I've understood that in a device like a capacitor the energy stored in the electric field between the plates corresponds to the work done by an external source in charging it, so similarly an electric field produced by a point charge would carry some energy as well and i was wondering if this comes from the energy required to ionise the atom because then if i take two different atoms lets say a sodium atom and a helium atom separately away from each other, and i do some work to ionize both of them i would need to do more work on the helium atom since it has a more stable configuration and hence the energy stored in the electric field should be more but because the charges on both of them are same wouldn't the electric field be same in both cases. so whats wrong in this and how does the energy in the field of a point charge originate
2 Answers
You should have searched the site first. Your question is one of extremely many duplicates, and ought, and would, be closed as one.
My focus here are for the detail-stuff that you also asked.
You should also do some formatting so that your question is not one big lump of words.
so similarly an electric field produced by a point charge would carry some energy as well and [I] was wondering if this comes from the energy required to ionise the atom
correct and correct.
[I] do some work to ionize both of them [I] would need to do more work on the helium atom since it has a more stable configuration and hence the energy stored in the electric field should be more
This is correct
but because the charges on both of them are same wouldn't the electric field be same in both cases.
The ionic radius of $\text{Na}^+$ is much larger than the ionic radius of $\text{He}^+$ and that is already a sufficient explanation for the discrepancy that you see. The electric field is thus different between the two cases only within the ionic radius of $\text{Na}^+$ yet giving the main contribution to the difference in energy that is observed.
You definitely have not yet learnt what is the energy stored in the electric field when you have a, say, uniform ball of charge. It is a simple homework exercise, and it should be more than illuminating for you to do it.
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Your thoughts are in the right direction. You are thinking about the potential energy of an electron near a nucleus. It takes energy to remove the electron. When the two are far apart, there is an electric field near the nucleus and near the electron. You should think of the electron and nucleus as forming a dipole.
When the two are close, there is also an electric field. The electromagnetic field keeps an atom together. Quantum mechanics makes it messy because the electron is in an orbital, not a particular location. You might need to think of the attraction as mediated by photons instead of a field.
But thinking that energy is gone when the atom is in its ground state leads to confusion. Energy differences are important, not energy itself. How much energy in in a particular configuration is an arbitrary choice.
Think of gravitational potential energy. A mass sits on a table, where $h = 0$. Using $E_0 = mgh$, you get $E_0 = 0$. You raise the mass a meter and let it fall. $E_1 = mg(1m)$. You can calculate things like how much kinetic energy it will have when it hits the table.
But you could also use the floor as $h=0$. You might get $E_0 = mg(1m)$ and $E_1 = mg(2m)$. You can repeat the calculation and get the same answer.
So you might consider that the electron and nucleus have gained potential energy when they are separated, and this energy comes from doing work on them. When they are separated, the dipole field is bigger. In this sense, doing work on the electron and nucleus has stored energy in the field.
But also see this. How is energy "stored in an electric field"?
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