Electrostatics charged spheres problem

In summary, we discussed two problems. The first one involved two charged spheres suspended by silk threads and the rate at which charge leaks off each sphere due to various sources like ions and moisture in the atmosphere. The second problem involved a thin wire ring with an electric charge and the incremental force on the ring when a point charge is placed at its center. The solution to this problem involves calculating the force on each element of the ring and integrating it, resulting in an answer of ∆T=(qqo)/(8π^2ε0r^2).
  • #1
Kolahal Bhattacharya
135
1
1)Two small equally charged spheres, each of mass m, are suspended from the same point by silk threads of length l.The distance between the spheres x<<l.Find the rate dq/dt with which the charge leaks off each sphere if their approach velocity varies as v=a/(x)^0.5, a is a constant.
The problem can be done by expressing q^2 in equilibrium condition and then differentiating w.r.t. time.But I wonder why the charge leakage will occur?What principle makes it and how?
2)A thin wire ring of radius R has an electric charge q. What will be the increment of the force streatching the wire if a point charge qo is placed at the ring's centre?
It appeared to me that the direct mathematical formulation of E field, inside and outside the ring is rather difficult.so i tried to calculate the potential due to the ring and point charge.But, the integration to find contribution of the ring turned hopelessly difficult.Please help.
Kolahal Bhattacharya.
 
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  • #2
1) Due to ions in atmosphere cancelling charges on the spheres. These charged particles can originate from various sources - natural radioactivity in the vicinity/ground/materials in the surroundings.

A larger source of discharge works as follows. Any uncharged particle approaching the sphere will be induced with an opposite charge closest to the sphere. This will attract it to the sphere. Once stuck on it it will gain the same charge as the sphere (the particle was initially neutral). Now it will be repelled by the sphere, flying off into space carrying away some of the charge on the sphere.

Another possible route of discharge happens when the threads absorb moisture out of the atmosphere. This will make them conductive, providing a path for discharge.
 
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  • #3
I understand.But could you please clarify, what feature of this problem makes the charged sphere to gradually leak out the charge.In other words, why the charge leakage is necessary in this problem?
What about my next problem?
 
  • #4
Kolahal Bhattacharya said:
I understand.But could you please clarify, what feature of this problem makes the charged sphere to gradually leak out the charge.In other words, why the charge leakage is necessary in this problem?

To be honest with you, this is one of Irodov's artificial sounding problems :smile:

What about my next problem?

On-axis field due to a ring is fairly easy to compute. But you don't need it here.

When you place the point charge at the center of the ring, the ring experiences a net outward (repulsive) force. Can you calculate the force on an element of the ring due to the charge and integrate it?
 
  • #5
I did it:
dF=k ∫(q0λdl)/r^2
put dl=r dφ
have dF=k ∫(q0λr dφ)/r^2
Then, dF=(kq0λ/r) ∫dφ
integrating o to 2 pi, F=...
The answer is (Irodov):∆T=(qqo)/(8π^2ε0r^2)
So this is not the way you led.
 
  • #6
Yeah that's it.
 

1. What is the concept of electrostatics charged spheres problem?

The electrostatics charged spheres problem refers to a scenario where two or more spheres with different charges are placed in close proximity to each other. This leads to an interaction between the charges, resulting in a force acting on each sphere.

2. How is the force between charged spheres calculated?

The force between charged spheres can be calculated using 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 the spheres. It can be expressed using the equation F = kQ1Q2/r^2, where k is the Coulomb's constant, Q1 and Q2 are the charges on the spheres, and r is the distance between them.

3. What is the principle of superposition in electrostatics charged spheres problem?

The principle of superposition states that the total force on a charged sphere is the vector sum of the individual forces from each other charged sphere. This means that the force between two charged spheres is not affected by the presence of other charged spheres in the system.

4. How does the distance between charged spheres affect the force between them?

As per Coulomb's Law, the force between charged spheres is inversely proportional to the square of the distance between them. This means that as the distance between the spheres increases, the force between them decreases. Conversely, as the distance decreases, the force increases.

5. What are some real-life applications of electrostatics charged spheres problem?

Electrostatics charged spheres problem has various real-life applications, such as in the functioning of Van de Graaff generators, electrostatic air cleaners, and electrostatic precipitators used in air pollution control. It also plays a crucial role in understanding the behavior of charged particles in the atmosphere, leading to advancements in weather forecasting and lightning protection systems.

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