Electric field lines of H2O molecule

In summary: You mean for the ion, not electron. Start by stating what the charge density functions should be over three ranges centred on the ion: 0 to R, R to d, and > d. Then try to figure out how to write that in ##\delta## functions. And don't confuse the ##\delta## function with its integral.
  • #1
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Homework Statement
In the limit R=0, e.g., when the Oxygen ion is a point charge:
a) Write down the volume charge density (15pts)
b) Draw the electric field lines far away from charges (25pts)
c) Draw the electric field lines near the point charges (25 points)
d) At finite radius R, draw the lines near the charges
Relevant Equations
p=q/v
I wanted to post my work so far to see if I am on the right path toward the correct answer so far.

I have attached a ss of the actual problem and my work in the attachments
IMG_0336.jpg


Screen Shot 2022-02-16 at 7.04.19 PM.png
 

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  • #2
Part (a) does not look correct. Remember, when you integrate the volume charge density over all space, you should get zero. Also, you are told to model the oxygen as a conducting sphere of radius R. Is the charge distributed uniformly over the volume of the sphere?

Part (c) needs some fixing. You must have twice as many lines going into the sphere as coming out of either one of the charges. Do you see why? Parts (b) and (d) look OK.
 
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  • #3
kuruman said:
Part (a) does not look correct. Remember, when you integrate the volume charge density over all space, you should get zero. Also, you are told to model the oxygen as a conducting sphere of radius R. Is the charge distributed uniformly over the volume of the sphere?

Part (c) needs some fixing. You must have twice as many lines going into the sphere as coming out of either one of the charges. Do you see why? Parts (b) and (d) look OK.
for part (a) it should be zero because I followed the diract delta function, I should get a spike at the center and zero all over space correct?

part (c), Is this due to having 2 electrons?
 
  • #4
quittingthecult said:
for part (a) it should be zero because I followed the diract delta function, I should get a spike at the center and zero all over space correct?

part (c), Is this due to having 2 electrons?
You need Dirac deltas for all three charges. When you put charge -2e on a conductor of radius R, does the charge go to the center?

For part (c) draw Gaussian surfaces around each charge. The number of electric field lines coming out or going in must be proportional to the enclosed charge.
 
  • #5
kuruman said:
You need Dirac deltas for all three charges. When you put charge -2e on a conductor of radius R, does the charge go to the center?

For part (c) draw Gaussian surfaces around each charge. The number of electric field lines coming out or going in must be proportional to the enclosed charge.
No it wouldn't go to the center. It would spread evenly on the surface. So for the electron it should be,
gif.gif
?
I am not sure about the protons though? I don't know the center of the protons.
 
  • #6
quittingthecult said:
No it wouldn't go to the center. It would spread evenly on the surface. So for the electron it should be,
View attachment 297216?
I am not sure about the protons though? I don't know the center of the protons.
You mean for the ion, not electron. Start by stating what the charge density functions should be over three ranges centred on the ion: 0 to R, R to d, and > d. Then try to figure out how to write that in ##\delta## functions. And don't confuse the ##\delta## function with its integral.

You are told to treat the protons as point charges.

In c) you are only asked for the field lines near the protons. Though it is not made very clear, d) is the corresponding question for the ion, and the figure should not show the protons.
 

What are electric field lines?

Electric field lines are imaginary lines that represent the direction and strength of an electric field. They point in the direction of the force that a positive test charge would experience if placed in the field.

How are electric field lines of a H2O molecule formed?

The electric field lines of a H2O molecule are formed due to the distribution of the positive and negative charges within the molecule. The oxygen atom has a slightly negative charge, while the hydrogen atoms have a slightly positive charge. This creates an electric dipole, with the electric field lines pointing from the positive to the negative charge.

Do the electric field lines of a H2O molecule extend infinitely?

No, the electric field lines of a H2O molecule do not extend infinitely. They are confined to the space around the molecule and do not extend beyond it.

What is the significance of the shape of the electric field lines of a H2O molecule?

The shape of the electric field lines of a H2O molecule indicates the direction and strength of the electric field. The closer the lines are together, the stronger the electric field is at that point. The direction of the lines also shows the direction in which a positive test charge would move if placed in the field.

How can the electric field lines of a H2O molecule be used to understand its properties?

The electric field lines of a H2O molecule can be used to understand its polarity and the strength of its dipole moment. The closer the electric field lines are together, the more polar the molecule is and the stronger its dipole moment. This information is important in understanding the molecule's interactions with other molecules and its behavior in an electric field.

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