Coulomb measured the deflection of sphere A when spheres A and B had equal charges and were a distance d apart. He then made the charge on B one-third the charge on A. How far apart would the two spheres then have had to be for A to have had the same deflection that it had before?
not 1/2
(9.0e^9)(1)(1)/(1)^2 = 9.0e^9
(9.0e^9)(1/4)(1) = 2.25e^9
2.25e^9/(1/2)^2 = 9.0e^9
1/2*d
Very far apart
To solve this problem, we can use the concept of Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's denote the charge on sphere A as Q_A, the charge on sphere B as Q_B, the initial distance between the spheres as d, and the new distance we want to find as d'.
According to the problem, when Q_A = Q_B and the distance is d, sphere A underwent a certain deflection. Now, the charge on B is one-third of A (Q_B = 1/3 Q_A), and we need to determine the new distance d' that would result in the same deflection for A.
We can set up the following equation using Coulomb's law:
F_initial = F_new
The initial force is given by:
F_initial = (k * Q_A * Q_B) / d^2
where k is the electrostatic constant. The new force will be:
F_new = (k * Q_A * Q_B) / d'^2
Since we want the two forces to be equal, we can set them equal to each other:
(k * Q_A * Q_B) / d^2 = (k * Q_A * Q_B) / d'^2
Q_A * Q_B are common on both sides, so we can cancel them out:
1 / d^2 = 1 / d'^2
To solve for d', we can rearrange the equation:
d'^2 = d^2
Finally, taking the square root of both sides, we find:
d' = d
Therefore, the new distance between the spheres, d', would be equal to the initial distance, d, in order for sphere A to have the same deflection as before, when the charge on B is one-third of the charge on A.
Please note that this answer assumes that the deflection of sphere A is solely determined by the electric force between spheres A and B, and no other forces or factors are influencing the deflection.