Stability of 4 Charged Particles at Square Corners

In summary, the conversation discusses the stability of a central point in a square with 4 positively charged particles, and whether there is a more elegant proof for this stability besides computing the 2nd partial derivatives of the potential energy. One suggestion is to calculate the force at a small displacement and show that it always points back to the center. Coulomb's law is mentioned as a relevant equation.
  • #1
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Homework Statement


Hi, I have a solution to this, but I am looking for a more elegant solution. If we are given 4 positively charged particles at the 4 corners of a square, is there a better proof for the stability of the central point of square for a 5th positively charged particle apart from (the clumsy way of) computing the 2nd partial derivatives of the U(x,y)...? Thanks!

Homework Equations


Coulomb's law

The Attempt at a Solution


computing the 2nd partial derivatives of the U(x,y)
 
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  • #2
in essence it's the same but how about just calculating the force at a small displacement and show it always points back to the centre?
 

FAQ: Stability of 4 Charged Particles at Square Corners

What is the "Stability of 4 Charged Particles at Square Corners" experiment?

The "Stability of 4 Charged Particles at Square Corners" experiment is a scientific study that investigates the behavior and stability of four charged particles when placed at the corners of a square-shaped container. This experiment is commonly used to understand the interactions between charged particles and how they affect the overall stability of a system.

What is the purpose of the experiment?

The purpose of the experiment is to study the equilibrium and stability of a system of four charged particles at the corners of a square container. By understanding the forces and interactions between the particles, scientists can gain insights into the behavior of charged particles in various systems and environments. This knowledge can also be applied to practical applications, such as in the design of electronic devices and materials.

How is the stability of the particles determined?

The stability of the particles is determined by analyzing the forces acting on them. In this experiment, the forces of attraction and repulsion between the particles are calculated using Coulomb's law. If the forces are balanced, the particles will remain in equilibrium and the system will be stable. However, if the forces are unbalanced, the particles will move and the system will be unstable.

What factors affect the stability of the particles?

There are several factors that can affect the stability of the particles in this experiment. These include the magnitude and direction of the charges, the distance between the particles, and the geometry of the container. Other factors such as external forces and changes in temperature can also influence the stability of the system.

What are the potential applications of this experiment?

The "Stability of 4 Charged Particles at Square Corners" experiment has potential applications in various fields, including physics, chemistry, and materials science. It can also be useful in understanding the behavior of charged particles in biological systems. Additionally, the findings from this experiment can be applied to the design and development of electronic devices, such as transistors and microchips.

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