Using Coulomb's law, the distance between the two like-charged table tennis balls with a force of repulsion of 8.2 x 10^-7 newtons and charges of 6.7 x 10^-9 coulombs each is found to be 0.70 meters. Here option B is correct.
To calculate the distance between the two charges using Coulomb's law, we apply the formula:
F = k * (|q_1 * q-2|) / r^2
Where F is the force between the charges, k is Coulomb's constant (9.0 × 10^9 N·m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
We know the force of repulsion (F) is 8.2 × 10^-7 newtons and each charge (q_1 and q_2) is 6.7 × 10^-9 coulombs. We can now rearrange the formula to solve for the distance r:
r^2 = k * (|q1 * q2|) / F
Plugging in the values:
r^2 = (9.0 × 10^9 * (6.7 × 10^-9 * 6.7 × 10^-9)) / 8.2 × 10^-7
r^2 = (9.0 × 10^9 * 44.89 × 10^-18) / 8.2 × 10^-7
r^2 = (404.01 × 10^-9) / 8.2 × 10^-7
r^2 = 0.4927 × 10^-2
Then, r = √(0.4927 × 10^-2)
r = √4.927 × 10^-4
r = 0.70 meters
Therefore, the distance between the two charges is 0.70 meters. Here option B is correct.