A charged rod is placed near an uncharged, nonconducting sphere suspended from a nonconducting wire, as shown below. Neither the rod nor anything else touches the sphere. (a) Will the rod and sphere exert forces on one another? If so, make a sketch showing the direction of the forces. (b) Would your answer to (a) change if the sphere were made out of conducting material? (c) What is the total charge on the sphere after the rod is placed close to it? (d) Do your answers to (a) and (c) violate Coulomb’s law? Explain.
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- Three charges are arranged as shown in the figure below. Find the magnitude and direction of the electrostatic force on the charge q = 5.16 nC at the origin. (Let r12 = 0.280 m.) Three-point charges lie along the axes in the x y-coordinate plane. Positive charge q is at the origin. A charge of 6.00 nC is at (r1 2, 0), where r1 2 > 0. A charge of −3.00 nC is at (0, −0.100 m).The figure below shows four small beads, each with a positive charge, at the corners of a square. The length of each side of the square is a. The bead at top-right has a charge of q; the one at lower-left has a charge of 8.0q; the other two each have a charge of 6.0g. (Assume that the +x-axis is to the right and the +y-axis is up along the page.) a 6.09 а 8.0g 6.0g a (a) What is the magnitude of the force on the bead with charge q? Express your answer in terms of k, q, and a in symbolic form. ka [12.485] F = a? What is the magnitude of the force due to each charge? (Be careful with distances.) What is the direction of each force? Using trigonometry, can you find the x- and y-components of each force? After finding the x- and y-components of the net force, how can you use them to find the magnitude of the net force? (b) What is the direction of the force on the bead with charge q? (Enter your answer in degrees counterclockwise from the +x-axis.) 45 ° counterclockwise from the +x-axisFive charges are arranged as shown in the figure; four identical charges form a square of side d while a fifth charge Q of mass m is suspended above the center of the square, a height d above its plane. (a) What is the charge Q if the charge is in equilibrium? (b) What type of equilibrium does the charge enjoy?
- Four identical charged particles (g = +10.1 µC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 64.2 cm and W = 14.6 cm. L (a) Calculate the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges. (b) Calculate the direction of the total electric force exerted on the charge at the lower left corner by the other three charges. ° (counterclockwise from the +x-axis)Four identical charged particles (q +10.4 pC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L 54.6 cm and W 14.7 cm L W (a) Calculate the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges. N (b) Calculate the direction of the total electric force exerted on the charge at the lower left corner by the other three charges. (counterclockwise from the x-axis)Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.140 N when their center-to-center separation is 63.8 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0403 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.)
- Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.120 N when their center-to-center separation is 55.0 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0511 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.) (a) Number Units (b) Number UnitsTwo identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.113 N when their center-to-center separation is 45.4 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0532 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.) Units (a) NumberT-0.05097 (b) NumberTo.04506 UnitsTcTwo identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.113 N when their center-to-center separation is 45.4 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0532 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.) (a) Number-0.000001 Units (b) NumberT0.0000026 UnitšTc