Understanding what a dipole's charge is

[Jaccobtw]

Homework Statement

If you have a dipole with an equal and opposite charge, how would you represent the the dipole moment p in terms of q and d?

Relevant Equations

p = qd

If they are equal and opposite, then wouldn't the net charge be zero? I don't know how else to reason this problem

p = 0d or just 0

 

[gneill]

Look up "dipole moment". The net charge is not particularly relevant, it's the fact that the two charges are separated by some fixed distance that is important. This will determine how the net electric field at some distance from the dipole will behave.

 

[kuruman]

In the expression $\vec p=q\vec d$, $q$ is conventionally the value of the positive charge, not the net charge. Vector $\vec d$ points from the negative charge towards the positive charge.

 

[Jaccobtw]

In the expression $\vec p=q\vec d$, $q$ is conventionally the value of the positive charge, not the net charge. Vector $\vec d$ points from the negative charge towards the positive charge.

Thanks you, does the dipole always have to be equal and opposite or can there be, for example, a +3 charge on one end and a -2 charge on the other end?

 

[gneill]

Thanks you, does the dipole always have to be equal and opposite or can there be, for example, a +3 charge on one end and a -2 charge on the other end?

Sure. But the math for the electric field at some distance from the dipole won't be particularly neat. Pure dipoles (with equal and opposite charges) are much easier to analyze.

 

[Jaccobtw]

Sure. But the math for the electric field at some distance from the dipole won't be particularly neat. Pure dipoles (with equal and opposite charges) are much easier to analyze.

Does this mean that the charge of a dipole q will always be in multiples of 1.67 * 10^-19, the charge of a proton? If not, how and why?

 

[Cutter Ketch]

Does this mean that the charge of a dipole q will always be in multiples of 1.67 * 10^-19, the charge of a proton? If not, how and why?

Yes. This has nothing to do with the nature of dipoles. It is one of the fundamental postulates of physics. Charge is always quantized and only occurs in integer multiples of the fundamental charge.

But wait! Quarks have thirds of the fundamental charge! Yes, but they only occur in groups which in sum have an integer charge. But what about fractionally charged quasiparticles in the quantum Hall effect? Well, those don’t count! But why not? Stop bothering me kid!

 

[Jaccobtw]

Look up "dipole moment". The net charge is not particularly relevant, it's the fact that the two charges are separated by some fixed distance that is important. This will determine how the net electric field at some distance from the dipole will behave.

Why is the dipole moment relevant? In other words, how does multiplying the charge of the positive particle in a dipole by the separation distance lead to anything relevant? What does it tell us.

 

[gneill]

Methinks you need to do a little research into dipoles.

 

[kuruman]

Why is the dipole moment relevant? In other words, how does multiplying the charge of the positive particle in a dipole by the separation distance lead to anything relevant? What does it tell us.

I concur with @gneill #9 and point out that the most important molecule to life as we know it (what is it?) has a dipole moment. For example, read the section "Biological importance of dipole interactions", here.

 

[Cutter Ketch]

Why is the dipole moment relevant? In other words, how does multiplying the charge of the positive particle in a dipole by the separation distance lead to anything relevant? What does it tell us.

Everything in our world is almost always and almost entirely neutral. For the most part, for every proton there is an electron. With a lot of energy that charge can be completely separated into unbalanced charges and big interesting things happen (from batteries to lightening). However, for considerably less energy the next most interesting thing that can happen is the charge can be slightly displaced creating a dipole. This is the most interesting thing you can do with net neutral charge in a net neutral world and the effects of dipoles are everywhere.

In an atom or molecule the change in the dipole moment as the electron changes from one energy state to another is what makes (and absorbs) light. And so many of the interesting features of light from the color of flowers to the best laser frequency for lasik, are all determined by dipole moments. The relatively free valence electrons in a metal can’t easily be fully removed from the sea of positive charge, but they can be pushed a little to one side to make a dipole. This, for example, makes a mirror reflective. Pushing the charge up and down an antenna to make an oscillating dipole is how you make and receive radio waves. The constraints of quantum mechanics cause the charge in some molecules to be slightly polarized. This polarity has huge consequences on the chemical properties. The polarized charge is largely the reason water is such a good solvent, and that is largely what makes life on Earth possible. It also causes water to expand slightly upon freezing making ice float.

The list goes on and on. Suffice it to say that polarized charge, being the simplest thing you can do with net neutral charge, is incredibly important in our everyday lives. Being able to precisely characterize a dipole field has been an important step in our understanding of many important phenomena.