Physics question about charges and conservation of energy

[JFK90787]

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OK I just don't get how conservation of energy is supposed to work with charges.

Imagine 2 positive charges being held very close together; they will have a lot of potential energy. When they get released, ΔPE +ΔKE=0. What I don't understand is that, according to that equation, as they move further apart, potential energy of each will decrease, so to conserve energy velocity will increase. But obviously this is wrong or their speed would increase forever as they move apart, which common sense tells us is wrong. Can anyone explain to me what I'm missing?

 

[Charles_Carmichael]

OK I just don't get how conservation of energy is supposed to work with charges.

Imagine 2 positive charges being held very close together; they will have a lot of potential energy. When they get released, ΔPE +ΔKE=0. What I don't understand is that, according to that equation, as they move further apart, potential energy of each will decrease, so to conserve energy velocity will increase. But obviously this is wrong or their speed would increase forever as they move apart, which common sense tells us is wrong. Can anyone explain to me what I'm missing?

Their velocity won't increase infinitely because their KE is restricted by the initial PE. Remember that ΔPE + ΔKE = 0, so ΔKE = -ΔPE. The change in KE can't exceed the change in PE, so they won't keep increasing their velocity forever.

For example, if ΔPE is 100J, then ΔKE is also 100J. Plug that into the KE = (1/2)mv^2 equation and you'll get an upper limit to velocity.

Hope this helps.

 

[JFK90787]

But when their KE is maxed out, what's to prevent them from moving further apart and continue decreasing the potential energy?

The thing is, I can imagine a real world scenario with something like gravitational potential - when all that potential energy is converted into kinetic, an object will hit the ground. For charges with velocity in an empty space, what's there to prevent the charges from moving further apart from each other forever, and thus decreasing their potential energy forever (and consequently increasing their kinetic energy)?

The thing that got me confused about this was a problem involving a positive and negative charge; they attract each other, so as they get close and closer, PE will approach negative infinity; this will mean the kinetic energy need to get infinitely high. But common sense tells us this won't happen

In other words, physics can go eat a dick

 

[JFK90787]

double post

 

[Charles_Carmichael]

But when their KE is maxed out, what's to prevent them from moving further apart and continue decreasing the potential energy?

The thing is, I can imagine a real world scenario with something like gravitational potential - when all that potential energy is converted into kinetic, an object will hit the ground. For charges with velocity in an empty space, what's there to prevent the charges from moving further apart from each other forever, and thus decreasing their potential energy forever (and consequently increasing their kinetic energy)?

The thing that got me confused about this was a problem involving a positive and negative charge; they attract each other, so as they get close and closer, PE will approach negative infinity; this will mean the kinetic energy need to get infinitely high. But common sense tells us this won't happen

In other words, physics can go eat a dick

Once they hit the max KE, they're not going to keep decreasing PE. In your example of an object falling, PE is completely converted to KE and the object stops because it encounters something that basically takes away all it's energy (the ground). The PE doesn't go below zero. Some of the KE of the object is transferred to the ground, some dissipates as heat, some escapes as sound, etc. Similarly, if the two positive charges keep moving away from each other, once they go past the 0 PE point, there's no more additional energy being "added" to the objects to keep increasing their velocity. They'll either continue maintaining constant velocity (if in a vacuum) or they will slow down as frictional forces (such as air resistance, collisions with other particles, etc.) dissipate away their energy.

Regarding your real world confusion about the positive and negative charges, I don't think PE gets higher as they get closer together. As they get closer together, PE decreases and reaches zero when they "stick." Remember that potential energy is the energy a system has that can be converted to work (or any other form of energy). If a positive and negative charge are stuck together, they don't have any incentive to do work; they're already at that happy state where they'll continue to stick to each other unless some outside force acts on them.

If you keep one charge fixed, but allow the other one to move, think of them coming together as "gravity" from the fixed charge pulls the free charge towards it and, once they stick, it's like the free charge hit the "ground."

Does this make sense?

 

[JFK90787]

They'll either continue maintaining constant velocity (if in a vacuum) or they will slow down as frictional forces (such as air resistance, collisions with other particles, etc.) dissipate away their energy.

This is my confusion, if they are in a vacuum, and they have velocity, won't they need to necessarily keep moving further and further part? And according to kQ1Q2/R^2, because they are moving further apart, won't potential energy always decrease due to the increasing distance between them while moving apart?

I need to go to sleep but I will check back tomorrow

 

[Charles_Carmichael]

This is my confusion, if they are in a vacuum, and they have velocity, won't they need to necessarily keep moving further and further part? And according to kQ1Q2/R^2, because they are moving further apart, won't potential energy always decrease due to the increasing distance between them while moving apart?

I need to go to sleep but I will check back tomorrow

Their PE will keep decreasing but it won't go below 0. Their ΔKE (after PE becomes 0) will be 0 because the velocity is constant (remember that ΔKE = KEf - KEi). There's no external source putting in more energy into the charges so they cannot increase their KE (remember that you can't create or destroy energy). They will keep moving further apart in a vacuum because no force is slowing them down. However, their energy is constant. It's just like pushing an object on ice (assume no friction or any other external frictional forces); the object will keep sliding on the ice forever but it's KE will not exceed beyond the initial energy put into it.

Hope this helps.

PS: kqq/r^2 is not the equation for electrical energy; it's the equation for electrical force. kqq/r is the equation for electrical potential energy (EPE = qV, where V = kq/r). And even based on this equation, the PE cannot go below zero, so there's an upper limit to the KE (and thus velocity) that the charges can have and they cannot exceed this upper limit without some external source putting energy into them.

 

[Akarat]

I just want to add a few things:

Strictly speaking, PE does keep decreasing but the equation for electrical potential energy: PE = kqq/r has the variable r, the distance, in the denominator. As the distance between the two charges becomes larger and larger, PE becomes VERY SMALL - it can be pretty much considered 0. Therefore, there won't be any additional PE to be converted into KE to keep increasing the velocity of the two charges.

Additionally, the equation for electrical force: F = kqq/r^2 also has the variable r (and it's squared in this). Once again, as the two charges get very far from one another, the force is so small that, the acceleration on the two charges can be considered negligible (F = ma). Therefore, the two charges will eventually experience an electrical force from each other of 0 N.

 

[Insulinshock]

In other words, physics can go eat a dick

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