Find the electric dipole moment for a water molecule

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SUMMARY

The electric dipole moment for a water molecule can be calculated using the formula μ = ∑(q_i r_i â) where q_i represents the discrete charges and r_i are the position vectors from a fixed origin. The discussion emphasizes the importance of modeling the water molecule accurately, either as a continuous charge distribution or a discrete one, to achieve precise results. The dipole moment is treated as a vector quantity, which is crucial for understanding the molecular behavior in an electric field.

PREREQUISITES
  • Understanding of electric dipole moments and their vector nature
  • Familiarity with charge distributions, both continuous and discrete
  • Basic knowledge of vector calculus and summation notation
  • Experience with molecular modeling techniques
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  • Study the application of vector calculus in physics, particularly in electrostatics
  • Explore molecular modeling software for simulating water molecules
  • Learn about the effects of electric fields on polar molecules
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Elder1994
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Homework Statement
Find the electric dipolar moment for a water molecule using the definition of the dipolar moment, after that find the electric field needed to move this molecule.
Relevant Equations
p = ∫ r' ρ(r') dV'
The equation that we saw in class is for a continuous charge distribution, I think that for this exercise I need to treat the system as a discrete charge distribution but I'm not sure. Also, I don't know how I can calculate the intensity of the electric field needed to move this charge.
 
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It all depends on how you model a water molecule. You may model it a linear molecule and apply defination(Crudest case) or you may go and use actual model of molecule and using the fact that dipole moments are vectors.

To answer your first question,the integral can be easily converted into sum:

$$\mu= \sum_{I} q_i r_i \hat r$$

Where ##r_i\text{'s}## are the position vectors from a suitable fixed origin.
 

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