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essential university physics
Essential University Physics 3rd Edition Volume 2 Richard Wolfsonby - Solutions
A flat surface with area 0.14 m2 lies in the x-y plane, in a uniform electric field E = 5.1î + 2.1ĵ + 3.5k̂ kN/C. Find the flux through the surface.
What’s the electric field strength in a region where the flux through a 1.0 cm x 1.0 cm flat surface is 65 Nm2/C, if the field is uniform and the surface is at right angles to the field?
A flat surface with area 2.0 m2 is in a uniform 850-N/C electric field. Find the electric flux through the surface when it’s(a) at right angles to the field,(b) at 45° to the field,(c) parallel to the field.
Charges +2q and -q are near each other. Sketch some field lines for this charge distribution, using eight lines for a charge of magnitude q.
The human heart consists largely of elongated muscle cells, some 100 ?m long and 15 ?min diameter. In its resting state, a cell contains two concentric layers of charge, which confine the electric field to the cell membrane (Fig. 20.38a). When the heart contracts, a wave of depolarization sweeps
The human heart consists largely of elongated muscle cells, some 100 ?m long and 15 ?min diameter. In its resting state, a cell contains two concentric layers of charge, which confine the electric field to the cell membrane (Fig. 20.38a). When the heart contracts, a wave of depolarization sweeps
The human heart consists largely of elongated muscle cells, some 100 ?m long and 15 ?min diameter. In its resting state, a cell contains two concentric layers of charge, which confine the electric field to the cell membrane (Fig. 20.38a). When the heart contracts, a wave of depolarization sweeps
The human heart consists largely of elongated muscle cells, some 100 ?m long and 15 ?min diameter. In its resting state, a cell contains two concentric layers of charge, which confine the electric field to the cell membrane (Fig. 20.38a). When the heart contracts, a wave of depolarization sweeps
A rod of length 2L lies on the x-axis, centered at the origin, and carries line charge density λ=λ0(x/L),where λ0 is a constant.(a) Find an expression for the electric field strength at points on the x-axis for x 7L.(b) Show that for x >>L your result has the 1/x3 dependence of a
A thin rod extends along the x-axis from x = 0 to x = L and carries line charge density λ = λ0(x/L)2,where λ0 is a constant. Find the electric field at x = -L.
Show that the field of an infinite, uniformly charged flat sheet is 2πkσ,where σ is the surface charge density. (This result is independent of distance from the sheet.)
A straight wire 10 m long carries 25 µC distributed uniformly over its length.(a) What’s the line charge density on the wire? Find the electric field strength (b) 15 cm from the wire axis, not near either end, and (c) 350 m from the wire. Make suitable approximations in both cases.
You measure the electric field on a dipole’s axis, at a distance from the dipole that’s large compared with the separation of the two charges in the dipole. If you maintain that distance but move to a point located at 45°from the dipole axis, by what factor will the magnitude of the electric
The electric field on the axis of a uniformly charged ring has magnitude 380 kN/C at a point 5.0 cm from the ring center. The magnitude 15 cm from the center is 160 kN/C; in both cases the field points away from the ring. Find(a) the ring’s radius and(b) its charge.
You’re taking physical chemistry, and your professor is discussing molecular dipole moments. Water, he says, has a dipole moment of “1.85 debyes,” while carbon monoxide’s dipole moment is only “0.12 debye.” Your physics professor wants these mo-ments expressed in SI. She tells you that
An electron is at the origin, and an ion with charge +5e is at x =10 nm. Find a point where the electric field is zero.
A 5.0 µm strand of DNA carries charge +e per nm of length. Treating it as a charged line, what’s the electric field strength 25 nm from the DNA, not near either end?
You have a job examining patent applications. You?re presented with the device in Fig. 20.30, which its inventor claims will separate isotopes of a particular element. Atoms are first stripped completely of their electrons, then accelerated from rest through an electric field chosen to give the
A dipole with dipole moment 1.5 nCm is oriented at 30°to a 4.0-MN/C electric field. Find(a) the magnitude of the torque on the dipole and(b) the work required to rotate the dipole until it’s anti parallel to the field.
Find the line charge density on a long wire if a 6.8µg particle carrying 2.1 nC describes a circular orbit about the wire with speed 280 m/s.
An electron is moving in a circular path around a long, uniformly charged wire carrying 2.5 nC/m. What’s the electron’s speed?
A thin rod lies on the x-axis between x = 0 and x =L and carries total charge Q distributed uniformly over its length. Show that the electric field strength for x = 7L is given by E = KQ/[x(x-L)].
Two 38.0 µC charges are attached to opposite ends of a spring with spring constant k =145 N/m and equilibrium length 52.6 cm. By how much does the spring stretch? You’ll need to use a computer or advanced calculator to solve the cubic equation that arises in this problem.
Two identical small metal spheres initially carry charges q1and q2. When they’re 1.0 m apart, they experience a 2.5-N attractive force. Then they’re brought together so charge moves from one to the other until they have the same net charge. They’re again placed 1.0 m apart, and now they repel
Three identical charges q form an equilateral triangle of side a, with two charges on the x-axis and one on the positive y-axis.(a) Find an expression for the electric field at points on the y-axis above the uppermost charge.(b) Show that your result reduces to the field of a point charge 3q for
You’re 1.44 m from a charge distribution that is well under 1 cm in size. You measure an electric field strength of 296 N/C due to this distribution. You then move to a distance of 2.16 m from the distribution, where you measure a field strength of 87.7 N/C. What’s the net charge of the
A dipole lies on the y-axis and consists of an electron at y = 0.60 nm and a proton at y = -0.60 nm. Find the electric field(a) Midway between the two charges;(b) At the point x =2.0 nm, y =0 nm;and(c) At the point x =-20 nm, y =0 nm.
(a) Find an expression for the electric field on the y-axis due to the two charges q in Fig. 20.7.(b) At what point is the field on the y-axis a maximum? -Net force F Force from q at a -Force from q at -a and this is the magnitude . . This is the y- component of the displacement vectors from ...
A proton is at the origin and an ion is at x =5.0 nm. If the electric field is zero at x =-5.0 nm,what’s the ion’s charge?
A 1.0 µC charge and a 2.0 µC charge are 10 cm apart. Find a point where the electric field is zero.
A 65-µCpoint charge is at the origin. Find the electric field at the points(a) x =50 cm, y =0 cm;(b) x =50 cm, y =50 cm;(c) x =25 cm, y =-75 cm.
DNA fragments introduced into an electrophoresis apparatus (see Application, page 360) generally carry negative charges equivalent to two extra electrons per base pair of nucleotide in the fragment. The table below shows the forces on several DNA fragments in an electroscopes apparatus, as a
In Fig. 20.29, take q1?=25 ?C and q2 =20 ?C.If the force on q1 points in the -x-direction, find(a) q3?(b) the magnitude of the force on q1 у (m) 2- 92 х (m) 3 2 FIGURE 20.29
In Fig. 20.29, take q1 = 68 ?C, q2 =? -34 ?C,and q3 = 15 ?C. Find the electric force on q3 у (m) 2- 92 х (m) 3 2 FIGURE 20.29
A negative charge -q lies midway between two positive charges +Q.What must Q be such that the electric force on all three charges is zero?
A charge 3q is at the origin, and a charge -2q is on the positive x-axis at x = a.Where would you place a third charge so it would experience no net electric force?
A 9.5 µC charge is at x =15 cm, y =5.0 cm and a -3.2µC charge is at x =4.4 cm, y =11 cm.Find the force on the negative charge.
A proton is on the x-axis at x =1.6 nm. An electron is on the y-axis at y =0.85 nm. Find the net force the two exert on a helium nucleus (charge +2e) at the origin.
Two charges, one whose magnitude is twice as large as the oth-er’s, are located 12.5 cm apart and experience an attractive force of 143 N.(a) What’s the magnitude of the larger charge?(b) Can you determine the sign of the larger charge?
A 2-g ping-pong ball rubbed against a wool jacket acquires a net positive charge of 1 µC.Estimate the fraction of the ball’s electrons that have been removed.
A proton moving to the right at 3.8*105m/s centers a region where a 56-kN/C electric field points to the left.(a) How far will the proton get before it momentarily stops?(b) Describe its subsequent motion.
How strong an electric field is needed to accelerate electrons in an X-ray tube from rest to one-tenth the speed of light in a distance of 5.0 cm?
In his famous 1909 experiment that demonstrated quantization of electric charge, R. A. Millikan suspended small oil drops in an electric field. With field strength 20 MN/C, what mass drop can be suspended when the drop carries 10 elementary charges?
Find the magnitude of the electric field due to a charged ring of radius a and total charge Q on the ring axis at distance a from the ring’s center.
The electric field 22 cm from a long wire carrying a uniform line charge density is 1.9 kN/C. What’s the field strength 38 cm from the wire?
The water molecule’s dipole moment is 6.2X10-30 Cm.What would be the separation distance if the molecule consisted of charges ±e(The effective charge is actually less because H and O atoms share the electrons.)
In Fig. 20.28, point Pis midway between the two charges. Find the electric field in the plane of the page (a) 5.0 cm to the left of P, (b) 5.0 cm directly above P, and (c) at P. +2.0 µC – 2.0 µC -5.0 cm- FIGURE 20.28 Exercise 29 P.
The electron in a hydrogen atom is 52.9 pm from the proton. At this distance, what’s the strength of the electric field due to the proton?
A -1.0µC charge experiences a 10î nN electric force in a certain electric field. What force would a proton experience in the same field?
The electric field inside a cell membrane is 8.0 MN/C. What’s the force on a singly charged ion in this field?
A 68-nC charge experiences a 150-mN force in a certain electric field. Find(a) The field strength (b) The force that a 35 µC charge would experience in the same field.
Find the magnitude of the electric force on a 2.0 µC charge in a 100-N/C electric field.
An electron experiences an electric force of 0.61 nN. What’s the field strength at its location?
A proton is at the origin and an electron is at the point x =0.41 nm, y =0.36 nm. Find the electric force on the proton.
A charge q is at the point x =1 m, y =0 m.Write expressions for the unit vectors you would use in Coulomb’s law if you were finding the force that q exerts on other charges located at(a) x =1 m, y =1 m;(b) the origin; (c) x =2 m, y =3 m.You’re not given the sign of q. Why doesn’t this
You break a piece of Styrofoam packing material, and it releases lots of little spheres whose electric charge makes them stick annoyingly to you. If two of the spheres carry equal charges and repel with a force of 21 mN when they’re 15 mm apart, what’s the magnitude of the charge on each?
An electron at Earth’s surface experiences a gravitational force meg.How far away can a proton be and still produce the same force on the electron? (Your answer should show why gravity is unimportant on the molecular scale!)
The electron and proton in a hydrogen atom are 52.9 pm apart. Find the magnitude of the electric force between them.
As they fly, honeybees may acquire electric charges of about 180 pC. Electric forces between charged honeybees and spider webs can make the bees more vulnerable to capture by spiders. How many electrons would a honeybee have to lose to acquire a charge of +180 pC?
Earth carries a net charge of about -5X105C. How many more electrons are there than protons on Earth?
Protons and neutrons are made from combinations of the two most common quarks, the u quark (charge +2/3e) and the d quark (charge -1/3e). How could three of these quarks combine to make(a) a proton(b) a neutron
A typical lightning flash delivers about 25 C of negative charge from cloud to ground. How many electrons are involved?
Suppose the electron and proton charges differed by one part in one billion. Estimate the net charge on your body, assuming it contains equal numbers of electrons and protons.
Is the electric force on a charged particle always in the direction of the field? Explain
Bohr’s correspondence principle states that quantum and classical mechanics must agree in a certain limit. Give an example.
Explain qualitatively why a particle confined to a finite region cannot have zero energy.
Does quantum tunneling violate energy conservation? Explain.
The ground-state wave function for a quantum harmonic oscillator has a single central peak. Why is this at odds with classical physics?
What’s the essential difference between the energy-level structures of infinite and finite square wells?
In terms of de Broglie’s matter-wave hypothesis, how does making the sides of a box different lengths remove the degeneracy associated with a particle confined to that box?
A particle is confined to a two-dimensional box whose sides are in the ratio 1:2. Are any of its energy levels degenerate? If so, give an example. If not, why not?
What did Einstein mean by his remark, loosely paraphrased, that “God does not play dice”?
What fundamental principle of physics, when combined with quantum mechanics, provides a theoretical basis for the existence of antimatter?
The electron in a hydrogen atom is somewhat like a particle confined to a three-dimensional box. In the atom, what plays the role of the confining box?
A friend who hasn’t studied physics asks you the size of a hydrogen atom. How do you answer?
How many quantum numbers are required to specify fully the state of a hydrogen atom?
Both the Bohr and Schrödinger theories predict the same groundstate energy for hydrogen. Do they agree about the angular momentum in the ground state? Explain.
Is it possible for a hydrogen atom to be in the 2d state? Explain.
Can the component of a quantized angular momentum measured on a given axis ever equal the magnitude of the angular momentum vector? Explain.
The electron is a spin-1/2 particle. Does this mean the electron’s intrinsic angular momentum is ½ ℏ? Explain.
How does the Stern–Gerlach experiment provide convincing evidence for space quantization?
Why is there no spin-orbit splitting in hydrogen’s ground state?
How does the exclusion principle explain the diversity of chemical elements?
Helium and lithium exhibit very different chemical behavior, yet they differ by only one unit of nuclear charge. Explain.
Why is stimulated emission essential for laser action?
What distinguishes a Bose–Einstein condensate from ordinary matter?
If you push two atoms together to form a molecule, the exclusion principle results in a repulsive interaction between the atoms. How does this repulsion come about?
Why do ionically bonded materials have high melting points?
The electrostatic attraction between oppositely charged ions is what binds atoms in an ionic molecule. Is the electric force involved in covalent bonding? Explain.
Does it make sense to distinguish individual NaCl molecules in a salt crystal? What about individual H2O molecules in an ice crystal? Explain.
Is it useful to think of the highest-energy electrons as “belonging” to individual atoms in an ionically bonded molecule? In a covalently bonded molecule?
What are the approximate relative magnitudes of the energies associated with electronic excitation of a molecule, with molecular vibration, and with molecular rotation?
Radio astronomers have discovered many complex organic molecules in interstellar space. Why were these discoveries made with radio telescopes and not optical telescopes?
In Fig. 18.17, why are rotational states excited at lower temperatures than vibrational states?
Would you expect solid hydrogen to conduct electricity? Why or why not?
The Fermi energy in metals is much higher than the thermal energy at typical temperatures. Why does this make the mean speed of conduction electrons nearly independent of temperature?
Why does the size of the band gap determine whether a material is an insulator or a semiconductor?
How would you expect the conductivity of an undoped semiconductor to depend on temperature? Why?
Name some technological innovations that might result from a room-temperature superconductor.
Suppose a room-temperature superconductor were discovered, but it had a very low critical field. In what way would this limit its practical applicability?
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