# What Volume Is Integrated Over for Dipole Moment in Griffiths' Electrodynamics?

• Wheelwalker
In summary, in "An Introduction to Electrodynamics," Griffiths defines the dipole moment as p=\int r' \rho(r') d\tau' and explains that the integration is done over all elements of volume ##\small d\tau'## in all of space where there is some nonzero charge density. Therefore, there is no need to integrate over regions where the integrand is zero.
Wheelwalker
In "An Introduction to Electrodynamics", Griffiths gives the following equation for the dipole moment: $p=\int r' \rho(r') d\tau'$. My question is, in general, what volume am I integrating over? It seems a bit arbitrary to me. I assume I'm integrating over whatever volume is enclosing the charge density $\rho(r')$?

You are summing over all elements of volume ##\small d\tau'## in all of space. However, there is no need to integrate over those parts of space where the integrand is zero. So, you are correct - you only need to integrate over regions where there is some nonzero charge density.

That makes sense to me. Thanks!

## 1. What is a dipole moment?

A dipole moment is a measure of the separation of positive and negative charges in a molecule. It is a vector quantity with both magnitude and direction, and is often represented by the symbol μ.

## 2. How is dipole moment calculated?

The dipole moment of a molecule can be calculated by multiplying the magnitude of the charge on each atom by the distance between them, and then summing all these values for each bond in the molecule.

## 3. What is the significance of dipole moment?

Dipole moment is an important property of molecules as it affects their physical and chemical properties. It can influence the polarity of a molecule, its boiling and melting points, and its interactions with other molecules.

## 4. How does dipole moment integration work?

Dipole moment integration is a computational method used to calculate the dipole moment of a molecule. It involves breaking down the molecule into small pieces and calculating the dipole moment of each piece, then summing them up to get the overall dipole moment of the molecule.

## 5. Why is dipole moment integration important in chemistry?

Dipole moment integration is important in chemistry as it allows for the accurate calculation of the dipole moment of a molecule, which is crucial in understanding the physical and chemical properties of the molecule. It is also used in the development of new materials and in drug design.

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