Two point charges are separated by 6 cm. The attractive force between them is 20 N. Find the force between them when they are separated by 12 cm. (Why can you solve this problem without knowing the magnitudes of the charges?)
i don't get it at all
Use the inverse square rule. You have doubled the separation distance. Look at Coulomb's law and see what that does to the force.
You can solve this problem without knowing the magnitudes of the charges because the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. This relationship is described by Coulomb's law.
Let's say the initial separation between the charges is 6 cm, and the force between them is 20 N.
Using Coulomb's law, we can write the equation as:
F₁ = k * (q₁ * q₂) / r₁²
where F₁ is the force between the charges, k is the electrostatic constant, q₁ and q₂ are the magnitudes of the charges, and r₁ is the initial separation between them.
Now, let's find the force when they are separated by 12 cm:
F₂ = k * (q₁ * q₂) / r₂²
where F₂ is the force between the charges when they are separated by 12 cm, and r₂ is the new separation.
Since we don't know the magnitudes of the charges, let's assume they are the same values for both cases:
F₁ = k * (q * q) / r₁²
F₂ = k * (q * q) / r₂²
We can see that the only changing factor is the distance between the charges (r₁ vs. r₂).
Using the ratio of the distances, we have:
(r₁ / r₂)² = (6 cm / 12 cm)²
= (1/2)²
= 1/4
Therefore, (r₁ / r₂)² = 1/4.
So, we can rewrite the equation for F₂ as:
F₂ = [(r₁ / r₂)²] * F₁
= (1/4) * 20 N
= 5 N
Hence, the force between the charges when they are separated by 12 cm is 5 N, regardless of the magnitudes of the charges.
To solve this problem without knowing the magnitudes of the charges, we can use Coulomb's Law. Coulomb's Law states that the force between two charged particles 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 ∝ (q₁ * q₂) / r²
Where:
F is the force between the charges
q₁ and q₂ are the magnitudes of the charges
r is the distance between the charges
In this problem, we have the following information:
- The initial separation distance between the charges is 6 cm, and the attractive force is 20 N.
- We want to find the force between the charges when they are separated by 12 cm.
Since we don't know the magnitudes of the charges, we can represent them as q₁ and q₂.
Now, let's use a proportionality relationship to find the force when the charges are separated by 12 cm. We can set up the following equation:
F₁ / F₂ = (r₁ / r₂)²
In this equation:
- F₁ and F₂ represent the forces at the initial and final separation distances.
- r₁ and r₂ represent the initial and final separation distances.
We can substitute the given values into the equation:
20 N / F₂ = (6 cm / 12 cm)²
Simplifying the equation:
20 N / F₂ = 0.5²
20 N / F₂ = 0.25
To solve for F₂, isolate it on one side of the equation:
F₂ = 20 N / 0.25
F₂ = 80 N
Therefore, the force between the charges when they are separated by 12 cm is 80 N, regardless of the magnitudes of the charges.