Two charged bodies exert a force of 0.415 N on each other. If they are moved so that they are one-third as far apart, what force is exerted?
.137
To calculate the force between the two charged bodies, you can use Coulomb's Law. Coulomb's Law states that the force between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:
F = (k * q1 * q2) / r^2
Where:
F is the force between the charged bodies.
k is the Coulomb's constant (k = 8.99 * 10^9 Nm^2/C^2).
q1 and q2 are the charges of the bodies.
r is the distance between the bodies.
Let's say that the force exerted between the bodies at the initial distance is 0.415 N. We'll denote this initial distance as r1.
Now, if the bodies are moved so that they are one-third as far apart, the new distance between them is r2.
We need to find out what the force, F2, will be at the new distance.
To do that, we can use the following proportional relationship:
F1 / F2 = (r2 / r1)^2
Substituting the known values:
0.415 N / F2 = (1/3)^2
Simplifying the equation:
0.415 N / F2 = 1/9
Cross multiplying:
F2 = 0.415 N * 9
F2 = 3.735 N
Therefore, at one-third the initial distance, the force exerted between the charged bodies is 3.735 N.