Imagine two equally charged objects that are hanging a certain distance from one another. How does the force between them change if the distance between them triples?
a
The force becomes 9x's greater
b
The force is 1/9 as great
c
The force is 1/3 as great
d
The force becomes 3x's greater
b) The force is 1/9 as great.
The force between two charged objects is inversely proportional to the square of the distance between them. This means that if the distance between them triples, the force between them will decrease by a factor of 9 (3 squared). Therefore, the force is 1/9 as great.
The force between two charged objects can be calculated using Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
F = k * (q1 * q2) / r^2
In this case, let's say the force between the two objects is F. If the distance between them triples, it means the new distance between them is 3 times the original distance (3r).
To determine how the force changes, we can compare the new force (F') to the original force (F) using the equation above:
F' = k * (q1 * q2) / (3r)^2
Simplifying the equation:
F' = k * (q1 * q2) / 9r^2
As we can see from the equation, the force becomes 1/9 as great as the original force.
Therefore, the correct answer is option b: The force is 1/9 as great.
The correct answer is option b: The force is 1/9 as great.
According to Coulomb's law, the force between two charged objects is inversely proportional to the square of the distance between them.
In this case, when the distance between the two objects triples, it means that the distance is multiplied by a factor of 3. Hence, the force between them will decrease by a factor of (3^2) or 9.
Therefore, the force between the objects will be 1/9th (1/9) as great as it was before the distance tripled.