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BREAD
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Homework Statement
This is problem 6.5 in Griffiths EM.
I can't understand why dipole moment does not depend on coordinate systems.
Why does not dipole moment depend on coordinates system?
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In summary, the dipole moment is a measure of the separation of charges within a molecule and is independent of the coordinate system. It remains constant even when the molecule rotates or translates in space, as it is based on the distribution of charges within the molecule. Changes in the coordinate system do not affect the dipole moment, making it a molecular property. The dipole moment can vary among different molecules depending on their charge distribution, with polar molecules having a nonzero dipole moment and nonpolar molecules having a dipole moment of zero.
This is problem 6.5 in Griffiths EM.
I can't understand why dipole moment does not depend on coordinate systems.
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pasmith
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He's saying that [itex]\mathbf{p}[/itex] is constant in space, so its spatial derivatives vanish. Presumably this was stated in the problem statement.
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pasmith said:
There is not such presumption stated in problem .
The solution is saying that " Dipole moment P doesn't depend on coordinates system" is a generalized and obvious idea
FAQ: Why does not dipole moment depend on coordinates system?
1. Why does the dipole moment not change when the coordinate system changes?
The dipole moment is a measure of the separation of positive and negative charges in a molecule. It is a vector quantity that is independent of the coordinate system because it is determined by the distribution of charges within the molecule, not by the orientation or position of the molecule itself. This means that regardless of how the coordinate system is defined, the dipole moment will remain the same.
2. How does the dipole moment stay constant even when the molecule rotates or translates in space?
The dipole moment is calculated by summing the vector products of the charge and distance for each atom in a molecule. Because this calculation is based on the distribution of charges within the molecule, it will not change even if the molecule itself moves or rotates in space. This is because the relative positions and charges of the atoms within the molecule remain the same regardless of its orientation.
3. Can the dipole moment be affected by changes in the coordinate system?
No, the dipole moment is not affected by changes in the coordinate system. As mentioned before, it is a property of the molecule itself and is determined by the distribution of charges within the molecule. Therefore, it will remain constant regardless of the changes in the coordinate system.
4. Why is the dipole moment sometimes referred to as a "molecular property"?
The dipole moment is often called a molecular property because it is a characteristic of the molecule itself, rather than an external factor. It is a result of the charges and their arrangements within the molecule, and is not influenced by the surrounding environment or external forces. This makes it a useful property for understanding and predicting the behavior of molecules.
5. Is the dipole moment the same for all molecules?
No, the dipole moment can vary among different molecules. It depends on the distribution and magnitude of charges within the molecule, which can differ based on the types of atoms and their arrangements. In general, molecules with polar bonds (unequal sharing of electrons) will have a nonzero dipole moment, while molecules with nonpolar bonds (equal sharing of electrons) will have a dipole moment of zero.