Can a Positive Charge be in Stable Equilibrium in the Center of a Square According to Earnshaw's Theorem?

  • Thread starter Thread starter lamp post
  • Start date Start date
  • Tags Tags
    Theorem
AI Thread Summary
A positive charge placed at the center of a square formed by four charges appears to be in equilibrium but is not in stable equilibrium. According to Earnshaw's theorem, no particle can achieve stable equilibrium under electrostatic forces alone. If the central charge is slightly displaced, it will not return to the center, confirming the lack of stability. The distinction between equilibrium and stable equilibrium is crucial in understanding this phenomenon. Thus, while the charge is balanced at the center, it is inherently unstable.
lamp post
Messages
11
Reaction score
0
we have got four charges placed at the ends of a square. if we palce a positive charge in the center, it appeares to be in stable equillibrium; yet earnshaw's theorem(that no particle can be in stable equillibrium if it is under the action of electrostatic forces only) holds. Why is that?
 
Physics news on Phys.org
Earnshaw's theorem

The charge at the center of the square is in equilibrium, yes. But it is not in stable equilibrium. Stable equilibrium means that if you move the charge slightly in any direction, then it should return to the center. In this case, as in every other case involving electrostatic forces only, if you move the charge, from the center, it will not return. Check that out.
 
Hello! Let's say I have a cavity resonant at 10 GHz with a Q factor of 1000. Given the Lorentzian shape of the cavity, I can also drive the cavity at, say 100 MHz. Of course the response will be very very weak, but non-zero given that the Loretzian shape never really reaches zero. I am trying to understand how are the magnetic and electric field distributions of the field at 100 MHz relative to the ones at 10 GHz? In particular, if inside the cavity I have some structure, such as 2 plates...
Back
Top