Dipole placed in a uniform electric field

[vcsharp2003]

Homework Statement

When an electric dipole is placed in a uniform electric field of $\vec E$ as shown in second diagram below, then does the non-uniform electric field due to the dipole superimpose with the uniform electric field to create a net non-uniform electric field?

Relevant Equations

$\vec E_{net} = \vec E_1 + \vec E_2 + \vec E_3 + ...$, which is the principle of superimposition of electric fields at a point

My understanding is that the uniform electric field $\vec E$ cannot be the net electric field since the dipole creates its own electric field as shown in first diagram below, which must superimpose with the uniform electric field. So, yes, the uniform electric field $\vec E$ around the dipole gets altered to a non-uniform electric field due to the principle of superimposition of electric fields.

Yet, and this gets confusing, when we are determining torque on the dipole as in second diagram, we are calculating the force on each charge as if only the uniform electric $\vec E$ exists without any modification/superimposition. So according to me, the force on each charge should not be just $qE$, but the vector sum of the forces due to the other charge and $qE$.

 

[DrClaude]

Yes, the total field is not the same due to the presence of the dipole. However, in the second case it is usually assumed that the two charges are held at a fixed distance ($d$ in the figure), and thus you want to consider only the effect of the external field on the dipole (often only as a function of the angle $\theta$).

 

[vcsharp2003]

Yes, the total field is not the same due to the presence of the dipole. However, in the second case it is usually assumed that the two charges are held at a fixed distance ($d$ in the figure), and thus you want to consider only the effect of the external field on the dipole (often only as a function of the angle $\theta$).

Why should the force due to the other charge be ignored? If it's ignored then there needs to be a valid reason for it.

 

[vcsharp2003]

However, in the second case it is usually assumed that the two charges are held at a fixed distance (d in the figure), and thus you want to consider only the effect of the external field on the dipole

I think the reason could be that the force due to each individual charge is very small compared to force due to field $\vec E$, but not sure.

 

[Steve4Physics]

Why should the force due to the other charge be ignored? If it's ignored then there needs to be a valid reason for it.

The 2 charges in a dipole are at a fixed separation. For an isolated stationary dipole, the attraction between the 2 charges must balanced by some additional (repulsive) force. If this were not the case, then (from a classical viewpoint at least) the 2 charges would accelerate towards each other.

So, for an isolated dipole, the resultant force on each charge is zero.

The additional force on each charge, from superimposing an external electric field, is therefore the new resultant force on each charge.

So the force from the external electric field can be treated as the only force on each charge.

 

[vcsharp2003]

If this were not the case, then (from a classical viewpoint at least) the 2 charges would accelerate towards each other.

That makes sense, but then the question comes up that what could be this extra repulsive force.

Also, I am thinking that even if we consider the attractive force on each charge, it will not contribute to any torque about a point on dipole's axis since this attractive force is always passing through such a point. So, for torque calculations we can ignore the attractive force. Does this seem like another reason for attractive force not being considered for torque calculations?

 

[jbriggs444]

That makes sense, but then the question comes up that what could be this extra repulsive force.

Maybe we have a positively charged metallic sphere and a negatively charge metallic sphere connected by a non-conducting rod. The whole assembly then looking something like a barbell.

Largely irrelevant though. The problem does not care how dipoles come to be or are maintained as such. It is enough that their properties (if they exist) can be calculated and, perhaps, compared to experimental results.

Also, I am thinking that even if we consider the attractive force on each charge, it will not contribute to any torque about a point on dipole's axis since this attractive force is always passing through such a point. So, for torque calculations we can ignore the attractive force. Does this seem like another reason for attractive force not being considered for torque calculations?

Yes.

 

[Steve4Physics]

That makes sense, but then the question comes up that what could be this extra repulsive force.

That depends on the nature of the dipole. In the case of atomic/molecular dipoles, a full explanation of the forces would have to be quantum-mechanical. I guess it depends on things like the electronegativity of different atoms.

Also, I am thinking that even if we consider the attractive force on each charge, it will not contribute to any torque about a point on dipole's axis since this attractive force is always passing through such a point. So, for torque calculations we can ignore the attractive force. Does this seem like another reason for attractive force not being considered for torque calculations?

Yes. That's a good reason. The internal (attractive and repulsive) forces will not contribute to torque arising from external fields. (This is generally true - not just for dipoles).

Aha! @jbriggs444 beat me to it.

 

[vcsharp2003]

Maybe we have a positively charged metallic sphere and a negatively charge metallic sphere connect by a non-conducting rod.

Great. Then we can say that the push force on each end charge by the rod cancels the electrostatic attractive force on the same charge. That is the only way dipole charges could remain stationary.

Thanks for providing this great example of a dumbbell that makes it very clear to me now.

 

[vcsharp2003]

In the case of atomic/molecular dipoles, a full explanation of the forces would have to be quantum-mechanical.

Ok. So, it could be a gravitational ( due to mass, not gravity force) or electrostatic force coming from atoms surrounding the dipole that results in force cancellation and a stationary dipole.

 

[Steve4Physics]

Ok. So, it could be a gravitational ( due to mass, not gravity force) or electrostatic force coming from atoms surrounding the dipole that results in force cancellation and a stationary dipole.

I assume you are referring to the force(s) that stops the opposite charges in the dipole from accelerating towards each other.

I don't understand what "it could be a gravitational (due to mass, not gravity force) means. The force must counteract the electrical attraction, so it can't be internal gravitation (which is always attraction). Also, internal gravitational forces between parts of a dipole are far too small to have any affect.

Some molecules are natural dipoles, e.g. water molecules. The reasons are not that simple. E.g. see https://chemistry.stackexchange.com/questions/1107/why-is-water-a-dipole

Some dipoles are temporary, 'created' by an applied external field. E.g. apply an electric field to a single atom. The field distorts the electron-cloud distribution so it is asymmetrical - one side positive the other side negative.

There is no general rule about the nature of the forces. You have to consider each type of dipole individually. Often the forces are irrelevant and you don't need to think about them - just consider the dipole as an entity whose internal structure is irrelevant.

 

[vcsharp2003]

I don't understand what "it could be a gravitational (due to mass, not gravity force) means. The force must counteract the electrical attraction, so it can't be internal gravitation (which is always attraction).

I meant the force given by $\frac {Gm_1m_2} {r^2}$ between a dipole particle and surrounding particles.
But if these gravitational forces are too small compared to electrostatic force between charges in a dipole, then it cannot balance the electrostatic force between charges in dipole.

It must be something else (probably not classical mechanical force) that holds the dipole charges in place.