Electrostatics physics help

In summary, a charged spherical shell has E=0 throughout its interior and the center is not a point of potential minimum according to Laplace's equation and Earnshaw's theorem. It also cannot be a point of unstable equilibrium and seems to be a point of neutral equilibrium, but this may need confirmation. However, if a conductor is introduced and the charge is moved inside, the surface charge distribution may affect the conclusion and result in an unstable equilibrium.
  • #1
Well,I think this is interesting.I invite people to think over it.
consider a charged spherical shell.Throughout its interior,E=0.
Now,consider the centre.From Laplace's equation and Earnshaw's theorem,this point is not a point of potential minimum.So,a charge at this point cannot be in stable equilibrium.Say,you displace it slightly.
What do you find.It just gets stagnant where you left it!
If this is not a point of stable eqlbm,it is not also a point of unstable equilibrium.
So,is it a point of neutral equilibrium?
Apparently seems so.But,I wish to confirm.
 
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  • #2
Kolahal Bhattacharya said:
it is not also a point of unstable equilibrium.

Why not?

Claude.
 
  • #3
if you displace it slightly, that is, if you nudge it: it will keep moving in that direction, eventually leaving the interior. Seems unstable.
 
  • #4
While it is the lowest value the potential can have, it doesn't have to count as stable equilibrium because the function is not derivable, and it's not a local minimum.
 
  • #5
I'm not sure the premise is set up correctly: If the sphere is _empty_, then yes E=0. But now there's some E once the charge is inserted.
 
  • #6
The center is not a point of minimum potential simply because the field is 0 throughout the sphere. Every point in the interior of the sphere is a point of "neutral equilibrium". What's so strange about that?
 
  • #7
I agree with HallsofIvy:
What's so strange about that?
However,think of the case,where you have a sphere on which charge can move.Say,a conductor.As you move the charge inside,the surface charge distribution may be affected.Then,what would be the conclusion?
 
  • #8
Kolahal Bhattacharya said:
I agree with HallsofIvy:

However,think of the case,where you have a sphere on which charge can move.Say,a conductor.As you move the charge inside,the surface charge distribution may be affected.Then,what would be the conclusion?

You would be dealing with an electrodynamics. However, the time it takes for the system to return to the electrostatic limit is extremely short.
 
  • #9
However,I found it.The resulting case will be unstable equilibrium.
 

1. What is electrostatics physics?

Electrostatics physics is a branch of physics that deals with the study of stationary electric charges and their interactions. It involves the study of electric fields, electric potential, and the behavior of charged particles under the influence of these fields.

2. How does electrostatics differ from electrodynamics?

Electrostatics deals with stationary charges, while electrodynamics deals with moving charges. In electrostatics, the electric field is constant, but in electrodynamics, it can change over time due to the movement of charges.

3. What is Coulomb's Law and how is it used in electrostatics?

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. It is used in electrostatics to calculate the force between two charged particles or to determine the electric field at a specific point.

4. What is an electric dipole?

An electric dipole is a pair of equal and opposite charges separated by a small distance. It is a fundamental concept in electrostatics and is used to explain the behavior of polar molecules and the formation of electric fields.

5. How is electrostatics applied in everyday life?

Electrostatics has various applications in everyday life, including in technologies such as batteries, generators, and electronic devices. It is also used in industrial processes like painting, air filters, and electrostatic precipitators. Additionally, electrostatic forces play a role in natural phenomena like lightning and the formation of auroras.

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