n Fig. 21-41, three identical conducting spheres initially have the following charges: sphere A, 7Q; sphere B, -8Q; and sphere C, 0. Spheres A and B are fixed in place, with a center-to-center separation that is much larger than the spheres. Two experiments are conducted. In experiment 1, sphere C is touched to sphere A and then (separately) to sphere B, and then it is removed. In experiment 2, starting with the same initial states, the procedure is reversed: Sphere C is touched to sphere B and then (separately) to sphere A, and then it is removed. What is the ratio of the electrostatic force between A and B at the end of experiment 2 to that at the end of experiment 1?
Diagram:
A ----------B
C
butuh bantuan
n Fig. 21-41, three identical conducting spheres initially have the following charges: sphere A, 7Q; sphere B, -8Q; and sphere C, 0. Spheres A and B are fixed in place, with a center-to-center separation that is much larger than the spheres. Two experiments are conducted. In experiment 1, sphere C is touched to sphere A and then (separately) to sphere B, and then it is removed. In experiment 2, starting with the same initial states, the procedure is reversed: Sphere C is touched to sphere B and then (separately) to sphere A, and then it is removed. What is the ratio of the electrostatic force between A and B at the end of experiment 2 to that at the end of experiment 1?
n Fig. 21-41, three identical conducting spheres initially have the following charges: sphere A, 7Q; sphere B, -8Q; and sphere C, 0. Spheres A and B are fixed in place, with a center-to-center separation that is much larger than the spheres. Two experiments are conducted. In experiment 1, sphere C is touched to sphere A and then (separately) to sphere B, and then it is removed. In experiment 2, starting with the same initial states, the procedure is reversed: Sphere C is touched to sphere B and then (separately) to sphere A, and then it is removed. What is the ratio of the electrostatic force between A and B at the end of experiment 2 to that at the end of experiment 1?
To solve this problem, we need to understand how the charges on the spheres redistribute when they are touched together.
In Experiment 1, sphere C is touched to sphere A and then sphere B. When two objects with different charges touch each other, the charges redistribute themselves until they reach a state of equilibrium. In this case, since sphere C is initially uncharged (0 charge), it will acquire a charge equal in magnitude but opposite in sign to the sphere it is touched to.
So, when sphere C is touched to sphere A, it acquires a charge of -7Q (equal in magnitude and opposite in sign to the charge on A). Then, when sphere C is touched to sphere B, it acquires a charge of +7Q (equal in magnitude and opposite in sign to the charge on B).
At the end of Experiment 1, the charges of the spheres are:
Sphere A: 7Q - 7Q = 0
Sphere B: -8Q + 7Q = -Q
Sphere C: 7Q
Now, let's move on to Experiment 2. In this experiment, starting with the same initial states as before, sphere C is touched to sphere B and then sphere A.
When sphere C is touched to sphere B, it acquires a charge of +8Q (equal in magnitude and opposite in sign to the charge on B). Then, when sphere C is touched to sphere A, it acquires a charge of -8Q (equal in magnitude and opposite in sign to the charge on A).
At the end of Experiment 2, the charges of the spheres are:
Sphere A: 7Q - 8Q = -Q
Sphere B: -8Q + 8Q = 0
Sphere C: -8Q
Now, let's calculate the electric force between spheres A and B at the end of each experiment.
The electrostatic force between two charged objects is given by Coulomb's law:
F = k * |q1 * q2| / r^2
Where:
F is the electric force between the charges q1 and q2.
k is the electrostatic constant (approximately 9 * 10^9 N m^2/C^2).
r is the distance between the centers of the two charges.
In both experiments, the charges on the spheres are different. So, let's calculate the ratio of the electrostatic force between A and B at the end of Experiment 2 to that at the end of Experiment 1.
For Experiment 1:
F1 = k * |0 * (-Q)| / r^2 = 0
For Experiment 2:
F2 = k * |(-Q) * 0| / r^2 = 0
Therefore, the ratio of the electrostatic force between A and B at the end of Experiment 2 to that at the end of Experiment 1 is:
F2/F1 = 0/0 = Undefined (since both forces are zero)
In conclusion, the ratio is undefined because the electric forces between spheres A and B at the end of both experiments are zero.