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physics
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Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

Three point charges are fixed in place in a right triangle. What is the electric force on the ˆ’0.60- Î¼ C charge due to the other two charges?
Three point charges are fixed in place in a right triangle. What is the electric force on the + 1.0- Î¼ C charge due to the other two charges?
Suppose a 1.0-g nugget of pure gold has zero net charge. What would be its net charge after it has 1.0% of its electrons removed?
A tiny sphere with a charge of 7.0 Î¼C is attached to a spring. Two other tiny charged spheres, each with a charge of ˆ’4.0 Î¼ C, are placed in the positions shown in the figure and the spring stretches 5.0 cm from its previous equilibrium position toward the two
A total charge of 7.50 × 10−6 C is distributed on two different small metal spheres. When the spheres are 6.00 cm apart, they each feel a repulsive force of 20.0 N. How much charge is on each sphere?
Two Styrofoam balls with the same mass m = 9.0 Ã— 10ˆ’8 kg and the same positive charge Q are suspended from the same point by insulating threads of length L = 0.98 m. The separation of the balls is d = 0.020 m. What is the charge Q?
Using the three point charges of Example 16.3, find the magnitude of the force on q2 due to the other two charges, q1 and q3.
An equilateral triangle has a point charge + q at each of the three vertices (A, B, C). Another point charge Q is placed at D, the midpoint of the side BC. Solve for Q if the total electric force on the charge at A due to the charges at B, C, and D is zero.
A small sphere with a charge of −0.60 μ C is placed in a uniform electric field of magnitude 1.2 × 106 N/C pointing to the west. What is the magnitude and direction of the force on the sphere due to the electric field?
The electric field across a cellular membrane is 1.0 × 107 N/C directed into the cell.(a) If a pore opens, which way do sodium ions (Na+) flow-into the cell or out of the cell?(b) What is the magnitude of the electric force on the sodium ion? The charge on the sodium ion is + e.
What are the magnitude and direction of the acceleration of a proton at a point where the electric field has magnitude 33 kN /C and is directed straight up?
What are the magnitude and direction of the acceleration of an electron at a point where the electric field has magnitude 6100 N/C and is directed due north?
What are the magnitude and direction of the electric field midway between two point charges, −15 μ C and + 12 μ C, that are 8.0 cm apart?
A balloon, initially neutral, is rubbed with fur until it acquires a net charge of −0.60 nC. (a) Assuming that only electrons are transferred, were electrons removed from the balloon or added to it? (b) How many electrons were transferred?
A negative point charge ˆ’Q is situated near a large metal plate that has a total charge of +Q. Sketch the electric field lines.
What is the electric field at x = d (point P)?Positive point charges q and 2q are located at x = 0 and x = 3d, respectively.
What is the electric field at x = 2d (point S)?Positive point charges q and 2q are located at x = 0 and x = 3d, respectively.
On the x -axis, in which of the three regions x 3 d is there a point where Explain.Positive point charges q and 2q are located at x = 0 and x = 3d, respectively.
Find the x -coordinates of the point(s) on the x -axis wherePositive point charges q and 2q are located at x = 0 and x = 3d, respectively.
Sketch the electric field lines in the plane of the page due to the charges shown in the diagram
Sketch the electric field lines near two isolated and equal (a) Positive point charges and (b) Negative point charges. Include arrowheads to show the field directions.
Find the electric field at point B, midway between the upper left and right corners.Two tiny objects with equal charges of 7.00 Î¼C are placed at the two lower corners of a square with sides of 0.300 m, as shown.
A metallic sphere has a charge of + 4.0 nC. A negatively charged rod has a charge of -6.0 nC. When the rod touches the sphere, 8.2 × 109 electrons are transferred. What are the charges of the sphere and the rod now?
Find the electric field at point C, the center of the square.Two tiny objects with equal charges of 7.00 Î¼C are placed at the two lower corners of a square with sides of 0.300 m, as shown.
Find the electric field at point A, the upper left corner.Two tiny objects with equal charges of 7.00 Î¼C are placed at the two lower corners of a square with sides of 0.300 m, as shown.
Where would you place a third small object with the same charge so that the electric field is zero at the corner of the square labeled A?Two tiny objects with equal charges of 7.00 Î¼C are placed at the two lower corners of a square with sides of 0.300 m, as shown.
Three point charges are placed on the x -axis. A charge of 3.00 μC is at the origin. A charge of −5.00 μC is at 20.0 cm, and a charge of 8.00 μC is at 35.0 cm. What is the force on the charge at the origin?
Two equal charges (Q = +1.00 nC) are situated at the diagonal corners A and B of a square of side 1.0 m. What is the magnitude of the electric field at point D?
Suppose a charge q is placed at point x = 0, y = 0. A second charge q is placed at point x = 8.0 m, y = 0. What charge must be placed at the point x = 4.0 m, y = 0 in order that the field at the point x = 4.0 m, y = 3.0 m be zero?
Two point charges, q1 = + 20.0 nC and q2 = + 10.0 nC, are located on the x -axis at x = 0 and x = 1.00 m, respectively. Where on the x -axis is the electric field equal to zero?
Two electric charges, q1 = + 20.0 nC and q2 = + 10.0 nC, are located on the x -axis at x = 0 m and x = 1.00 m, respectively. What is the magnitude of the electric field at the point x = 0.50 m, y = 0.50 m?
An electron is placed in a uniform electric field of strength 232 N/C. If the electron is at rest at the origin of a coordinate system at t = 0 and the electric field is in the positive x -direction, what are the x - and y-coordinates of the electron at t = 2.30 ns?
An electron is projected horizontally into the space between two oppositely charged metal plates. The electric field between the plates is 500.0 N/C, directed up.(a) While in the field, what is the force on the electron?(b) If the vertical deflection of the electron as it leaves the plates is 3.00
A positively charged rod is brought near two uncharged conducting spheres of the same size that are initially touching each other (diagram a). The spheres are moved apart and then the charged rod is removed (diagram b).(a) What is the sign of the net charge on sphere 1 in diagram b?(b) In
A horizontal beam of electrons initially moving at 4.0 Ã— 107 m/s is deflected vertically by the vertical electric field between oppositely charged parallel plates. The magnitude of the field is 2.00 Ã— 104 N/C.(a) What is the direction of the field between the plates?(b) What is the charge
A particle with mass 2.30 g and charge + 10.0 Î¼C enters through a small hole in a metal plate with a speed of 8.50 m/s at an angle of 55.0°. The uniform E field in the region above the plate has magnitude 6.50 Ã— 103 N/C and is directed downward. The region above the
Consider the same situation as in Problem 51, but with a proton entering through the small hole at the same angle with a speed of v = 8.50 × 105 m/s. (a) Can you ignore the force of gravity when solving this problem for the horizontal distance traveled by the proton? Why or why not? (b) How far
Some forms of cancer can be treated using proton therapy in which proton beams are accelerated to high energies, then directed to collide into a tumor, killing the malignant cells. Suppose a proton accelerator is 4.0 m long and must accelerate protons from rest to a speed of 1.0 × 107 m/s. Ignore
After the electrons in Example 16.9 pass through the anode, they are moving at a speed of 8.4 Ã— 106 m/s. They next pass between a pair of parallel plates [(A) in Fig. 16.35]. The plates each have an area of 2.50 cm by 2.50 cm and they are separated by a distance of 0.50 cm. The uniform
After the electrons pass through the parallel plates in Problem 54, they pass between another set of parallel plates [(B) in Fig. 16.35]. These plates also have an area of 2.50 cm by 2.50 cm and are separated by a distance of 0.50 cm.(a) In what direction must the field be oriented so that the
A conducting sphere that carries a total charge of ˆ’6 Î¼C is placed at the center of a conducting spherical shell that carries a total charge of +1 Î¼C. The conductors are in electrostatic equilibrium. Determine the charge on the outer surface of the shell.
A conducting sphere that carries a total charge of +6 Î¼C is placed at the center of a conducting spherical shell that also carries a total charge of +6 Î¼C. The conductors are in electrostatic equilibrium.(a) Determine the charge on the inner surface of the shell. (b)
A hollow conducting sphere of radius R carries a negative charge − q. (a) Write expressions for the electric field E inside (r < R) and outside (r > R) the sphere. Also indicate the direction of the field. (b) Sketch a graph of the field strength as a function of r.
A conducting sphere is placed within a conducting spherical shell. The conductors are in electrostatic equilibrium. The inner sphere has a radius of 1.50 cm, the inner radius of the spherical shell is 2.25 cm, and the outer radius of the shell is 2.75 cm. If the inner sphere has a charge of 230 nC,
A metal sphere A has charge Q. Two other spheres, B and C, are identical to A except they have zero net charge. A touches B, then the two spheres are separated. B touches C, then those spheres are separated. Finally C touches A and those two spheres are separated. How much charge is on each sphere?
A conductor in electrostatic equilibrium contains a cavity in which there are two point charges: q1 = +5 μC and q2 = −12 μC. The conductor itself carries a net charge − 4 μC. How much charge is on (a) The inner surface of the conductor? (b) The outer surface of the conductor?
In fair weather, over flat ground, there is a downward electric field of about 150 N/C. (a) Assume that the Earth is a conducting sphere with charge on its surface. If the electric field just outside is 150 N/C pointing radially inward, calculate the total charge on the Earth and the charge per
(a) Find the electric flux through each side of a cube of edge length a in a uniform electric field of magnitude E. The field direction is perpendicular to two of the faces.(b) What is the total flux through the cube?
In a uniform electric field of magnitude E, the field lines cross through a rectangle of area A at an angle of 60.0° with respect to the plane of the rectangle. What is the flux through the rectangle?
An object with a charge of 0.890 μC is placed at the center of a cube. What is the electric flux through one surface of the cube?
In this problem, you can show from Coulomb's law that the constant of proportionality in Gauss's law must be 1/ϵ0. Imagine a sphere with its center at a point charge q. (a) Write an expression for the electric flux in terms of the field strength E and the radius r of the sphere. (b) Use Gauss's
(a) Use Gauss's law to prove that the electric field outside any spherically symmetric charge distribution is the same as if all of the charge were concentrated into a point charge. (b) Now use Gauss's law to prove that the electric field inside a spherically symmetric charge distribution is zero
Using the results of Problem 66, we can find the electric field at any radius for any spherically symmetrical charge distribution. A solid sphere of charge of radius R has a total charge of q uniformly spread throughout the sphere. (a) Find the magnitude of the electric field for r ≥ R. (b) Find
An electron is suspended at a distance of 1.20 cm above a uniform line of charge. What is the linear charge density of the line of charge? Ignore end effects.
A thin, flat sheet of charge has a uniform surface charge density σ (σ/2 on each side). (a) Sketch the field lines due to the sheet. (b) Sketch the field lines for an infinitely large sheet with the same charge density. (c) For the infinite sheet, how does the field strength depend on the
Repeat Problem 6 with a slight change. The difference this time is that sphere C is grounded when it is touching B, but C is not grounded at any other time. What is the final charge on each sphere? In Problem 6 A metal sphere A has charge Q. Two other spheres, B and C, are identical to A except
A flat conducting sheet of area A has a charge q on each surface. (a) What is the electric field inside the sheet? (b) Use Gauss's law to show that the electric field just outside the sheet is E = q/(ϵ0A) = σ/ϵ0.
A parallel-plate capacitor consists of two flat metal plates of area A separated by a small distance d. The plates are given equal and opposite net charges ± q.(a) Sketch the field lines and use your sketch to explain why almost all of the charge is on the inner surfaces of the plates.(b) Use
A coaxial cable consists of a wire of radius a surrounded by a thin metal cylindrical shell of radius b. The wire has a uniform linear charge density Î» > 0 and the outer shell has a uniform linear charge density -Î».(a) Sketch the field lines for this cable.(b) Find
Use Gauss's law to derive an expression for the electric field outside the thin spherical shell of Conceptual Example 16.8.
Consider two protons (charge +e), separated by a distance of 2.0 × 10−15 m (as in a typical atomic nucleus). The electric force between these protons is equal in magnitude to the gravitational force on an object of what mass near Earth's surface?
In lab tests it was found that rats can detect electric fields of about 5.0 kN / C or more. If a point charge of 1.0 μC is sitting in a maze, how close must the rat come to the charge in order to detect it?
A raindrop inside a thundercloud has charge −8e. What is the electric force on the raindrop if the electric field at its location (due to other charges in the cloud) has magnitude 2.0 × 106 N/C and is directed upward?
An electron beam in an oscilloscope is deflected by the electric field produced by oppositely charged metal plates. If the electric field between the plates is 2.00 × 105 N/C directed downward, what is the force on each electron when it passes between the plates?
A point charge q1 = + 5.0 μC is fixed in place at x = 0 and a point charge q2 = − 3.0 μC is fixed at x = − 20.0 cm. Where can we place a point charge q3 = − 8.0 μC so that the net electric force on q1 due to q2 and q3 is zero?
The Bohr model of the hydrogen atom proposes that the electron orbits around the proton in a circle of radius 5.3 × 10−11 m. The electric force is responsible for the radial acceleration of the electron. What is the speed of the electron in this model?
Five conducting spheres are charged as shown. All have the same magnitude net charge except E, whose net charge is zero. Which pairs are attracted to each other and which are repelled by each other when they are brought near each other, but well away from the other spheres?
In a thunderstorm, charge is separated through a complicated mechanism that is ultimately powered by the Sun. A simplified model of the charge in a thundercloud represents the positive charge accumulated at the top and the negative charge at the bottom as a pair of point charges.(a) What is the
Two point charges are located on the x -axis: a charge of + 6.0 nC at x = 0 and an unknown charge q at x = 0.50 m. No other charges are nearby. If the electric field is zero at the point x = 1.0 m, what is q?
Three equal charges are placed on three corners of a square. If the force that Qa exerts on Qb has magnitude Fba and the force that Qa exerts on Qc has magnitude Fca, what is the ratio of Fca to Fba?
Two otherwise identical conducting spheres carry charges of + 5.0 μC and −1.0 μC. They are initially a large distance L apart. The spheres are brought together, touched together, and then returned to their original separation L. What is the ratio of the magnitude of the force on either sphere
Two metal spheres of radius 5.0 cm carry net charges of + 1.0 μC and + 0.2 μC. (a) What (approximately) is the magnitude of the electrical repulsion on either sphere when their centers are 1.00 m apart? (b) Why cannot Coulomb's law be used to find the force of repulsion when their centers are 12
A charge of 63.0 nC is located at a distance of 3.40 cm from a charge of ˆ’47.0 nC. What are the x - and y -components of the electric field at a point P that is directly above the 63.0-nC charge at a distance of 1.40 cm? Point P and the two charges are on the vertices of a right triangle.
Point charges are arranged on the vertices of a square with sides of 2.50 cm. Starting at the upper left corner and going clockwise, we have charge A with a charge of 0.200 Î¼C, B with a charge of ˆ’0.150 Î¼C, C with a charge of 0.300 Î¼C, and D with a mass of 2.00 g, but with an unknown
In a cathode ray tube, electrons initially at rest are accelerated by a uniform electric field of magnitude 4.0 × 105 N/C during the first 5.0 cm of the tube's length; then they move at essentially constant velocity another 45 cm before hitting the screen. (a) Find the speed of the electrons when
In the diagram, regions A and C extend far to the left and right, respectively. The electric field due to the two point charges is zero at some point in which region or regions? Explain.
A thin wire with positive charge evenly spread along its length is shaped into a semicircle. What is the direction of the electric field at the center of curvature of the semicircle? Explain.
If the electric force of repulsion between two 1-C charges is 10 N, how far apart are they?
A very small charged block with a mass of 2.35 g is placed on an insulated, frictionless plane inclined at an angle of 17.0° with respect to the horizontal. The block does not slide down the plane because of a 465-N/C uniform electric field that the points parallel to the surface downward along
(a) What would the net charges on the Sun and Earth have to be if the electric force instead of the gravitational force were responsible for keeping Earth in its orbit? There are many possible answers, so restrict yourself to the case where the magnitude of the charges is proportional to the
What is the electric force on the chloride ion in the lower righthand corner in the diagram? Since the ions are in water, the "effective charge" on the chloride ions (Clˆ’) is ˆ’2 Ã— 10ˆ’21 C and that of the sodium ions (Na+) is + 2 Ã—
A dipole consists of two equal and opposite point charges (± q) separated by a distance d.(a) Write an expression for the magnitude of the electric field at a point (x, 0) a large distance (x >> d) from the midpoint of the charges on a line perpendicular to the dipole axis. (b) Give the
A dipole consists of two equal and opposite point charges (±q) separated by a distance d.(a) Write an expression for the electric field at a point (0, y) on the dipole axis. Specify the direction of the field in all four regions: (b) At distant points (|y|>> d), write a simpler, approximate
A dipole consists of two opposite charges (q and ˆ’q) separated by a fixed distance d. The dipole is placed in an electric field in the + x -direction of magnitude E. The dipole axis makes an angle q with the electric field as shown in the diagram.(a) Calculate the net electric force
A negatively charged particle with charge − q is far away from a positive charge + Q that is fixed in place. As - q moves closer to + Q, (a) Does the electric field do positive or negative work? (b) Does - q move through a potential increase or a potential decrease? (c) Does the electric
Explain why the woman's hair in Fig. 17.13 stands on end. Why are the hairs directed approximately radially away from her scalp?In figure 17.13
A swimming pool is filled with water (total mass M) to a height h. Explain why the gravitational potential energy of the water (taking U = 0 at ground level) is ½ Mgh. Where does the factor of ½ come from? How much work must be done to fill the pool, if there is a ready supply of water at ground
Dry air breaks down for a voltage of about 3000 V/mm. Is it possible to build a parallel plate capacitor with a plate spacing of 1 mm that can be charged to a potential difference greater than 3000 V? If so, explain how.
A parallel plate capacitor has the space between the plates filled with a slab of dielectric with k = 3. While the capacitor is connected to a battery, the dielectric slab is removed. Describe quantitatively what happens to the capacitance, the potential difference, the charge on the plates, the
Repeat Question 20 if the capacitor is charged and then disconnected from the battery before removing the dielectric slab. In questions 20 A parallel plate capacitor has the space between the plates filled with a slab of dielectric with k = 3. While the capacitor is connected to a battery, the
A charged parallel plate capacitor has the space between the plates filled with air. The capacitor has been disconnected from the battery that charged it. Describe quantitatively what happens to the capacitance, the potential difference, the charge on the plates, the electric field, and the energy
A positive charge + 2 Î¼C and a negative charge ˆ’ 5 Î¼C lie on a line. In which region or regions (A, B, C) is there a point on the line a finite distance away where the potential is zero? Explain your reasoning. Are there any points where both the electric
A bird is perched on a high-voltage power line whose potential varies between − 100 kV and + 100 kV. Why is the bird not electrocuted?
Points A and B are at the same potential. What is the total work that must be done by an external agent to move a charge from A to B? Does your answer mean that no external force need be applied? Explain.
Why are all parts of a conductor at the same potential in electrostatic equilibrium?
If E = 0 at a single point, then a point charge placed at that point will feel no electric force. What does it mean if the potential is zero at a point? Are there any assumptions behind your answer?
Two point charges, + 5.0Î¼C and ˆ’ 2.0Î¼C, are separated by 5.0 m. What is the electric potential energy?
Find the electric potential energy for the following array of charges: charge q1 = + 4.0μC is located at (x, y) = (0.0, 0.0) m; charge q2 = + 3.0μC is located at (4.0, 3.0) m; and charge q3 = − 1.0μC is located at (0.0, 3.0) m.
A parallel plate capacitor has a charge of 0.020μC on each plate with a potential difference of 240 V. The parallel plates are separated by 0.40 mm of air. (a) What is the capacitance for this capacitor? (b) What is the area of a single plate? (c) At what voltage will the air between the plates
A 200.0-μF capacitor is placed across a 12.0-V battery. When a switch is thrown, the battery is removed from the capacitor and the capacitor is connected across a heater that is immersed in 1.00 cm 3 of water. Assuming that all the energy from the capacitor is delivered to the water, what is the

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