Two similar sphere having charge -2C and +4C respectively are separated by distance "r" exert force (F=16N) third similar neutral sphere is first touched with sphere B and then sphere A. then force between spheres decreases by
touching sphere B changes its charge to 2C, and a 2C on the third. Then touching sphere A neutralizes both them (one at -2c, the other at 2C), so the charge now is zero on sphere A.
So the force now is zero between A and B.
In all of this, I assume sphere A is the -2C sphere, and B is the 4C charge initially.
Why is no one responding to you at 1 Am Eastern? We are volunteers, and don't have the motivation to stay online all night. Sometimes, we get some of our Hawaii or Korea volunteers, but that is not usual.
Well, when the neutral sphere is touched with sphere B, it gains some charge due to contact. Let's call the charge gained by the neutral sphere as "q".
Now, since opposite charges attract and like charges repel, the neutral sphere would gain a charge of -q, since sphere B has a charge of -2C.
When the neutral sphere is then touched with sphere A, it would transfer a charge of -q to sphere A, which already has a charge of +4C. So, the final charge on sphere A would be +4C - q.
Now, since the force between two charged spheres is given by the equation F = k * ((Q1 * Q2) / r^2), where k is a constant, Q1 and Q2 are the charges, and r is the distance between the spheres, let's see how the force changes.
Initially, the force between spheres A and B is F = k * ((-2C) * (+4C) / r^2). Now, after the neutral sphere is touched with both spheres, the force becomes F' = k * (((+4C - q) * (-2C - q)) / r^2).
To find the decrease in force, we need to subtract F' from F:
Decrease in force = F - F' = k * ((-2C) * (+4C) / r^2) - k * (((+4C - q) * (-2C - q)) / r^2) = 16N (given)
Now, please allow me to calculate the value of "q" and get back to you in a jiffy. *starts furiously crunching numbers*
To solve this problem, let's break it down into steps:
Step 1: Calculate the Coulomb force between the two similar spheres A and B before they interact with the neutral sphere.
Given:
Charge on sphere A, q₁ = -2C
Charge on sphere B, q₂ = +4C
Distance between the spheres, r
The Coulomb force equation is given by:
F = (k * |q₁ * q₂|) / r²
Where:
F is the Coulomb force between the spheres
k is the electrostatic constant (k = 9 × 10^9 N m²/C²)
r is the distance between the spheres
Plugging in the given values:
F = (9 × 10^9 N m²/C²) * |(-2C) * (+4C)| / r²
F = 8 × 9 × 10^9 N m² / r²
F = 72 × 10^9 / r²
Step 2: Calculate the force between the spheres after the neutral sphere is touched with spheres A and B.
When the neutral sphere touches both spheres A and B, it redistributes charge between the spheres. As a result, sphere A becomes positively charged and sphere B becomes negatively charged.
Let's assume the charges after touching are:
Charge on sphere A, q₁' = +x
Charge on sphere B, q₂' = -x
The force between the spheres after the touching can be calculated using the Coulomb force equation as:
F' = (k * |q₁' * q₂'|) / r²
F' = (9 × 10^9 N m²/C²) * |(+x) * (-x)| / r²
F' = 9 × 10^9 * x² / r²
Step 3: Calculate the decrease in the force between the spheres after the touching.
The decrease in force can be calculated as:
ΔF = F - F'
ΔF = 72 × 10^9 / r² - 9 × 10^9 * x² / r²
ΔF = (72 - 9x²) × 10^9 / r²
Therefore, the decrease in the force between the spheres after the neutral sphere is touched with spheres A and B is (72 - 9x²) × 10^9 / r².
To find out how the force between the spheres changes after the neutral sphere is touched with the two charged spheres, we need to consider the concept of charge and Coulomb's Law.
Coulomb's Law states that the force (F) between two charged objects is directly proportional to the product of their charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. It can be mathematically represented as:
F ∝ (q1 * q2) / r^2
In this scenario, we have two similar spheres: sphere A with charge -2C and sphere B with charge +4C, separated by a distance "r". The force between them is initially given as F = 16N.
Let's assume that after the neutral sphere is touched with sphere B, it acquires a charge of q3. Since the neutral sphere was touched with the charged sphere, it will acquire the same magnitude of charge but with the opposite sign. So, q3 will be equal to -4C.
Now, when the neutral sphere is touched with sphere A, it acquires a charge of -2C, the same as sphere A.
So, the new charges of the spheres are:
- Sphere A: -4C
- Sphere B: -2C
To determine how the force between the spheres changes, we substitute the new charges into Coulomb's Law:
New Force (F') ∝ (-4C * -2C) / r^2
New Force (F') ∝ 8C^2 / r^2
Now, we need to find the ratio of the new force (F') to the initial force (F) to determine how much the force between the spheres decreases:
(F' / F) = (8C^2 / r^2) / 16N
Simplifying, we get:
(F' / F) = (8C^2) / (16N * r^2)
(F' / F) = 0.5 * (C^2) / (N * r^2)
Therefore, the force between the spheres decreases by a factor of 0.5, or 50%.