torque and Efield

[chiddler]

You know how you get stuck at some concept and you spend the next 5 hours staring at the same page?

Yeah!

So i'd really appreciate some help.

First, TBR gives an electric dipole as p = qL. I do not understand what this means or what this equation tells.

Next, i'm given this figure. I understand that a torque develops, but I cannot imagine why there would be actual rotation. If rotation is to form, then the charges would have to go against the Efield at some point in their rotation.

For this to be possible, wouldn't there have to be an extremely specific set of values for Efield and the two q's? If E field is too large, then they will separate easily. If Efield is too small, then they will neglect the Efield and converge. And the value of q has similar effect.

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[MedPR]

You know how you get stuck at some concept and you spend the next 5 hours staring at the same page?

Yeah!

So i'd really appreciate some help.

First, TBR gives an electric dipole as p = qL. I do not understand what this means or what this equation tells.

Next, i'm given this figure. I understand that a torque develops, but I cannot imagine why there would be actual rotation. If rotation is to form, then the charges would have to go against the Efield at some point in their rotation.

For this to be possible, wouldn't there have to be an extremely specific set of values for Efield and the two q's? If E field is too large, then they will separate easily. If Efield is too small, then they will neglect the Efield and converge. And the value of q has similar effect.

!

You have your image tagged as img and url. It won't show unless someone types in the url.

For p=qL, p is just how strong the dipole is. The strength of a dipole is determined by the length of the bond and the charge distribution. For instance, there is a dipole between both HF and HI bonds, but since the bond length for HI is so much longer than for HF, the dipole moment (p) is greater for HI. HI is more polar than HF. The p=qL equation is something you intuitively use almost everytime you consider acid/base or polarity in general. It is just a way of quantifying a concept you already know.

I'm sure someone will correct me if I'm wrong, but the torque in that image is not permanent. Torque only exists to align the dipole with the electric field. Once the dipole is aligned, it doesn't rotate anymore, there is no net torque. The electric field is always pushing the positive end of the dipole in one direction (to the right in this example) and the negative end of the dipole in the opposite (180deg) direction (to the left in this example). This force is constant so long as the electric field remains constant. In other words, the force is responsible for aligning (torquing) the dipole, and also for keeping the dipole aligned.

Also, I don't think the charges will separate, and here's why. In that figure, assume the arrow heads are the location of a negatively charged plate, and the start of the arrows (left side) are a positive plate. This is consistent with the fact that the lines show the direction a positive charge will migrate; so it should make sense.

Now, once the dipole finishes aligning, it will stop rotating. At this point, lets look only at the negative pole. What forces are acting on it? It is being pulled to the left due to attraction to the positive plate as well as repulsion from the negative plate. It is also being pulled to the right due to attraction to the positive end of the dipole. What about the positive end of the dipole? It is being pulled to the right due to repulsion from the positive plate as well as attraction from the negative plate. It is also being pulled to the left due to the attractive force of the negative end of the dipole. Since this figure depicts two charges of equal magnitude (+q and -q) the net force on the dipole is 0 regardless of how big the electric field is. All leftward forces are canceled by rightward forces and vice versa. If netforce is 0, how will the dipole separate? It won't.

I suppose if the electric field is negligible, then the two ends of the dipole could end up running into each other, but if you think about it from a chemistry point of view, there are intramolecular forces that will prevent this. Iodine sucks away Hydrogens only electron, but the repulsive force between both nuclei is enough to keep them separated, yet not enough to spontaneously break the bond.

 

[chiddler]

fixed

 

[chiddler]

HI is more polar than HF

you're mistaken. the opposite is true!

reading the latter part of your response soon.

 

[MedPR]

you're mistaken. the opposite is true!

reading the latter part of your response soon.

That's true. Bad example, but I think the concept is the same. Greater p = greater dipole moment = more polar bond.

Use C-H and H-F instead.

 

[SaintJude]

Yes, oh my goodness--I feel the same level of frustration at this point!

Anyway, one of the things I've really taken to heart in electrostatics is the fact force is the only determinant of the direction of charge. On not such an intellectual level as MedPr,...Imagine the dipole is a pen. You shift the tip of the pin to the right & the bottom of the pen to the left. Try it! The pen will rotate clockwise.

 

[chiddler]

Perhaps you're right. But think of a spring: at equilibrium there are no net forces acting on the spring (ie, no acceleration) yet the kinetic energy from the acceleration moments before causes oscillation.

So yes i'll agree that there are no forces after they are aligned (equilibrium position of spring), but the momentum it carries is still there. This either causes rotation or SHM.

 

[chiddler]

Yes, oh my goodness--I feel the same level of frustration at this point!

Anyway, one of the things I've really taken to heart in electrostatics is the fact force is the only determinant of the direction of charge. On not such an intellectual level as MedPr,...Imagine the dipole is a pen. You shift the tip of the pin to the right & the bottom of the pen to the left. Try it! The pen will rotate clockwise.

actually he gave me this example in a PM lol. So i understand the concept of what should happen, but i'm not understanding how or if it indeed does.

 

[MedPR]

actually he gave me this example in a PM lol. So i understand the concept of what should happen, but i'm not understanding how or if it indeed does.

It's exactly the same concept as torque on a see-saw, except the force is based on the charges q and the electric field E instead of the weight of things sitting on the seasaw.

Edit: Maybe it's better to think of it as a propeller, like on an old school airplane, since the force of the electric field is only in 1 direction, as opposed to two different forces on a see-saw. So you push (or pull) one part of the propeller. That part that directly experienced the force of you pushing will move in the same direction as you pushed. Since it is not experiencing any linear motion (you didn't push it so hard that the nose of the airplane crashes into the ground), it will just rotate in whatever direction you initiated torque in.

 

[chiddler]

and the masses are equal. so with an initial push, and only conservative forces, it's SHM!

 

[MedPR]

and the masses are equal. so with an initial push, and only conservative forces, it's SHM!

I guess so, if you think of the restoring force as the torque that aligns the dipole with the electric field. Once this happens, there is no more motion of the dipole, at least not in a constant electric field.

 

[chiddler]

Once this happens, there is no more motion of the dipole, at least not in a constant electric field.

Why not?

 

[MedPR]

Why not?

Good question. The force that makes the dipole rotate and align with the electric field is torque, right? The equation for torque is Torque=Frsintheta. When the dipole aligns with the field, theta becomes 0. sin0 = 0, torque = 0.

 

[chiddler]

Two things. First I realized that they are also moving away from each other so the force they exert on each other is reduced over time.

Second, I don't understand how that phrase is used. With wiki's help, dipole moment is the separation between two charges. If the two are in the psuedo-SHM that i've described (apart, aligned, apart, aligned. the distance of oscillation should decrease because the force they exert on each other decreases as they go further apart) then the dipole should remain static only after they are far enough not to influence each other at r = infinity

hope this makes sense.

 

[MedPR]

Two things. First I realized that they are also moving away from each other so the force they exert on each other is reduced over time.

Second, I don't understand how that phrase is used. With wiki's help, dipole moment is the separation between two charges. If the two are in the psuedo-SHM that i've described (apart, aligned, apart, aligned. the distance of oscillation should decrease because the force they exert on each other decreases as they go further apart) then the dipole should remain static only after they are far enough not to influence each other at r = infinity

hope this makes sense.

Why are they moving away from each other? The net force in an electric field is 0.

 

[chiddler]

Why are they moving away from each other? The net force in an electric field is 0.

how do you know that?

 

[MedPR]

how do you know that?

Because TBR told me so Right under the figure we have been talking about.

...we find that the net force on an electric dipole in a uniform external electric field is zero

Also because the negative pole is being pulled just as hard to the left as the positive pole is being pulled to the right. F=qE. Since q1 and q2 are equal in magnitude and opposite in sign, and the electric field is uniform (field lines are the same distance apart at all points), F=-qE and F=qE are equal and opposite, thus no net force.

It's like a tug of war where neither side is pulling hard enough to win.

 

[chiddler]

RIGHT but that's assuming that the charges are just strong enough and or distant enough to cause a force equal and opposite the F=qE. Is this correct?

Because it makes it seem like a completely useless thought experiment.

 

[MedPR]

RIGHT but that's assuming that the charges are just strong enough and or distant enough to cause a force equal and opposite the F=qE. Is this correct?

Because it makes it seem like a completely useless thought experiment.

i'd also like to point out to you, and anybody else reading, that i misinterpreted "CLOCKWISE" to mean rotation. there is no rotation this just indicated direction of torque.

As far as I know, the force an object experiences in a uniform electric field is independent of distance. F=qE only takes into account the charge of the particle and the strength of the electric field. Since the field is uniform and the charge of both particles here is equal in magnitude, the force they experience must be equal in magnitude as well.

I think I am misunderstanding/missing what you are saying...

I'm also confused about why there is no rotation. Correct me if I'm wrong, but by definition, rotational motion is caused by a non-zero net torque. In other words, anywhere there is torque there is also rotation.

 

[chiddler]

As far as I know, the force an object experiences in a uniform electric field is independent of distance. F=qE only takes into account the charge of the particle and the strength of the electric field. Since the field is uniform and the charge of both particles here is equal in magnitude, the force they experience must be equal in magnitude as well.

I think I am misunderstanding/missing what you are saying...

I'm also confused about why there is no rotation. Correct me if I'm wrong, but by definition, rotational motion is caused by a non-zero net torque. In other words, anywhere there is torque there is also rotation.

Yes, I thought...well it doesn't matter what I thought. There is rotation. I confused myself D:

What I mean is that look at the net forces on a charge:

Fnet = qE + kqq/r^2 = 0

therefore

qE = kqq/r^2

this is a very precise condition. the charges and distance apart must be very specific for this to occur without them being pulled apart. For example, if q is fixed, and then you bring the two charges too far apart, then qE cannot equal kqq/r^2. Therefore the net forces are not at 0 and they will move apart.

 

[chiddler]

why doesn't EK or princeton have anything on this? nor did i learn this in my physics class.

 

[MedPR]

You're missing a negative sign. Consider this:

Fnet=kq1q2/r^2 + Eq = 0
So -Eq=kq1q2/r^2

So, as you say, for net force = 0:
One of the charges must be negative and one must be positive, since it is a dipole. We will save this fact for the end because it is simpler that way (at least for me).

Eq1=kq1q2/r^2
E=kq2/r^2

Now, do the same thing for the other charge.

Eq2=kq1q2/r^2
E=kq1/r^2

so kq2/r^2=kq1/r^2

k is just coloumbs constant, so we can throw that out. r^2 is a relationship between both charges, so we can throw that out too.

You are left with q2=q1. Remember how we said one must be positive and one must be negative? Make one negative, and you are left with q2=-q1 as the only condition for Fnet=0.

 

[chiddler]

i understand your math.

don't understand it conceptually. how can fnet = 0 if they are very far away such that their influence on each other is very low?

 

[MedPR]

i understand your math.

don't understand it conceptually. how can fnet = 0 if they are very far away such that their influence on each other is very low?

It doesn't matter how close or how far the two charges are in relation to each other. By F=kq1q2/r^2, each charge exerts an equal magnitude force on the other at all values for r.

Let's say they are so far apart that their influence on each other is zero. Would you agree that this situation is equivalent to putting each charge into two separate, but identical electric fields? Hopefully you do, because that's what the following is counting on.

So you have two point charges, +q and -q. You also have two identical electric fields. E1 and E2.

When you put +q into E1, it is immediately repelled by the positive end of E1 and attracted by the negative end of E1 with some net force F.

When you put -q into E2 (which is equivalent to E1) it is immediately repelled by the negative end of E2 and attracted by the positive end of E2 with some net force F.

-F + F = 0.

 

[milski]

You cannot have the field be both kq1/r^2 and kq2/r^2 if q1 and q2 have opposite charges. While a lot of times it's ok to leave the signs until the end of the problem, you still need to observe at least the relative signs of the charges in the system to one another. The above can be true only for E=q1=q2=0 and yes, in the case the charges will not move.

 

[chiddler]

oh i see.

medpr i'm very sorry to have dragged this out for so long.

I'll concede that Fnet = 0, but then you asked me earlier:

Why are they moving away from each other? The net force in an electric field is 0.

Ok. Fnet is 0 but does this mean that the charges are not capable of moving away from each other? As you described, if they are not influencing one another, then Fnet = 0. Add back influence (and Fnet is still 0), they exert equal and opposite forces to one another but this force can be small enough such that F=qE can be greatly stronger. Therefore, if qE is greatly stronger then they are moving away from each other.

 

[MedPR]

oh i see.

medpr i'm very sorry to have dragged this out for so long.

I'll concede that Fnet = 0, but then you asked me earlier:

Why are they moving away from each other? The net force in an electric field is 0.

Ok. Fnet is 0 but does this mean that the charges are not capable of moving away from each other? As you described, if they are not influencing one another, then Fnet = 0. Add back influence (and Fnet is still 0), they exert equal and opposite forces to one another but this force can be small enough such that F=qE can be greatly stronger. Therefore, if qE is greatly stronger then they are moving away from each other.

No, it helps me understand this as well. It's probably my fault that I can't explain it clearly enough.

I think I see what you are saying now. If the E is huge, then the -q will be pulled with some gigantic force to the left, and the +q will be pulled with some equally gigantic force to the right. So why don't the charges separate? I have no idea. I would guess it has something to do with the bond strength being several orders of magnitude greater than the electric field strength.

 

[chiddler]

Hmm that's a good point.

assuming the bond between the two charges is strong enough, then there will be SHM motion similar to a seesaw as was suggested earlier. probably.