What does q x d represent in dipole moment calculations?

[iScience]

i have an intuition of electric field lines, and force. All quantities yielded from an operation between two quantities should hold meaning. what meaning does the value "q x d" hold? I'm looking for intuition/ an intuitive grasp of the dipole moment.

 

[Jolb]

A dipole can be understood by thinking of it as two charges, q and -q, held apart from each other by a small distance d. So a dipole is neutral overall but it will respond to electric fields since it wants to align with field lines, and it will accelerate in regions of nonconstant field, since (in the q, -q picture) different magnitude forces will act on the two sides of the dipole.

An "ideal dipole" would correspond to the limit d→0, qd=constant.

A dipole moment qd characterizes the strength of a dipole. The larger the value qd, the more torque the dipole will feel in a uniform field, or alternatively, the more force it will feel in a field gradient.

There are other ways to understand dipoles too. For example, all magnets are dipoles (there is no such thing as a magnetic "charge" or monopole). But one could think of a magnetic dipole as a small conducting loop where an ideal magnetic dipole corresponds to the limit of the loop's diameter approaching zero. (This is a more realistic model than thinking of the magnetic dipole as two oppositely charged magnetic monopoles.)

Localized charge configurations can be analyzed in the "far field" regime (r>>d) in terms of their "monopole moment", corresponding to the net charge of the distribution, their "dipole moment", corresponding to the distribution's net dipole moment, their "quadrupole moment" (a quadrupole can be thought of as two opposing dipoles separated by d), their "octopole moment" (two opposing quadrupoles separated by d), etc. If you specify all the 2ⁿ-pole moments and their direction, this completely specifies the field generated by any localized charge distribution, provided you're interested in the field much farther away from the distribution than the distribution's size.

 

[Astrum]

i have an intuition of electric field lines, and force. All quantities yielded from an operation between two quantities should hold meaning. what meaning does the value "q x d" hold? I'm looking for intuition/ an intuitive grasp of the dipole moment.

I hope that you're referring to the equation for the dipole moment of a set of point charges:

$$\vec{p}=\sum ^n _{i = 1} q_i \vec{r}_i $$

The dipole moment is NOT the cross product of the charge and distance, so avoid using "x" to show multiplication.

What exactly is confusing you? It's hard to give help when your question is so broad.

 

[jtbell]

I hope that you're referring to the equation for the dipole moment of a set of point charges:

$$\vec{p}=\sum ^n _{i = 1} q_i \vec{r}_i $$

In the US at least, most physics students first encounter the dipole moment in an introductory physics course, for two charges of equal magnitude q and opposite polarity, separated by a distance d. In that case, the magnitude of the dipole moment is p = qd.

 

[Astrum]

In the US at least, most physics students first encounter the dipole moment in an introductory physics course, for two charges of equal magnitude q and opposite polarity, separated by a distance d. In that case, the magnitude of the dipole moment is p = qd.

Yeah, but I'm confused with using "x" to show multiplication. It makes me wonder if he thought $\vec{p} = q \times \vec{r}$

And we all know that's wrong on so many levels