Need help on E&M problem

Jan 2020
1
0
Chicago
Hi. I'm not sure how to find the charge on Q. I thought dipole moments were only between 1 positive and 1 negative charge of equal magnitude. Also, why is my teacher asking for the number of electrons in Q? If it's water molecule, then aren't there 1 electron in each hydrogen atom?

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Apr 2015
1,159
305
Somerset, England
I thought dipole moments were only between 1 positive and 1 negative charge of equal magnitude
A dipole moment is a vector.
It has magnitude (equal to the separated charge)
and direction (directed along the line between the centres of positive and negative)
Yes because like in a capacitor, if you separate charge the positive and negative are equal and opposite.

So in this case p is the vector sum of two dipole moments (which are not drawn - you should draw the vectors in and you will see that components along the direction of p add and those at right angles to it cancel)

If it's water molecule, then aren't there 1 electron in each hydrogen atom?
When you separate charge in a capacitor there are a large number of electrons involved.
When you separate charge within a molecule like this the amount of separation is less than the charge on the electron.
This is called partial separation.
Each hydrogen atom shares two electrons with the oxygen to form the bonds.
So that is four shared electrons in all in the molecule.
Each hydrogen contributes its single electron and the oxygen contributes 2 electrons, making the four.
What the partial separation means is that the pull of the oxygen nucleus is much greater than the pull of each of the hydrogen nuclei on the respective shared bonding pairs.
So the sharing is unequal.
This can be viewed as the electrons spending more time in the vicinity of the oxygen than the hydrogen
or it can be viewed as a slight shift of the centre of charge towards the oxygen.
Either way has the same effect as if a small amount of charge was actually separated.
It is a pity that your teacher did not use the delta q to show this is a small amount of the charge on each electron pair.
This is also why the separation is 2q on the oxygen and q on each hydrogen.

Also, why is my teacher asking for the number of electrons in Q?
So when you have drawn the vector diagram and solved for q you will have a value in coulombs.
You can look up the charge, in coulombs, carried by an electron and divide one by the other to get the 'number of electrons'
Don't expect this number to be a whole number of electrons (it is less than 1).
Remember that each of the single dipole vectors are made up of a vector with a single q at each end multiplied by the 100 picometre separation and pointing at 52.5 degrees from p.
 
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