# Where does potential energy go?

## Main Question or Discussion Point

Where does the potential energy go??

hello..

One of my friend asked me this question, and i had no answer to it. moreover the professors response to it seemed unsatisfactory.

The question is: Suppose we have a dipole in a uniform External Electric field, which causes it to rotate (or undergo simple harmonic motion). The energy used to bring about the rotation is stored as the potential energy of the system. Let the dipole moment be θ aligned with the electric field. So there is a some amount of energy used to hold it in that position, and as soon as it is released it tends to align itself in the direction of the electric field. What if we remove the Electric field when the dipole was still making θ angle with earlier existing Electric field. Now in absence of an electric field the dipole should not rotate, then where is the energy gone which was stored in it earlier??

This same thing can be taken with respect to gravity. Suppose we have a body at a height h from the surface of earth then "mgh" amount of energy is stored in the body. If the energy holding it is removed it it falls towards the earth. Now suppose we put the gravity off (lets assume we can). Now the body will not fall... So where does the potential energy stored in the body go??

As an answer to this my professor only said that we can't compare two such systems in presence and absence of gravity or electric field. I have been thinking about this all the while, and the only thing that came to my mind is that we have described the idea of potential energy as the amount of work done against a force acting on the body, when the effect is removed the cause should vanish too... but still it is quite confusing..

So please tell me where does this energy go, if it actually goes somewhere??
Looking forward to your reply..

Any help is appreciated.

## Answers and Replies

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Simon Bridge
Science Advisor
Homework Helper

So there is a some amount of energy used to hold it in that position.
This is not correct - it does not take any energy to hold something in position.

eg. Your chair expends no energy holding you up.

If we could magically switch gravity off, then it would take some effort to do this. It would take the same effort as to remove the object (you) to infinity (where PE=0).

The electric field is a tad more complex, because a changing field generates a magnetic field, but the principle is the same: the presence of the dipole in the field means it is harder to shut the field down.

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This is not correct - it does not take any energy to hold something in position.

eg. Your chair expends no energy holding you up.
Isn't the electromagnetic force holding you against the pull of gravity when you sit on the chair??
If we could magically switch gravity off, then it would take some effort to do this. It would take the same effort as to remove the object (you) to infinity (where PE=0).
So according to this, the potential energy is not lost anywhere, in fact is used to switch off gravity, right?

Simon Bridge
Science Advisor
Homework Helper

Isn't the electromagnetic force holding you against the pull of gravity when you sit on the chair??
Yes - but it does not use any energy to do this.

So according to this, the potential energy is not lost anywhere, in fact is used to switch off gravity, right?
When you switch "external" gravity off, the potential energy increases. (The mass you are watching the PE of has it's own gravity remember.)

For instance ... PE=mgh (being the usual approximation) ... decreasing the potential means bringing the ground closer. Switching gravity off is the same as removing the gound completely ... i.e. the same as taking the ground very far away: so h gets very big - so PE gets very big. (IRL, gravitational potential energy of a mass is the amount of work you need to do to bring the mass from a very long way away to where it is. For gravity, since it is attractive, that is less than zero.)

Therefore, the process of switching gravity off requires you to input energy from someplace else. Notice we don't need to know the details of doing this to know that it takes energy? We can be very confident about this because conservation of energy is the toughest Law we know of.

Andrew Mason
Science Advisor
Homework Helper

If we could magically switch gravity off, then it would take some effort to do this. It would take the same effort as to remove the object (you) to infinity (where PE=0).
Or you could say that if we could magically switch gravity off then energy would magically disappear. Since this is magic there is no need to be constrained by a law of conservation of energy.

AM

Dale
Mentor

The question is: Suppose we have a dipole in a uniform External Electric field, which causes it to rotate (or undergo simple harmonic motion). The energy used to bring about the rotation is stored as the potential energy of the system. Let the dipole moment be θ aligned with the electric field. So there is a some amount of energy used to hold it in that position, and as soon as it is released it tends to align itself in the direction of the electric field. What if we remove the Electric field when the dipole was still making θ angle with earlier existing Electric field. Now in absence of an electric field the dipole should not rotate, then where is the energy gone which was stored in it earlier??
The electric field stores a certain amount of energy: http://en.wikipedia.org/wiki/Electric_field#Energy_in_the_electric_field

When you rotate the dipole you increase the E field and thereby increase the energy stored in the field. When you remove the field, work is done, either on matter or on fields in some other location. The energy that went into rotating the charge increases the amount of work done during removal of the field.

Yes - but it does not use any energy to do this.

When you switch "external" gravity off, the potential energy increases. (The mass you are watching the PE of has it's own gravity remember.)

For instance ... PE=mgh (being the usual approximation) ... decreasing the potential means bringing the ground closer. Switching gravity off is the same as removing the gound completely ... i.e. the same as taking the ground very far away: so h gets very big - so PE gets very big. (IRL, gravitational potential energy of a mass is the amount of work you need to do to bring the mass from a very long way away to where it is. For gravity, since it is attractive, that is less than zero.)

Therefore, the process of switching gravity off requires you to input energy from someplace else. Notice we don't need to know the details of doing this to know that it takes energy? We can be very confident about this because conservation of energy is the toughest Law we know of.
How do you know that in the first case no work is done but for the second one while removing gravity you will need to do some work??
According to the idea of work , it is done against a force...here what is the force that is opposing the removal of gravity??

Dale
Mentor

How do you know that in the first case no work is done but for the second one while removing gravity you will need to do some work??
Because there is no change in energy for the first one but there is a change in energy for the second one. Therefore no work is done in the first but work is done in the second.

According to the idea of work , it is done against a force...here what is the force that is opposing the removal of gravity??
Gravity.

By the way, the more general definition of work is that work is a transfer of energy by any mechanism other than heat. So it isn't always necessary to identify a force, although it is easy to do so in this case.

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Simon Bridge
Science Advisor
Homework Helper

Or you could say that if we could magically switch gravity off then energy would magically disappear. Since this is magic there is no need to be constrained by a law of conservation of energy.

AM
Ah well, yes, though that sort of approach does not help OP understand conservation of energy. You are right though - at some point we will end up just having to tell him something like that: not everything we can conceive of exists in Nature.

One of the things that comes up a lot at SF and Fantasy conventions is why so many authors can't let their ultra-tech and magic just do away with these pesky conservation laws as an extension of whatever unexplained approach produced the effect in the first place.

Generally you get better stories if not just anything can happen. Niven, for example, puts a bit of effort in making his tech violate as few laws as possible - transfer booths conserve momentum and energy (albeit in a hand-wavy fashion) for eg. Why not just say that the momentum gets taken care of as part of the "magic" or teleport technology? He does something similar in The Magic Goes Away.

The above would be a Nivinsian constraint on how magically switching gravity off would work.

How do you know that in the first case no work is done but for the second one while removing gravity you will need to do some work??
As DaleSpam says, no change in energy for one case and there is a change in energy for the other.
According to the idea of work , it is done against a force...here what is the force that is opposing the removal of gravity??
By that idea, it requires a motion in relation to a force. In that case - the object is not moving with or against a force. In the second case, the distinct mechanism is not given - we don't know what movement, if any, happens. Fortunately, there is another way of viewing work - as DaleSpam points out.

If we have an anti-gravity machine - this is how you work out how much energy it needs to switch it on. There's lots of fun stuff about changing gravity etc around and about... though further discussion of anti-gravity should go in another forum.

hello..

One of my friend asked me this question, and i had no answer to it. moreover the professors response to it seemed unsatisfactory.

The question is: Suppose we have a dipole in a uniform External Electric field, which causes it to rotate (or undergo simple harmonic motion). The energy used to bring about the rotation is stored as the potential energy of the system. Let the dipole moment be θ aligned with the electric field. So there is a some amount of energy used to hold it in that position, and as soon as it is released it tends to align itself in the direction of the electric field. What if we remove the Electric field when the dipole was still making θ angle with earlier existing Electric field. Now in absence of an electric field the dipole should not rotate, then where is the energy gone which was stored in it earlier??

This same thing can be taken with respect to gravity. Suppose we have a body at a height h from the surface of earth then "mgh" amount of energy is stored in the body. If the energy holding it is removed it it falls towards the earth. Now suppose we put the gravity off (lets assume we can). Now the body will not fall... So where does the potential energy stored in the body go??

As an answer to this my professor only said that we can't compare two such systems in presence and absence of gravity or electric field. I have been thinking about this all the while, and the only thing that came to my mind is that we have described the idea of potential energy as the amount of work done against a force acting on the body, when the effect is removed the cause should vanish too... but still it is quite confusing..

So please tell me where does this energy go, if it actually goes somewhere??
Looking forward to your reply..

Any help is appreciated.
Let me start by saying that concepts of Potential Energy(PE) and Kinetic Energy(KE) are relative, PE is relative to the existence of the source that is exerting force or torque, KE is relative to the observer.

There is NO meaning of PE at a point or place, PE is always the difference between the PE at two positions. Similarly there is NO meaning of KE of an object, it is not an absolute concept, it is relative to the observer.

In other words, you can choose the PE to be zero at the angle θ, and negative at the center. So, when you remove the force exerting source there is NO problem, but the actual concept is that these energies are relative concepts.

I hope it helps

Thanks everyone!!

I happen to discuss this with my professor (it's another one) and having read and discussed this here i could understand what he explained..
So i got my doubt cleared..

Just to mention: the basic problem was : I was restricting myself to the system and did not see the surroundings where the energy was getting transferred in some or the other form as you all have mentioned.. So the problem is solved!!
Thanks a lot..