Dipole placed in a uniform electric field

In summary: Since the attractive force is always passing through a point on the dipole's axis, torque calculations can ignore it.
  • #1
vcsharp2003
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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##.

electric-field-positive-negative-point-charge.jpg


electric-dipole-in-unofrm-electric-field.gif
 
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  • #2
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##).
 
  • #3
DrClaude said:
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.
 
  • #4
DrClaude said:
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.
 
  • #5
vcsharp2003 said:
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.
 
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  • #6
Steve4Physics said:
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?
 
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  • #7
vcsharp2003 said:
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.
vcsharp2003 said:
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.
 
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  • #8
vcsharp2003 said:
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.
vcsharp2003 said:
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.
 
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  • #9
jbriggs444 said:
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.
 
  • #10
Steve4Physics said:
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.
 
  • #11
vcsharp2003 said:
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.
 
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  • #12
Steve4Physics said:
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.
 
Last edited:

Related to Dipole placed in a uniform electric field

1. What is a dipole in a uniform electric field?

A dipole in a uniform electric field refers to a system in which two equal and opposite charges are separated by a small distance. This creates a dipole moment, which is the measure of the strength and direction of the dipole.

2. How is the dipole moment related to the electric field?

The dipole moment is directly proportional to the electric field. This means that as the electric field increases, the dipole moment also increases. The direction of the dipole moment is in the same direction as the electric field.

3. What is the net force on a dipole in a uniform electric field?

The net force on a dipole in a uniform electric field is zero. This is because the two equal and opposite charges experience equal and opposite forces, resulting in a net force of zero.

4. How does the orientation of the dipole affect the electric field?

The orientation of the dipole affects the electric field by changing the direction and strength of the electric field. When the dipole is aligned with the electric field, the electric field is stronger. When the dipole is perpendicular to the electric field, the electric field is weaker.

5. What is the potential energy of a dipole in a uniform electric field?

The potential energy of a dipole in a uniform electric field is given by the formula U = -pEcosθ, where p is the dipole moment, E is the electric field, and θ is the angle between the dipole moment and the electric field. The potential energy is at a minimum when the dipole is aligned with the electric field and at a maximum when the dipole is perpendicular to the electric field.

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