a, respectively. What is the net electric flux through a sphere of radius 2a centered(a) At the origin(b) At x = 2a?
A tetrahedron has an equilateral triangle base with 20-cm long edges and three equilateral triangle sides. The base is parallel to the ground, and a vertical uniform electric field of strength 200
FIGURE P24.30 shows four sides of a 3.0 cm Ã— 3.0 cm Ã— 3.0 cm cube.a. What are the electric fluxes Î¦1 to Î¦4 through sides 1 to 4?b. What is the
Find the electric fluxes Î¦1to Î¦5through surfaces 1 to 5 in FIGURE P24.29. 4.0 m 400 N/C 2.0 m 4. (2 30° FIGURE P24.29
A thin, horizontal, 10-cm-diameter copper plate is charged to 3.5 nC. If the electrons are uniformly distributed on the surface, what are the strength and direction of the electric fielda. 0.1 mm
FIGURE EX24.27 shows a hollow cavity within a neutral conductor.A point charge Q is inside the cavity. What is the net electric flux through the closed surface that surrounds the conductor? Closed
The conducting box in FIGURE EX24.26 has been given an excess negative charge. The surface density of excess electrons at the center of the top surface is 5.0 Ã— 1010 electrons/m2.
The electric field strength just above one face of a copper penny is 2000 N/C. What is the surface charge density on this face of the penny?
A spark occurs at the tip of a metal needle if the electric field strength exceeds 3.0 × 106 N/C, the field strength at which air breaks down. What is the minimum surface charge density for
55.3 million excess electrons are inside a closed surface. What is the net electric flux through the surface?
The net electric flux through an octahedron is -1000 N m2/C. How much charge is enclosed within the octahedron?
What is the net electric flux through the cylinder of FIGURE EX24.21? +. FIGURE EX24.21 +100 nC +1 nC (inside) -100 nC
What is the net electric flux through the torus (i.e., doughnut shape) of FIGURE EX24.20? +) -1 nC (inside) +100 nC FIGURE EX24.20
FIGURE EX24.19 shows three Gaussian surfaces and the electric flux through each. What are the three charges q1, q2, and q3? Pc =-2gle, = -qle, Ф 92 Фв 3 Зд/eo 93 FIGURE EX24.19
FIGURE EX24.18 shows three charges. Draw these charges on your paper four times. Then draw two-dimensional cross sections of three-dimensional closed surfaces through which the electric flux is (a)
FIGURE EX24.17 shows three charges. Draw these charges on your paper four times. Then draw two-dimensional cross sections of three-dimensional closed surfaces through which the electric flux is (a)
What is the net electric flux through the two cylinders shown in FIGURE EX24.16? Give your answer in terms of R and E.a.b. 2R 2R
A 1.0 cm × 1.0 cm × 1.0 cm box with its edges aligned with the xyz-axes is in the electric field E = (350x + 150)î N/C, where x is in meters. What is the net electric flux through the box?
A 3.0-cm-diameter circle lies in the xz-plane in a region where the electric field is E = (1500î + 1500ĵ - 1500k̂) N/C. What is the electric flux through the circle?
A 2.0 cm × 3.0 cm rectangle lies in the xz-plane. What is the magnitude of the electric flux through the rectangle ifa. E = (100î - 200k̂) N/C?b. E = (100î - 200ĵ) N/C?
A 2.0 cm × 3.0 cm rectangle lies in the xy-plane. What is the magnitude of the electric flux through the rectangle ifa. E = (100î - 200k̂) N/C?b. E = (100î- 200ĵ) N/C?
The electric flux through the surface shown in FIGURE EX24.11 is 25 N m2/C. What is the electric field strength? în 60° 10 cm X 20 cm FIGURE EX24.11

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