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physics
modern physics

Physics 5th edition James S. Walker - Solutions

A point charge at the origin of a coordinate system produces the electric field E(vector) = (56,000 N/C)x̂ on the x axis at the location x = -0.65 m. Determine the sign and magnitude of the charge.
Find the orbital radius for which the kinetic energy of the electron in Example 19-4 is 1.51 eV. (1 eV = 1 electron volt = 1.6 × 10-19 J.)
Suppose 7.5 × 1010 electrons are transferred to a balloon by rubbing it on your hair. Treating the balloon and your hair as point charges separated by 0.15 m, what is the force of attraction between them?
When a charged balloon sticks to a wall, the downward gravitational force is balanced by an upward static friction force. The normal force is provided by the electrical attraction between the charged balloon and the equal but oppositely charged polarization induced in the wall's molecules. If the
Four lightweight, plastic spheres, labeled A, B, C, and D, are suspended from threads in various combinations, as illustrated in FIGURE 19-47. It is given that the net charge on sphere D is +Q, and that the other spheres have net charges of +Q, - Q, or 0. From the results of the four experiments
Four pairs of conducting spheres, all with the same radius, are shown in FIGURE 19-36, along with the net charge placed on them initially. The spheres in each pair are now brought into contact, allowing charge to transfer between them. Rank the pairs of spheres in order of increasing magnitude of
Find (a) the direction and (b) the magnitude of the net electric field at the center of the equilateral triangle in Figure 19-40. Give your answers in terms of the angle Î¸, as defined in Figure 19-40, and E, the magnitude of the electric field produced by any one of the charges at the center of
A small object of mass 0.0150 kg and charge 3.1 µC hangs from the ceiling by a thread. A second small object, with a charge of 4.2 µC, is placed 1.2 m vertically below the first charge. Find(a) The electric field at the position of the upper charge due to the lower charge(b) The tension in the
The electric field at a radial distance of 47.7 cm from the thin charged wire shown in Figure 19-46 has a magnitude of 35,400 N/C.(a) Using the result given in Problem 68, what is the magnitude of the charge per length on this wire?(b) At what distance from the wire is the magnitude of the electric
Three charges are placed at the vertices of an equilateral triangle of side a = 0.93 m, as shown in FIGURE 19- 48. Charges 1 and 3 are +7.3 ÂµC; charge 2 is -7.3 ÂµC.(a) Find the magnitude and direction of the net force acting on charge 3.(b) If charge 3 is moved to the origin, will the net
The cell membrane in a nerve cell has a thickness of 0.12 mm.(a) Approximating the cell membrane as a parallel-plate capacitor with a surface charge density of 5.9 × 10-6 C/m2, find the electric field within the membrane.(b) If the thickness of the membrane were doubled, would your answer to part
A square with sides of length L has a point charge at each of its four corners. Two corners that are diagonally opposite have charges equal to +3.25 µC; the other two diagonal corners have charges Q. Find the magnitude and sign of the charges Q such that each of the +3.25-µC charges experiences
Two small plastic balls hang from threads of negligible mass. Each ball has a mass of 0.22 g and a charge of magnitude q. The balls are attracted to each other, and the threads attached to the balls make an angle of 20.0° with the vertical, as shown in FIGURE 19-49. Find(a) The magnitude of the
A small sphere with a charge of +2.44 µC is attached to a relaxed horizontal spring whose force constant is 89.2 N/m. The spring extends along the x axis, and the sphere rests on a frictionless surface with its center at the origin. A point charge Q = -8.55 µC is now moved slowly from infinity to
Twelve identical point charges q are equally spaced around the circumference of a circle of radius R. The circle is centered at the origin. One of the twelve charges, which happens to be on the positive x axis, is now moved to the center of the circle. Find(a) The direction(b) The magnitude of the
When a nerve impulse propagates along a nerve cell, the electric field within the cell membrane changes from 7.0 × 105 N/C in one direction to 3.0 × 105 N/C in the other direction. Approximating the cell membrane as a parallel plate capacitor, find the magnitude of the change in charge density on
A system of 1525 particles, each of which is either an electron or a proton, has a net charge of -5.456 × 10-17 C.(a) How many electrons are in this system?(b) What is the mass of this system?
The Electric Field of the Earth The Earth produces an approximately uniform electric field at ground level. This electric field has a magnitude of 110 N/C and points radially inward, toward the center of the Earth.(a) Find the surface charge density (sign and magnitude) on the surface of the
An object of mass m = 2.5 g and charge Q = +42 µC is attached to a string and placed in a uniform electric field that is inclined at an angle of 30.0° with the horizontal (FIGURE 19-50). The object is in static equilibrium when the string is horizontal. Find(a) The magnitude of the
Four identical charges, +Q, occupy the corners of a square with sides of length a. A fifth charge, q, can be placed at any desired location. Find the location of the fifth charge, and the value of q, such that the net electric force acting on each of the original four charges, +Q, is zero.
Two charges, + q and - q, occupy two corners of an equilateral triangle, as shown in FIGURE 19-51.(a) If q = 1.8 µC and r = 0.50 m, find the magnitude and direction of the electric field at point A, the other vertex of the triangle. Let the direction angle be measured counterclockwise from
FIGURE 19-52 shows an electron entering a parallel-plate capacitor with a speed of 5.45 Ã— 106 m/s. The electric field of the capacitor has deflected the electron downward by a distance of 0.618 cm at the point where the electron exits the capacitor. Find(a) The magnitude of the electric field
Two identical conducting spheres are separated by a fixed center to- center distance of 35 cm and have different charges. Initially, the spheres attract each other with a force of 0.099 N. The spheres are now connected by a thin conducting wire. After the wire is removed, the spheres are positively
How many electrons must be transferred away from a bee to produce a charge of +93.0 pC? A. 1.72 × 10-9 B. 5.81 × 108 C. 1.02 × 1020 D. 1.49 × 1029
Suppose two bees, each with a charge of 93.0 pC, are separated by a distance of 1.20 cm. Treating the bees as point charges, what is the magnitude of the electrostatic force experienced by the bees? (In comparison, the weight of a 0.140-g bee is 1.37 × 10-3 N.)A. 6.01 × 10-17 NB. 6.48 × 10-9 NC.
The force required to detach a grain of pollen from an avocado stamen is approximately 4.0 × 10-8 N. What is the maximum distance at which the electrostatic force between a bee and a grain of pollen is sufficient to detach the pollen? Treat the bee and pollen as point charges, and assume the
Pollen of the lisianthus plant requires a force 10 times that of the avocado pollen to be detached. If the lisianthus pollen has the same electric charge as does the avocado pollen, at what maximum distance can the same bee detach lisianthus pollen, assuming point charges?A. 0.12 cmB. 1.4 cmC. 4.0
We say that a capacitor stores charge, yet the total charge in a capacitor is zero; that is, Q + (-Q) = 0. In what sense does a capacitor store charge if the net charge within it is zero?
If the electric field is zero in some region of space is the electric potential zero there as well? Explain.
Explain why equipotentials are always perpendicular to the electric field?
A capacitor is connected to a battery and fully charged. What becomes of the charge on the capacitor when it is disconnected from the battery? What becomes of the charge when the two terminals of the capacitor are connected to one another?
An electron is released from rest in a region of space with a nonzero electric field. As the electron moves, does it experience an increasing or decreasing electric potential? Explain
A spark plug in a car has electrodes separated by a gap of 0.025 in. To create a spark and ignite the air-fuel mixture in the engine, an electric field of 3.0 × 106 V/m is required in the gap.(a) What potential difference must be applied to the spark plug to initiate a spark?(b) If the separation
The electric potential a distance r from a point charge q is 2.70 × 104 V. One meter farther away from the charge the potential is 6140 V. Find the charge q and the initial distance r?
When the potential difference between the plates of a capacitor is increased by 3.25 V, the magnitude of the charge on each plate increases by 13.5 (C. What is the capacitance of this capacitor?
The electric potential a distance r from a point charge q is 155 V, and the magnitude of the electric field is 2240 N/C. Find the values of q and r?
Electric eels produce an electric field within their body. In which direction does the electric field point? a. Toward the head b. Toward the tail c. Upward d. Downward
As a rough approximation, consider an electric eel to be a parallel- plate capacitor with plates of area 1.8 × 10-2 m2 separated by 2.0 m and filled with a dielectric whose dielectric constant is k = 95. What is the capacitance of the eel in this model?a. 8.0 × 10-14 Fb. 7.6 × 10-12 Fc. 1.5 ×
In terms of the parallel-plate model of the previous problem, how much charge does an electric eel generate at each end of its body when it produces a voltage of 650 V?a. 1.2 × 10-14 Cb. 5.2 × 10-11 Cc. 4.9 × 10-9 Cd. 6.1 × 10-5 C
How much energy is stored by an electric eel when it is charged up to 650 V? Use the same parallel-plate model discussed in the previous two problems.a. 1.8 × 10-17 Jb. 1.7 × 10-8 Jc. 1.6 × 10-6 Jd. 2.0 × 10-2 J
Suppose the charge -2q at x = 1.00 m is replaced with a charge -3q, where q = 4.11 × 10-9 C. The charge +q is at the origin. (a) Is the electric potential positive, negative, or zero at the point x = 0.333 m? Explain. (b) Find the point between x = 0 and x = 1.00 m where the electric potential
Suppose we can change the location of the charge -2q on the x axis. The charge +q (where q = 4.11 × 10-9 C) is still at the origin. (a) Where should the charge -2q be placed to ensure that the electric potential vanishes at x = 0.500 m? (b) With the location of -2q found in part (a), where does
Suppose the charge +q at the origin is replaced with a charge +5q, where q = 4.11 × 10-9 C. The charge -2q is still at x = 1.00 m. (a) Is there a point in the region x > 0 where the electric potential passes through zero? (b) Find the location between x = 0 and x = 1.00 m where the electric
A uniform electric field with a magnitude of 1200 N/C points in the negative x direction, as shown in FIGURE 20-27.(a) What is the difference in electric potential, Î”V = VB - VA, between points A and B?(b) What is the difference in electric potential, Î”V = VB - VC, between points B and
A typical 12-V car battery can deliver 2.0 × 105 C of charge. If the energy supplied by the battery could be converted entirely to kinetic energy, what speed would it give to a 1600-kg car that is initially at rest?
Living cells actively "pump" positive sodium ions (Na+) from inside the cell to outside the cell. This process is referred to as pumping because work must be done on the ions to move them from the negatively charged inner surface of the membrane to the positively charged outer surface. Given that
The electric potential of a system as a function of position along the x axis is given in FIGURE 20-28.(a) In which of the regions, 1, 2, 3, or 4, do you expect Ex to be greatest? In which region does Ex have its greatest magnitude? Explain.(b) Calculate the value of Ex in each of the regions, 1,
Points A and B have electric potentials of 332 V and 149 V, respectively. When an electron released from rest at point A arrives at point C, its kinetic energy is KA. When the electron is released from rest at point B, however, its kinetic energy when it reaches point C is KB = 2KA. What are(a) The
An electron is released from rest in a region of space with a nonzero electric field.(a) As the electron moves, does the electric potential energy of the system increase, decrease, or stay the same?(b) Choose the best explanation from among the following:I. Because the electron has a negative
Calculate the speed of (a) A proton (b) An electron after each particle accelerates from rest through a potential difference of 355 V?
NASA's Deep Space 1 and Dawn spacecraft employed ion thrusters in which xenon ions with a charge of +1.60 × 10-19 C and a mass of 2.18 × 10-25 kg are accelerated through a potential difference of 1315 V. What is the speed of the xenon ions as they exit the thruster?
Find the potential difference required to accelerate protons from rest to 10% of the speed of light. (Above this speed, relativistic effects start to become significant.)
A uniform electric field of magnitude 3.8 × 105 N/C points in the positive x direction. Find the change in electric potential energy of a 7.5-(C charge as it moves from the origin to the points(a) (0, 6.0 m);(b) (6.0 m, 0); and(c) (6.0 m, 6.0 m).
A particle with a mass of 3.8 g and a charge of +0.045 (C is released from rest at point A in Figure 20-27.(a) In which direction will this charge move?(b) What speed will it have after moving through a distance of 5.0 cm? The electric field has a magnitude of 1200 N/C.(c) Suppose the particle
In the microscopic view of electrical conduction in a copper wire, electrons are accelerated by an electric field and then collide with metal atoms after traveling about 3.9 × 10-8 m. If an electron begins from rest and is accelerated by a field of 0.065 N/C, what is its speed when it collides
A proton has an initial speed of 5.5 × 105 m/s.(a) What potential difference is required to bring the proton to rest?(b) What potential difference is required to reduce the initial speed of the proton by a factor of 2?(c) What potential difference is required to reduce the initial kinetic energy
In FIGURE 20-29, q1 = +1.8 nC and q2 = -2.1 nC, and the side length of the square is 0.10 m.Figure 20-29,(a) What is the electric potential at point A?(b) What is the electric potential at point B?
In Figure 20-29, it is given that q1 = +Q.Figure 20-29,(a) What value must q2 have if the electric potential at point A is to be zero?(b) With the value for q2 found in part (a), is the electric potential at point B positive, negative, or zero? Explain.
The charge q1 in Figure 20-29 has the value +Q.Figure 20-29,(a) What value must q2 have if the electric potential at point B is to be zero?(b) With the value for q2 found in part (a), is the electric potential at point A positive, negative, or zero? Explain.
It is given that the electric potential is zero at the center of the square in Figure 20-29.Figure 20-29,(a) If q1 = +Q, what is the value of the charge q2?(b) Is the electric potential at point A positive, negative, or zero? Explain.(c) Is the electric potential at point B positive, negative, or
The electric potential 1.6 m from a point charge q is 3.8 × 104 V. What is the value of q?
A point charge of 9.2 (C is at the origin. What is the electric potential at (a) (3.0 m, 0); (b) (-3.0 m, 0); and (c) (3.0 m, -3.0 m)?
The hydrogen atom consists of one electron and one proton. In the Bohr model of the hydrogen atom, the electron orbits the proton in a circular orbit of radius 0.529 × 10-10 m. What is the electric potential due to the proton at the electron's orbit?
A uniform electric field of magnitude 6.8 × 105 N/C points in the positive x direction. Find the change in electric potential between the origin and the points(a) (0, 6.0 m);(b) (6.0 m, 0); and(c) (6.0 m, 6.0 m)?
How far must the point charges q1 = +6.22 (C and q2 = -22.1 (C be separated for the electric potential energy of the system to be -106 J?
Four different arrangements of point charges are shown in FIGURE 20-30. In each case the charges are the same distance from the origin. Rank the four arrangements in order of increasing electric potential at the origin, taking the potential at infinity to be zero. Indicate ties where
Point charges +4.1 (C and -2.2 (C are placed on the x axis at (11 m, 0) and (-11 m, 0), respectively.(a) Sketch the electric potential on the x axis for this system.(b) Your sketch should show one point on the x axis between the two charges where the potential vanishes. Is this point closer to the
In FIGURE 20-31, the charge q = 4.11 Ã— 10-9 C.Figure 20-31,(a) Find the electric potential at x = 0.500 m. (b) Find the value of x between 0 and 1.00 m where the electric potential is zero.
In Figure 20-31, the charge q = 3.67 Ã— 10-9 C.Figure 20-31,(a) Find the value of x between -1.00 m and 0 where the electric potential is zero.(b) At values of x to the left of -1.00 m, do you expect the electric potential to be greater than, less than, or equal to zero?(c) Calculate the
A charge of 4.07 (C is held fixed at the origin. A second charge of 3.45 (C is released from rest at the position (1.25 m, 0.570 m).(a) If the mass of the second charge is 2.36 g, what is its speed when it moves infinitely far from the origin?(b) At what distance from the origin does the second
A charge of 20.2 (C is held fixed at the origin.(a) If a -5.25-(C charge with a mass of 3.20 g is released from rest at the position (0.925 m, 1.17 m), what is its speed when it is halfway to the origin?(b) Suppose the -5.25-(C charge is released from rest at the point x = 1/2 (0.925 m) and y = ½
A charge of -2.505 μC is located at (3.055 m, 4.501 m), and a charge of 1.875 μC is located at (-2.533 m, 0).(a) Find the electric potential at the origin.(b) At one point on the line connecting these two charges the potential is zero. Find this point?
Shows three charges at the corners of a rectangle.(a) How much work must be done to move the +2.7-μC charge to infinity?(b) Suppose, instead, that we move the -6.1-μC charge to infinity. Is the work required in this case greater than, less than, or the same as when we moved the +2.7-μC charge to
How much work must be done to move the three charges in Figure 20-32 infinitely far from one another?Figure 20-32,
In a typical living cell, the electric potential inside the cell is 0.070 V lower than the electric potential outside the cell. The thickness of the cell membrane is 0.10 (m. What are the magnitude and direction of the electric field within the cell membrane?
(a) Find the electric potential at point P in FIGURE 20-33.(b) Suppose the three charges shown in Figure 20-33 are held in place. A fourth charge, with a charge of +4.82 μC and a mass of 2.33 g, is released from rest at point P. What is the speed of the fourth charge when it has moved infinitely
A square of side a has a charge +Q at each corner. What is the electric potential energy of this system of charges?
A square of side a has charges +Q and -Q alternating from one corner to the next, as shown in FIGURE 20-34. Find the electric potential energy for this system of charges.Figure 20-34,
(a) Is the electric potential at point 1 in Figure 20-26 greater than, less than, or equal to the electric potential at point 3?Figure 20-26,(b) Choose the best explanation from among the following: I. The electric field lines point to the right, indicating that the electric potential is greater at
Imagine sketching a large number of equipotential surfaces in Figure 20-26, with a constant difference in electric potential between adjacent surfaces.Figure 20-26,(a) Would the equipotentials at point 2 be more closely spaced, be less closely spaced, or have the same spacing as equipotentials at
Two point charges are on the x axis. Charge 1 is +q and is located at x = -1.0 m; charge 2 is -2q and is located at x = 1.0 m. Make sketches of the equipotential surfaces for this system(a) Out to a distance of about 2.0 m from the origin and(b) Far from the origin. In each case, indicate the
Shows a series of equipotentials in a particular region of space, and five different paths along which an electron is moved.(a) Does the electric field in this region point to the right, to the left, up, or down? Explain.(b) For each path, indicate whether the work done on the electron by the
Consider a region in space where a uniform electric field E = 6500 N/C points in the negative x direction.(a) What is the orientation of the equipotential surfaces? Explain.(b) If you move in the positive x direction, does the electric potential increase or decrease? Explain.(c) What is the
A given system has the equipotential surfaces shown in FIGURE 20-36.(a) What are the magnitude and direction of the electric field?(b) What is the shortest distance one can move to undergo a change in potential of 10.0 V?Figure 20-36,
A given system has the equipotential surfaces shown in Figure 20-36.Figure 20-36,(a) What is the electric potential at the point (2.0 cm, 2.0 cm)?(b) How much work is done by the electric force when a 0.10-C charge is moved from the point (2.0 cm, 2.0 cm) to the point (4.0 cm, 4.0 cm)?
An old-fashioned computer monitor accelerates electrons and directs them to the screen in order to create an image. If the accelerating plates are 0.953 cm apart, and have a potential difference of 22,500 V, what is the magnitude of the uniform electric field between them?
A 0.75-(F capacitor is connected to a 9.0-V battery. How much charge is on each plate of the capacitor?
It is desired that 7.7 (C of charge be stored on each plate of a 5.2-(F capacitor. What potential difference is required between the plates?
To operate a given flash lamp requires a charge of 38 (C. What capacitance is needed to store this much charge in a capacitor with a potential difference between its plates of 9.0 V?
It can be shown that the capacitance of a conducting sphere of radius R is R/k, where k is the Coulomb's law constant, k = 8.99 × 109 N ( m2/C2. In this arrangement the second conductor of the capacitor is taken to be a concentric conducting spherical shell of infinite radius. Treating the Earth
A parallel-plate capacitor is made from two aluminum-foil sheets, each 3.8 cm wide and 6.1 m long. Between the sheets is a Teflon strip of the same width and length that is 0.025 mm thick. What is the capacitance of this capacitor? (The dielectric constant of Teflon is 2.1.)
A parallel-plate capacitor is constructed with circular plates of radius 0.051 m. The plates are separated by 0.25 mm, and the space between the plates is filled with a dielectric with dielectric constant k. When the charge on the capacitor is 1.8 (C the potential difference between the plates is
A parallel-plate capacitor has plates with an area of 0.012 m2 and a separation of 0.88 mm. The space between the plates is filled with a dielectric whose dielectric constant is 2.0.(a) What is the potential difference between the plates when the charge on the capacitor plates is 4.7 (C?(b) Will
A 72-nF parallel-plate capacitor has plates that sandwich a dielectric layer that is 75 mm thick. (a) In order to reduce the capacitance, should the thickness of the dielectric layer be increased or decreased?(b) Calculate the thickness of the dielectric layer that would reduce the capacitance
Consider a parallel-plate capacitor constructed from two circular metal plates of radius R. The plates are separated by a distance of 1.5 mm.(a) What radius must the plates have if the capacitance of this capacitor is to be 1.0 (F?(b) If the separation between the plates is increased, should the
A parallel-plate capacitor has plates of area 3.75 × 10-4 m2. What plate separation is required if the capacitance is to be 1580 pF? Assume that the space between the plates is filled with(a) Air(b) Paper.
A parallel-plate capacitor has plates separated by 0.95 mm. If the electric field between the plates has a magnitude of(a) 1.2 × 105 V/m or(b) 2.4 × 104 N/C, what is the potential difference between the plates?
A parallel-plate capacitor filled with air has plates of area 0.0066 m2 and a separation of 0.45 mm.(a) Find the magnitude of the charge on each plate when the capacitor is connected to a 12-V battery.(b) Will your answer to part (a) increase, decrease, or stay the same if the separation between
Suppose that after walking across a carpeted floor you reach for a doorknob and just before you touch it a spark jumps 0.50 cm from your finger to the knob. Find the minimum voltage needed between your finger and the doorknob to generate this spark?
(a) What plate area is required for an air-filled, parallel-plate capacitor with a plate separation of 2.6 mm to have a capacitance of 22 pF?(b) What maximum voltage can be applied to this capacitor without causing dielectric breakdown?

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