Consider a system consisting of two oppositely charged spheres hanging by strings and separated by a distance r1, as shown in the accompanying illustration. Suppose they are separated to a larger distance r2 , by moving them apart along a track.
What is the potential energy, postive of negative or reamins the saem?
What effect does it do on the total energy/
What can you say about the q and w in this process?
The potential energy increases.
Delta E is positive for the process.
The sign q is undetermined; w is positive.
PE increases
Well, well, well, let's unravel this electrifying situation!
First things first, when the oppositely charged spheres are brought closer together, their potential energy would be negative. Why negative, you ask? Well, when objects of opposite charges get together, they can't help but attract each other. It's like a romantic comedy, but with electrical charges. So, their potential energy decreases, resulting in a negative value.
Now, when the spheres are separated to a larger distance, the potential energy increases. And just like that, we have a positive potential energy! It's like a rollercoaster ride, only for charges.
But what about the total energy, you inquire? Well, the total energy of the system is conserved. It remains the same throughout the process. Just like my love for laughter, energy cannot be created or destroyed, only transferred.
Lastly, let's talk about q and w. Q refers to the charge of the spheres, and w represents the work done on the system. In this process, q remains constant since the charge of the spheres doesn't change. However, the work done on the system is negative when the spheres are brought closer together and positive when they are separated.
So, in a nutshell, potential energy changes, total energy remains the same, and q and w play their parts in this electrifying dance.
The potential energy of a system of two oppositely charged spheres depends on the distance between them. When the spheres are separated to a larger distance (r2) by moving them apart along a track, the potential energy of the system increases. This increase in potential energy is usually positive.
Regarding the effect on the total energy, in this case, the total energy of the system also increases. The total energy of the system is the sum of the kinetic energy and potential energy. As the potential energy increases, the total energy of the system increases as well.
In terms of q (charge) and w (work), during this process of separating the spheres, the charge (q) remains the same as it does not change. However, work (w) is done in order to move the spheres apart. In this case, work is done against the electrostatic force between the charged spheres. The work done is positive as the force and displacement are in the same direction.
To determine the potential energy of the system, we need to consider the equation for electric potential energy:
PE = k * (|q1 * q2|) / r
where PE is the potential energy, k is a constant (Coulomb's constant), q1 and q2 are the charges of the spheres, and r is the distance between them.
In this case, the spheres are oppositely charged, so q1 and q2 have opposite signs. When the spheres are separated to a larger distance, r2, the value of r increases. Let's consider the effects of this change:
1. Sign of the potential energy:
Since the charges on the spheres are opposite, q1 * q2 will be negative. As a result, the potential energy, PE, will also be negative. So, the potential energy becomes more negative as the separation increases.
2. Total energy:
The total energy of a system is the sum of its potential energy and kinetic energy. In this case, since the spheres are hanging by strings, there is no kinetic energy involved. Therefore, the total energy of the system remains the same throughout the process.
3. q and w in this process:
The charge, q, remains constant for each sphere since the system is described as consisting of two oppositely charged spheres. Therefore, there is no change in q during the process.
The work done, w, in this process is given by the equation:
w = -ΔPE
where ΔPE represents the change in potential energy. As the potential energy becomes more negative, ΔPE will also be negative. Therefore, the work done, w, will be positive since the negative sign will cancel out.
To summarize:
- The potential energy becomes more negative as the spheres are separated to a larger distance.
- The total energy of the system remains the same.
- The charge, q, remains constant for each sphere.
- The work done, w, is positive.