Two charges attract each other with a force of 16N. What will be the new force if the distance between them is reduced to 1/2 of its original value?
Two identical charges repel each other with a force
of 16N. If the distance between the charges is doubled, the force will be?
The force between two charges is given by 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. Mathematically, it can be expressed as:
F ∝ (q1 x q2) / r^2
Given that the initial force (F) is 16N, we can set up the equation as follows:
16N ∝ (q1 x q2) / r^2
Now, let's assume that reducing the distance to 1/2 of its original value results in a new force (F').
To find the new force, we need to determine the relationship between the changes in force and distance. Since the distance is reduced to half, the new distance (r') will be r/2.
Using the same equation, but with the new variables, we get:
F' ∝ (q1 x q2) / (r/2)^2
∝ 4(q1 x q2) / r^2
This tells us that the new force is four times the original force.
Therefore, the new force will be four times the original force, which is:
F' = 4 x 16N = 64N
To find the new force between the two charges when the distance between them is reduced to half its original value, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Mathematically, Coulomb's Law can be represented as:
F = k * (|q1 * q2|) / r^2
Where:
F is the electrostatic force between the charges,
k is Coulomb's constant (k = 9 x 10^9 N·m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
In this case, we are given that the original force F1 is 16N. Let's assume the original distance between the charges is d.
So, we have:
F1 = k * (q1 * q2) / d^2
Now, when the distance is reduced to half its original value (d/2), we can calculate the new force F2 as:
F2 = k * (q1 * q2) / (d/2)^2
To find the ratio between the two forces, we can divide the two equations:
F2 / F1 = (k * (q1 * q2) * d^2) / (k * (q1 * q2) * (d/2)^2)
Simplifying, we get:
F2 / F1 = (k * (q1 * q2) * d^2) / (k * (q1 * q2) * (d^2 / 4))
The k, q1, and q2 will cancel out in the equation, and simplifying further:
F2 / F1 = d^2 / (d^2 / 4)
F2 / F1 = 4
Therefore, we conclude that the new force F2 will be four times the original force F1.
In this case, the new force will be 16N x 4 = 64N.
the force is inversely proportional to the square of the distance (inverse-square relation)
the new force is 4 times the original
1 / (1/2)² = 1 / (1/4) = 4