Two charges, qA and qB, are separated by a distance, d, and exert a force, F, on each other. Analyze Coulomb's law and answer the following questions.
What new force will exist if d is cut in half?
What new force will exist if qA is tripled and d is doubled?
and your thinking is ...?
d would be 1/4 * F
qA and d would be 6 * F
If the distance, d, between two charges is cut in half:
According to Coulomb's law, the force between two charges is inversely proportional to the square of the distance between them. This means that if the distance is reduced to half, the force will increase by a factor of 4 (since (1/2)^2 = 1/4). Therefore, the new force will be four times the original force.
If charge qA is tripled and distance d is doubled:
Coulomb's law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. If qA is tripled, the force exerted by qA on qB will also triple. If the distance, d, is doubled, the force will decrease by a factor of 4 (since 2^2 = 4). Therefore, the new force will be (3 * 1/4) = 3/4 times the original force.
Coulomb's law states that the force, F, between two charges, qA and qB, separated by a distance, d, is given by the equation:
F = (k * |qA * qB|) / d^2
where k is the electrostatic constant.
Let's analyze each question separately:
1. What new force will exist if d is cut in half?
To determine the new force, F_new, we need to substitute the new distance, d_new, into the Coulomb's law equation. Since d is halved, the new distance becomes d_new = d/2.
F_new = (k * |qA * qB|) / (d/2)^2 = (k * |qA * qB|) / (d^2/4) = 4 * (k * |qA * qB|) / d^2
Therefore, if the distance, d, is cut in half, the new force, F_new, will be four times greater than the original force, F.
2. What new force will exist if qA is tripled and d is doubled?
To determine the new force, F_new, with these changes, we substitute the new charge, qA_new, and the new distance, d_new, into the Coulomb's law equation. Since qA is tripled, the new charge becomes qA_new = 3qA. And since d is doubled, the new distance becomes d_new = 2d.
F_new = (k * |qA_new * qB|) / d_new^2 = (k * |3qA * qB|) / (2d)^2 = (3/4) * (k * |qA * qB|) / d^2
Therefore, if qA is tripled and d is doubled, the new force, F_new, will be three-fourths (0.75) of the original force, F.