Ch 21: Electric Charge and Electric Field
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Problem 12
The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4×10−15 m. (b) What magnitude of electric field does it produce at the distance of the electrons, which is about 1.0×10−10 m?Problem 21
Just How Strong Is the Electric Force? Suppose you had two small boxes, each containing 1.0 g of protons. (a) If one were placed on the moon by an astronaut and the other were left on the earth, and if they were connected by a very light (and very long!) string, what would be the tension in the string? Express your answer in newtons and in pounds. Do you need to take into account the gravitational forces of the earth and moon on the protons? Why? (b) What gravitational force would each box of protons exert on the other box?
Problem 21
Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (b) How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude 1.00 * 10^4 N (roughly 1 ton)? Assume that the spheres may be treated as point charges.Problem 21
Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (c) What fraction of all the electrons in each sphere does this represent?Problem 21
Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 3.33 * 10^-21 N?Problem 21
Two small plastic spheres are given positive electric charges. When they are 15.0 cm apart, the repulsive force between them has magnitude 0.220 N. What is the charge on each sphere (a) if the two charges are equal andProblem 21
Two small plastic spheres are given positive electric charges. When they are 15.0 cm apart, the repulsive force between them has magnitude 0.220 N. What is the charge on each sphere (b) if one sphere has four times the charge of the other?Problem 21
Point charges q1 = -4.5 nC and q2 = +4.5 nC are separated by 3.1 mm, forming an electric dipole. (b) The charges are in a uniform electric field whose direction makes an angle of 36.9° with the line connecting the charges. What is the magnitude of this field if the torque exerted on the dipole has magnitude 7.2 * 10^-9 N•m?Problem 21
Torque on a Dipole. An electric dipole with dipole moment p is in a uniform external electric field E. (a) Find the orientations of the dipole for which the torque on the dipole is zero.Problem 21
Three point charges are arranged on a line. Charge q3 = +5.00 nC and is at the origin. Charge q2 = -3.00 nC and is at x = +4.00 cm. Charge q1 is at x = +2.00 cm. What is q1 (magnitude and sign) if the net force on q3 is zero?Problem 21
Three point charges are arranged along the x-axis. Charge q1 = +3.00 mC is at the origin, and charge q2 = -5.00 mC is at x = 0.200 m. Charge q3 = -8.00 mC. Where is q3 located if the net force on q1 is 7.00 N in the -x-direction?Problem 21
Torque on a Dipole. An electric dipole with dipole moment p is in a uniform external electric field E. (b) Which of the orientations in part (a) is stable, and which is unstable? (Hint: Consider a small rotation away from the equilibrium position and see what happens.)Problem 21
Torque on a Dipole. An electric dipole with dipole moment p is in a uniform external electric field E. (c) Show that for the stable orientation in part (b), the dipole's own electric field tends to oppose the external field.Problem 21
Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (a) How many electrons does each sphere contain? (The atomic mass of aluminum is 26.982 g/mol, and its atomic number is 13.)Problem 21
A very long, straight wire has charge per unit length 3.20 * 10^-10 C/m. At what distance from the wire is the electricfield magnitude equal to 2.50 N/C?Problem 21
CP A proton is traveling horizontally to the right at 4.50 * 10^6 m/s. (a) Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of 3.20 cm.Problem 21
CP A proton is traveling horizontally to the right at 4.50 * 10^6 m/s. (b) How much time does it take the proton to stop after entering the field?Problem 21
CP A proton is traveling horizontally to the right at 4.50 * 10^6 m/s. (c) What minimum field (magnitude and direction) would be needed to stop an electron under the conditions of part (a)?Problem 21
A +8.75-mC point charge is glued down on a horizontal frictionless table. It is tied to a -6.50-mC point charge by a light, nonconducting 2.50-cm wire. A uniform electric field of magnitude 1.85 * 10^8 N/C is directed parallel to the wire, as shown in Fig. E21.34.
(a) Find the tension in the wire.
Problem 21
A +8.75-mC point charge is glued down on a horizontal frictionless table. It is tied to a -6.50-mC point charge by a light, nonconducting 2.50-cm wire. A uniform electric field of magnitude 1.85 * 10^8 N/C is directed parallel to the wire, as shown in Fig. E21.34.
(b) What would the tension be if both charges were negative?
Problem 21
Two positive point charges q are placed on the x-axis, one at x = a and one at x = -a. (a) Find the magnitude and direction of the electric field at x = 0.Problem 21
Electric Field of the Earth. The earth has a net electric charge that causes a field at points near its surface equal to 150 N/C and directed in toward the center of the earth. (a) What magnitude and sign of charge would a 60-kg human have to acquire to overcome his or her weight by the force exerted by the earth's electric field?Problem 21
(a) Calculate the magnitude and direction (relative to the +x-axis) of the electric field in Example 21.6. Example 21.6: A point charge q = -8.0 nC is located at the origin. Find the electric-field vector at the field point x = 1.2 m, y = -1.6 m.Problem 21
CP A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.60 cm distant from the first, in a time interval of 3.20 * 10^-6 s. (a) Find the magnitude of the electric field.Problem 21
CP A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.60 cm distant from the first, in a time interval of 3.20 * 10^-6 s. (b) Find the speed of the proton when it strikes the negatively charged plate.Problem 21
A -4.00-nC point charge is at the origin, and a second -5.00-nC point charge is on the x-axis at x = 0.800 m. (a) Find the electric field (magnitude and direction) at each of the following points on the x-axis: (i) x = 0.200 m; (ii) x = 1.20 m; (iii) x = -0.200 m. (b) Find the net electric force that the two charges would exert on an electron placed at each point in part (a).Problem 21
A -4.00-nC point charge is at the origin, and a second -5.00-nC point charge is on the x-axis at x = 0.800 m. (a) Find the electric field (magnitude and direction) at each of the following points on the x-axis: (i) x = 0.200 m; (ii) x = 1.20 m; (iii) x = -0.200 m. (b) Find the net electric force that the two charges would exert on an electron placed at each point in part (a).
Problem 21
A point charge q1 = -4.00 nC is at the point x = 0.600 m, y = 0.800 m, and a second point charge q2 = +6.00 nC is at the point x = 0.600 m, y = 0. Calculate the magnitude and direction of the net electric field at the origin due to these two point charges.
Problem 21
Electric Field of the Earth. The earth has a net electric charge that causes a field at points near its surface equal to 150 N/C and directed in toward the center of the earth. (b) What would be the force of repulsion between two people each with the charge calculated in part (a) and separated by a distance of 100 m? Is use of the earth's electric field a feasible means of flight? Why or why not?Problem 21
A charge of -6.50 nC is spread uniformly over the surface of one face of a nonconducting disk of radius 1.25 cm. (d) Why is the field in part (a) stronger than the field in part (b)? Why is the field in part (c) the strongest of the three fields?
