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:
Well, this situation sounds electrifying! Let's see if I can crack a joke while explaining the concept.
When two spheres with opposite charges get close, it's like the start of a shocking romance. Sphere A is negative (-2C), while Sphere B is positive (+4C). They're attracted to each other, and the distance between them is "r".
Now, when a neutral sphere gets involved, things get even more interesting. Let's call it Sphere C.
When Sphere C touches Sphere B, it's like a spark of friendship. However, Sphere C is still neutral, so it won't contribute any charge. But it changes the electric environment between Sphere A and Sphere B.
When Sphere C touches Sphere A, it's like another spark, but this time, it's like they instantly became best friends. This causes a redistribution of charges between Sphere A and Sphere B.
Now, what happens to the force between Sphere A and Sphere B?
After Sphere C touches Sphere A, the force between them decreases. But by how much? Hmm...
To figure this out, we need to understand Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges (Q1 * Q2) and inversely proportional to the square of the distance between them (r^2).
So, initially, the force between Sphere A and Sphere B was 16N. Now, after Sphere C gets involved, it decreases, but we need to determine the exact amount.
Since Sphere A is negative and Sphere B is positive, they attract each other. So, when they come closer due to the influence of Sphere C, their force decreases.
But without knowing the precise charges of Sphere A and Sphere B after Sphere C's involvement, it's impossible to calculate the exact decrease in force. We would need more information about the redistribution of charges between the spheres.
So, my answer is: The decrease in force depends on how the charges are redistributed, which we don't know. But something tells me that Sphere C's interference made quite a shocking impact, leaving Sphere A and Sphere B with a different kind of charge in their electrifying relationship!
To find out how the force between the spheres changes when the third neutral sphere is touched with sphere B and then sphere A, we need to consider the principles of electrostatics.
1. Initially, the two spheres have charges of -2C and +4C respectively. The force between them is given as F = 16N.
2. When the third sphere, which is neutral, is touched with sphere B, some charge is transferred between them until they reach equilibrium.
3. Since sphere B has a charge of -2C, it will lose some negative charge to the neutral sphere. Let's assume it loses xC of charge.
4. The neutral sphere will then acquire a charge of -xC.
5. Sphere B now has a charge of (-2C - xC) = (-2 - x)C.
6. Now, when the neutral sphere is touched with sphere A, the charges are transferred until equilibrium is reached again.
7. Sphere A has a charge of +4C, and since the neutral sphere has a charge of -xC, it will acquire a charge of -(-x)C = xC.
8. Sphere A now has a charge of (+4C + xC) = (4 + x)C.
9. The new force between the spheres can be calculated using Coulomb's law, which states that F = k * (q1 * q2) / r^2, where k is the electrostatic constant, q1 and q2 are the charges on the spheres, and r is the separation distance.
10. Let's assume that the separation distance remains unchanged.
11. Initially, F = 16N, so we have 16 = k * ((-2C) * (+4C)) / r^2.
12. After the charges are transferred, the new force is given by F' = k * ((-2 - x)C) * ((4 + x)C) / r^2.
13. To find how the force changes, we need to calculate the ratio of the old force to the new force: F'/F = (k * ((-2 - x)C) * ((4 + x)C) / r^2) / (k * ((-2C) * (+4C)) / r^2).
14. Simplifying the expression, we get F'/F = ((-2 - x) * (4 + x)) / (-2 * 4) = ((-2 - x) * (4 + x)) / -8.
15. Expanding the expression, we have F'/F = (8 + 2x - 4x - x^2) / -8 = (8 - 2x - x^2) / -8.
Therefore, the force between the spheres decreases by a factor of (8 - 2x - x^2) / 8.
To determine how the force between the two spheres changes when a third neutral sphere is touched with both spheres A and B, we need to apply Coulomb's Law and the principle of superposition.
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. It can be expressed as:
F = (k * q1 * q2) / r^2
where F is the force, k is the electrostatic constant, q1 and q2 are charges of the respective objects, and r is the distance between them.
Initially, we have two spheres, A and B, with charges of -2C and +4C, respectively. Let the distance between them be r1. The force between A and B is given as 16N.
F1 = 16N
Now, when a third neutral sphere is touched with both spheres A and B, the charges redistribute due to the principle of superposition. The third sphere becomes charged while spheres A and B may have different charges as well.
Let the new charges of spheres A, B, and the third sphere be q1', q2', and q3', respectively. The distance between the spheres remains r.
Now, the force between A and B after the redistribution of charges can be expressed as:
F2 = (k * q1' * q2') / r^2
Since the third sphere is neutral, it does not contribute to the force between A and B. Therefore, we can write:
F2 = (k * q1' * q2') / r^2 = F1
Simplifying the equation, we have:
(q1' * q2') / r^2 = (q1 * q2) / r1^2
Since r = r1, we can cancel out r^2 from both sides:
(q1' * q2') = (q1 * q2)
Now, we can substitute the given charges:
(-2C * q2') = (-2C * 4C)
Simplifying further, we get:
q2' = 4C
So, the final charge on sphere B is 4C.
To determine how the force between A and B changes, we need to calculate the new force F2 using the new charges:
F2 = (k * q1' * q2') / r^2 = (k * (-2C) * 4C) / r^2
Since we know that F2 = F1, we can rearrange the equation to find the decrease in force:
(F1 - F2) / F1 * 100%
Substituting the given values, we have:
(16N - [(k * (-2C) * 4C) / r^2]) / 16N * 100%