Electric Potential: Why Is It Equal in Both Spheres?

[Jalo]

Homework Statement

Imagine two conductor spheres with radius r1 and r2, so that r1 > r2.
The two spheres are connected by a infinitely long wire, and the total charge of the system is Q.
What's the ratio of the potential of the first sphere by the potential of the second sphere?

Homework Equations

The Attempt at a Solution

I solved the problem. However to accomplish that I had to say that the electric potential is equal in both spheres, and that's what I'm having trouble understanding.
Why is the electric potential equal in both spheres?

Thanks in advance!

 

[Simon Bridge]

The two spheres are connected by a conductor.

 

[Jalo]

The two spheres are connected by a conductor.

Could you be more specific?
I know that they are connected by a conductor, but why does that result in them having the same charge?

 

[Simon Bridge]

Any two conductors which are electrically connected must have the same voltage. (NOT charge.)
You know this... if only from your work on electric circuits.

If there is a potential difference between the spheres then what would you expect to have in the wire joining them?

 

[Nickie]

As a scientist, it is important to understand the concept of electric potential and how it relates to the behavior of charged particles. In this scenario, we have two conductor spheres with different radii, connected by a wire and having a total charge of Q. The question is asking for the ratio of the potential of the first sphere to the potential of the second sphere.

First, let's define electric potential. Electric potential is the amount of potential energy per unit charge at a given point in an electric field. In other words, it is a measure of the amount of work needed to move a unit of charge from one point to another in an electric field.

In this scenario, both spheres are connected by a wire, which means that they are in the same electric field. This also means that the potential at any point on the wire is the same, as the potential is a property of the electric field. Therefore, the potential at the surface of both spheres must also be the same.

To understand why the electric potential is equal in both spheres, we can look at the behavior of charged particles in an electric field. When a charged particle is placed in an electric field, it will experience a force and move in the direction of the field. However, when it reaches a surface of a conductor, the charge will redistribute itself on the surface in such a way that the electric field inside the conductor is zero. This is known as electrostatic equilibrium.

In this scenario, both spheres are conductors, meaning that the charges on their surfaces will redistribute to create a zero electric field inside. This results in the electric potential at the surface of both spheres being equal. Therefore, the ratio of the potential of the first sphere to the potential of the second sphere is 1:1.

In conclusion, the electric potential is equal in both spheres because of the concept of electrostatic equilibrium, where the charges on the surface of conductors redistribute to create a zero electric field inside. This is an important concept to understand in the study of electric potential and its applications in various fields of science and technology.