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physics
electricity and magnetism

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

Compute the electric field at a point 4.0 cm from q2 along a line running toward q3 in Fig. 15.27.
Two equal and opposite point charges form a dipole, as shown in Fig. 15.29.(a) Add the electric fields due to each end at point P, thus graphically determining the direction of the field there. (b) Derive a symbolic expression for the magnitude of the electric field at point P, in terms of k, q,
A solid conducting sphere is surrounded by a thick, spherical conducting shell. Assume that a total charge +Q is placed at the center of the sphere and released. (a) After equilibrium is reached, the inner surface of the shell will have (1) negative, (2) zero, (3) positive charge. (b) In terms of
A glass rod rubbed with silk acquires a charge of + 8.0 x 10-10 C. (a) Is the charge on the silk (1) positive, (2) zero, or (3) negative? Why? (b) What is the charge on the silk, and how many electrons have been transferred to the silk? (c) How much mass has the glass rod gained or lost?
In Exercise 39, what is the electric field direction In exercise A solid conducting sphere is surrounded by a thick, spherical conducting shell. Assume that a total charge +Q is placed at the center of the sphere and released. (a) In the interior of the solid sphere, (b) Between the sphere and
In Exercise 39, write expressions for the electric field magnitude In exercise A solid conducting sphere is surrounded by a thick, spherical conducting shell. Assume that a total charge +Q is placed at the center of the sphere and released. (a) In the interior of the solid sphere, (b) Between
A flat, triangular piece of metal with rounded corners has a net positive charge on it. Sketch the charge distribution on the surface and the electric field lines near the surface of the metal (including their direction).
Approximate a metal needle as a long cylinder with a very pointed, but slightly rounded, end. Sketch the charge distribution and outside electric field lines if the needle has an excess of electrons on it.
An electrically neutral thin, square metal slab, measuring 5.00 cm on a side, is placed in a uniform external field that is perpendicular to its square area. (a) If the top of the slab becomes negatively charged, what is the direction of the external field? (b) If the external field strength is
Suppose a Gaussian surface encloses both a positive point charge that has six field lines leaving it and a negative point charge with twice the magnitude of charge of the positive one. What is the net number of field lines passing through the Gaussian surface?
A Gaussian surface has sixteen field lines leaving it when it surrounds a point charge of + 10.0μC and seventy-five field lines entering it when it surrounds an unknown point charge. (a) The magnitude of the unknown charge is (1) greater than 10.0μC, (2) equal to 10.0 μC, (3) less than 10.0
If ten field lines leave a Gaussian surface when it completely surrounds the positive end of an electric dipole, what would the count be if the surface surrounded (a) Just the other end? (b) What if it surrounded both ends?
On average, the electron and proton in a hydrogen atom are separated by a distance of 5.3 x 10-11 m(Fig. 15.30). Assuming the orbit of the electron to be circular,(a) What is the electric force on the electron? (b) What is the electron€™s orbital speed? (c) What is the magnitude of the
A negatively charged pith ball (mass 6.00 x 10-3, charge – 1.50nC) is suspended vertically from a light nonconducting string of length 15.5 cm. This apparatus is then placed in a horizontal uniform electric field. After being released, the pith ball comes to a stable position at an angle of to
A rubber rod rubbed with fur acquires a charge of – 4.8 x 10-9 C. (a) Is the charge on the fur (1) positive, (2) zero, or (3) negative? Why? (b) What is the charge on the fur, and how much mass is transferred to or from the rod? (c) How much mass has the rubber rod lost or gained?
A positively charged particle with a charge of 9.35 pC is suspended in equilibrium in the electric field between two oppositely charged horizontal parallel plates. The square plates each have a charge of 5.50 x 10-5C, are separated by 6.25 mm, and have an edge length of 11.0 cm. (a) Which plate
An electron starts from one plate of a charged closely spaced (vertical) parallel plate arrangement with a velocity of 1.60 x 104 m/s to the right. Its speed on reaching the other plate, 2.10 cm away, is 4.15 x 104 m/s. (a) What type of charge is on each plate? (b) What is the direction of the
An electron in a computer monitor enters midway between two parallel oppositely charged plates, as shown in Fig. 15.31. The initial speed of the electron is 6.15 x 107 m/s and its vertical deflection (d) is 4.70 mm.(a) What is the magnitude of the electric field between the plates? (b) Determine
For an electric dipole, the product qd is called the dipole moment and is given the symbol p. Here d is the distance between poles and q is the magnitude of the charge on either end. The dipole moment vector has a magnitude of qd and, by convention, points from the negative to the positive end.
A proton is fired into a uniform electric field, opposite to the direction of the field. The proton’s speed upon entering the field is 3.15 x 105 m/s, and it comes to rest 5.25 cm after entering the field. (a) What is the electric field strength? (b) What is the proton’s velocity when it is
An electric dipole has charges of ± 4.55pC that are separated by 6.00 cm. The dipole lies on the x-axis and its center is at the origin. Located at y = + 4.00 is a point charge carrying a charge of – 2.50pC. (a) Determine the net force on the dipole and its initial center of mass acceleration
An initially uncharged electroscope is polarized by bringing a negatively charged rubber rod near the bulb. If the bulb end of the electroscope acquires a net charge of +2.50pC, how many electrons are on the leaf end?
An initially neutral electrscope is charged by induction by bringing near a positively charged object. If 3.22 x 108 electrons flow through the ground wire to Earth and the ground wire is then removed, what is the net charge on the electrscope?
An electron that is a certain distance from a proton is acted on by an electrical force. (a) If the electron were moved twice that distance away from the proton, would the electrical force be (1) 2, (2) 1/2, (3) 4, or (4) 1/4 times the original force? Why? (b) If the initial electric force is F,
Two identical point charges are a fixed distance apart. By what factor would the magnitude of the electric force between them change if (a) One of their charges were doubled and the other were halved, (b) Both their charges were halved, and (c) One charge were halved and the other were left
(a) What is the approximate shape of the equipotential surfaces inside the axon cell membrane? (b) Under resting potential conditions, where inside the membrane is the region of highest electric potential? (c) What about during reversed polarity conditions?
(a) If a proton is accelerated from rest by a potential difference of 1 million volts, how much kinetic energy does it gain? (b) How would your answer to part (a) change if the accelerated particle had twice the charge of the proton (same sign) and four times the mass?
(a) Can the electric field at a point be zero while there is also a nonzero electric potential at that point? (b) Can the electric potential at a point be zero while there is also a nonzero electric field at that point? Explain. If your answer to either part is yes, give an example.
If the plates of an isolated parallel plate capacitor are moved farther apart from each other, does the energy storage increase, decrease, or remain the same? Explain.
If the potential difference across a capacitor is doubled, what happens to (a) The charge on the capacitor and (b) The energy stored in the capacitor?
A capacitor is connected to a 12-V battery. If the plate separation is tripled and the capacitor remains connected to the battery, (a) By what factor does the charge on the capacitor change? (b) By what factor does the energy stored in the capacitor change? (c) By what factor does the electric
Give several reasons why a conductor would not be a good choice as a dielectric for a capacitor.
A parallel plate capacitor is connected to a battery and then disconnected. If a dielectric is inserted between the plates, what happens to (a) The capacitance, (b) The volt-age across the capacitor’s plates, and (c) The electric field between the plates?
When a proton approaches another fixed proton, what happens to (a) The kinetic energy of the approaching pro-ton, (b) The electric potential energy of the system, and (c) The total energy of the system?
Explain why the electric field between two parallel plates of a capacitor decreases when a dielectric is inserted if the capacitor is not connected to a power sup-ply, but remains the same when it is connected to a power supply.
Under what conditions would two capacitors in series have the same voltage across them? What if they were in parallel?
Under what conditions would two capacitors in parallel have the same charge on them? What if they were in series?
You have N (an even number ≥ 2) identical capacitors, each with a capacitance of C. In terms of N and C, what is their total effective capacitance? (a) If they are all connected in series? (b) If they are all connected in parallel? (c) If two halves (N/2 each) are connected in series and these
Sketch the topographic map you would expect as you walk away from the ocean up a gently sloping uniform beach. Label the gravitational equipotentials as to relative height and potential value. Show how to predict, from the map, which way a ball would accelerate if it was initially rolled up the
A pair of parallel plates is charged by a 12-V battery. If the electric field between the plates is 1200 N/C, how far apart are the plates?
How much work is required to completely separate two charges (each -1.4μC) and leave them at rest if they were initially 8.0 mm apart?
It takes + 6.0J of work to move two charges from a large distance apart to 1.0 cm from one another. If the charges have the same magnitude, (a) How large is each charge, and (b) What can you tell about their signs?
A + 2.0-μC charge is initially 0.20 m from a fixed charge and is then moved to a position 0.50 m from the fixed charge. (a) How much work is required to move the charge? (b) Does the work depend on the path through which the charge is moved?
An electron is moved from point A to point B and then to point C along two legs of an equilateral triangle with sides of length 0.25 m (Fig. 16.23). If the horizontal electric field is 15 V/m,(a) What is the magnitude of the work required? (b) What is the potential difference between points A and
Compute the energy necessary to bring together (from a very large distance) the charges in the configuration shown in Fig. 16.24.
Compute the energy necessary to bring together (from a very large distance) the charges in the configuration shown in Fig. 16.25.
What is the value of the electric potential at(a) The center of the triangle and(b) A point midway between q2 and q3 in Fig. 16.24?
What is the value of electric potential at(a) The center of the square and(b) A point midway between q1 and q4 in Fig. 16.25?
In a computer monitor, electrons are accelerated from rest through a potential difference in an €œelectron gun€ arrangement (Fig. 16.26).(a) Should the left side of the gun be at (1) a higher, (2) an equal, or (3) a lower potential than the right side? Why? (b) If the
A pair of parallel plates is charged by a 12-V battery. How much work is required to move a particle with a charge of – 4.0μC from the positive to the negative plate?
A uniform electric field of 10 kV/m points vertically upward. How far apart are the equipotential planes that differ by 100 V?
In Exercise 20, if the ground is designated as zero potential, how far above the ground is the equipotential surface corresponding to 7.0 kV? In exercise A uniform electric field of 10 kV/m points vertically upward. How far apart are the equipotential planes that differ by 100 V?
Determine the potential 2.5 mm from the negative plate of a pair of parallel plates separated by 20.0 mm and connected to a 24-V battery.
Relative to the positive plate in Exercise 22, where is the point with a potential of 14 V? In exercise Determine the potential 2.5 mm from the negative plate of a pair of parallel plates separated by 20.0 mm and connected to a 24-V battery.
If the radius of the equipotential surface of a point charge is 10.5 m and is at a potential of (compared to zero at infinity), what are the magnitude and sign of the point charge?
(a) The equipotential surfaces in the neighborhood of a positive point charge are spheres. Which sphere is associated with the higher electric potential: (1) the smaller one, (2) the larger one, or (3) they are associated with the same potential? (b) Calculate the amount of work (in
The potential difference between the cloud and ground in a typical lightning discharge may be up to 100 MV (million volts). What is the gain in kinetic energy of an electron accelerated through this potential difference? Give your answer in both electron-volts and joules. (Assume that there are no
In a typical Van de Graaff linear accelerator, protons are accelerated through a potential difference of 20 MV. What is their kinetic energy if they started from rest? Give your answer in (a) eV, (b) keV, (c) MeV, (d) GeV, (e) joules.
In Exercises 27 and 28, compute the speed of the proton and alpha particle after being accelerated. In exercise In a typical Van de Graaff linear accelerator, protons are accelerated through a potential difference of 20 MV. What is their kinetic energy if they started from rest?
If it takes + 1.6 x 10-5J to move a positively charged particle between two charged parallel plates, (a) What is the charge on the particle if the plates are connected to a 6.0-V battery? (b) Was it moved from the negative to the positive plate or from the positive to the negative plate?
Calculate the voltage required to accelerate a beam of protons initially at rest, and calculate their speed if they have a kinetic energy of (a) 3.5 eV, (b) 4.1 keV, and (c) 8.0 x 10-16 J.
Repeat the calculation in Exercise 30 for electrons instead of protons. In repeat Calculate the voltage required to accelerate a beam of protons initially at rest, and calculate their speed if they have a kinetic energy of (a) 3.5 eV, (b) 4.1 keV, and (c) 8.0 x 10-16 J.
Two large parallel plates are separated by 3.0 cm and connected to a 12-V battery. Starting at the negative plate and moving 1.0 cm toward the positive plate at a angle (Fig. 16.27),(a) What value of potential would be reached, assuming the negative plate were defined as zero potential? (b) Repeat
Consider a point midway between the two large charged plates in Fig. 16.27. Compute the change in electric potential if from there you moved (a) 1.0 mm toward the positive plate, (b) 1.0 mm toward the negative plate, and (c) 1.0 mm parallel to the plates. What do your answers tell you about the
Repeat Exercise 33 if the plates are instead connected to a 24-V battery. Also determine the electric field (direction and magnitude) at the midway point between the plates. Compare your answers to Exercise 33 and comment on the source of any differences. In exercise Consider a point midway between
How much charge flows through a 12-V battery when a 2.0-μF capacitor is connected across its terminals?
A parallel plate capacitor has a plate area of 0.525 m2 and a plate separation of 2.15 mm. What is its capacitance?
What plate separation is required for a parallel plate capacitor to have a capacitance of 9.00 nF if the plate area is 0.425 m2?
(a) For a parallel plate capacitor with a fixed plate separation distance, a larger plate area results in (1) a larger capacitance value, (2) an unchanged capacitance value, (3) a smaller capacitance value. (b) A 2.50-nF parallel plate capacitor has a plate area of 0.514 m2. If the plate area is
A 12.0-V battery remains connected to a parallel plate capacitor with a plate area of 0.224 m2 and a plate separation of 5.24 mm. (a) What is the charge on the capacitor? (b) How much energy is stored in the capacitor? (c) What is the electric field between its plates?
An electron is accelerated by a uniform electric field (1000 V/m) pointing vertically upward. Use Newton’s laws to determine the electron’s velocity after it moves 0.10 cm from rest.
If the plate separation of the capacitor in Exercise 39 changed to 10.48 mm after the capacitor is disconnected from the battery, how do your answers change? In exercise A12.0-V battery remains connected to a parallel plate capacitor with a plate area of 0.224 m2 and a plate separation of 5.24 mm.
Current state-of-the-art capacitors are capable of storing many times the energy of older ones. Such a capacitor, with a capacitance of 1.0 F, is able to light a small 0.50-W bulb at steady full power for 5.0 s before it quits. What is the terminal voltage of the battery that charged the capacitor?
A 1.50-F capacitor is connected to a 12.0-V battery for a long time, and then is disconnected. The capacitor briefly runs a 1.00-W toy motor for 2.00 s. After this time, (a) by how much has the energy stored in the capacitor decreased? (b) What is the voltage across the plates? (c) How much
Two parallel plates have a capacitance value of 0.17μF when they are 1.5 mm apart. They are connected permanently to a 100-V power supply. If you pull the plates out to a distance of 4.5 mm, (a) What is the electric field between them? (b) By how much has the capacitor’s charge changed? (c)
A 50-pF capacitor is immersed in silicone oil, which has a dielectric constant of 2.6. When the capacitor is connected to a 24-V battery, (a) What will be the charge on the capacitor? (b) How much energy is stored in the capacitor?
The dielectric of a parallel plate capacitor is to be a slab of glass that completely fills the volume between the plates. The area of each plate is 0.50 m2. (a) What thickness should the glass have if the capacitance is to be 0.10μF? (b) What is the charge on the capacitor if it is connected to
A parallel plate capacitor has a capacitance of with air between the plates. The capacitor is connected to a 12-V battery and charged. The battery is then removed. When a dielectric is placed between the plates, a potential difference of 5.0 V is measured across the plates. (a) What is the
An air-filled parallel plate capacitor has rectangular plates with dimensions of 6.0 cm x 8.0 cm. It is connected to a 12-V battery. While the battery remains connected, a sheet of 1.5-mm-thick Teflon (dielectric constant of 2.1) is inserted and completely fills the space between the plates. (a)
What is the equivalent capacitance of two capacitors with capacitances of 0.40μF and 0.60μF when they are connected (a) In series and (b) In parallel?
(a) Repeat Exercise 4, but find the speed by using energy methods. Find the direction in which the electron is moving by considering electric potential energy changes. In exercise An electron is accelerated by a uniform electric field (1000 V/m) pointing vertically upward. Use Newton’s laws to
Two identical capacitors are connected in series and their equivalent capacitance is 1.0μF. What is each one’s capacitance value? Repeat the calculation if, instead, they were connected in parallel.
(a) Two capacitors can be connected to a battery in either a series or parallel combination. The parallel combination will require (1) more, (2) equal, (3) less energy from a battery than the series combination. Why? (b) Two uncharged capacitors, one with a capacitance of 0.750μFand the other
For the arrangement of three capacitors in Fig. 16.28, what value of C1 will give a total equivalent capacitance of 1.7Î¼F?
(a) Three capacitors of equal capacitance are connected in parallel to a battery, and together they acquire a certain total charge Q from that battery. Will the charge on each capacitor be (1) Q, (2) 3Q, or (3) Q/3? (b) Three capacitors of each are connected in parallel to a 12-V battery. What is
(a) If you are given three identical capacitors, you can obtain (1) three, (2) five, (3) seven different capacitance values. (b) If the three capacitors each have a capacitance of 1.0μF, what are the different values of equivalent capacitance?
What are the maximum and minimum equivalent capacitances that can be obtained by combinations of three capacitors of 1.5 μF, 2.0 μF, and 3.0 μF?
If the capacitance of C1 is 0.10 Î¼F,(a) What is the charge on each of the capacitors in the circuit in Fig. 16.28?(b) How much energy is stored in each capacitor?
Four capacitors are connected in a circuit as illustrated in Fig. 16.29. Find the charge on, the voltage difference across, and the energy stored for each of the capacitors.
A tiny dust particle in the form of a long thin needle has charges of ±7.14 pC on its ends. The length of the particle is 3.75μm. (a) Which location is at a higher potential: (1) above the positive end, (2) above the positive end, or (3) both locations are at the same potential? (b) Compute the
A vacuum tube has a vertical height of 50.0 cm. An electron leaves from the top at a speed of 3.2 x 106 m/s downward and is subjected to a “typical” Earth field of downward. (a) Use energy methods to determine whether it reaches the bottom surface of the tube. (b) If it does, with what speed
Consider two points at different distances from a positive point charge. (a) The point closer to the charge is at a (1) higher, (2) equal, (3) lower potential than the point farther away. Why? (b) How much different is the electric potential 20 cm from a charge of 5.5μC compared to 40 cm from
A helium atom with one electron already removed (a positive helium ion) consists of a single orbiting electron and a nucleus of two protons. The electron is in its minimum orbital radius of 0.027 nm. (a) What is the potential energy of the system? (b) What is the centripetal acceleration of the
Suppose that the three capacitors in Figure 16.22 have the following values: C1 = 0.15 μF, C2 = 0.25 μF, and C3 = 0.30 μF. (a) What is the equivalent capacitance of this arrangement? (b) How much charge will be drawn from the battery? (c) What is the voltage across each capacitor? (d) What
Two very large horizontal parallel plates are separated by 1.50 cm. An electron is to be suspended at rest in midair between them. (a) The top plate should be at (1) a higher potential, (2) an equal potential, (3) a lower potential compared with the bottom plate. Explain. (b) What voltage across
Before attempting this one, see Insight 16.1, Electric Potential and Nerve Signal Transmission and Learn by Drawing 16.2 on graphical relationships between and V. Suppose an (axon) cell membrane is experiencing the end of a stimulus event and the voltage across the cell membrane is instantaneous at
In Exercise 63, assume that the inside and outside surfaces of the axon membrane act like a parallel plate capacitor with an area of 1.1 x 10-9 m2. (a) Estimate the capacitance of an axon’s membrane, assuming it is filled with lipids with a dielectric constant of 3.0. (b) How much charge would
Two parallel plates, 9.25 cm on a side, are separated by 5.12 mm. (See Fig. 16.30a.)(a) Determine their capacitance if the volume from one plate to midplane is filled with a material of dielectric constant 2.55 and the rest is filled with a different material of dielectric constant 4.10. (b) If
Repeat Exercise 65 except fill the volume from one edge to the middle with the same two materials. (Do you see two capacitors in parallel?)In exercise(a) Determine their capacitance if the volume from one plate to midplane is filled with a material of dielectric constant 2.55 and the rest is filled
A capacitor (5.70μF) is connected in a series arrangement with a second capacitor (2.30μF) and a 12-V battery. (a) How much charge is stored on each capacitor? (b) What is the voltage drop across each capacitor? The battery is then removed, leaving the two capacitors isolated. (c) If the

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