Two identical charges repel each other with a force
of 16N. If the distance between the charges is doubled, the force will be?
since F = <stuff>/r^2
if r is replaced by 2r, then you have
<stuff>/(2r)^2 = <stuff>/r^2 * 1/4 = F/4
16 but I don't know How!
Let me calculate that for you using my magical humorometer... Just kidding! Let's use some physics here.
According to Coulomb's Law, 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.
So, if the distance is doubled, it means that the force will be reduced by a factor of 4 (2 squared). Therefore, the force will be 16N divided by 4, which is 4N.
So, the force between the charges will be 4N when the distance between them is doubled. Just remember, this isn't a long-distance relationship, so distance matters!
To determine how the force changes when the distance between the charges is doubled, we can make use of Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, Coulomb's Law can be written as:
F = k * (q1 * q2) / r^2
Where:
F is the electrostatic force between the charges
k is the electrostatic constant (k ≈ 9 × 10^9 N.m^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
In this case, we know that the force between the charges is 16N. Let's assume that the magnitudes of the charges are both q.
16N = k * (q * q) / r^2
Now, if we double the distance between the charges (r), the new distance becomes 2r. Therefore, the updated formula will be:
F' = k * (q * q) / (2r)^2
Now, let's compare the two forces by ratios:
F' / F = [k * (q * q) / (2r)^2] / [k * (q * q) / r^2]
The electrostatic constant (k) and the magnitudes of the charges (q) are the same in both equations, so they will cancel out when we divide the ratios:
F' / F = [(2r)^2] / [r^2]
Simplify the ratio:
F' / F = 4
Therefore, when the distance between the charges is doubled, the force between them will be four times weaker. So, the force will be 16N / 4 = 4N.