How does the electroscope lose electrons to the Earth?

[vcsharp2003]

Homework Statement

I am trying to understand why the positively charged end when earthed would result in electron flow from postively charged end to earth. The exact steps outlined in the book are as in image below.

Relevant Equations

None

I get step 1, in which due to electrostatic induction the top part of electroscope gets positively charged while the leaves of electroscope become negatively charged.

Now if we Earth the positively charged end of electroscope as shown in step 2, then electrons must flow from Earth to positively charged end. But the book says the excess electrons from leaves flow to earth, even though positively charged end is earthed. This is confusing to me.

Perhaps, the electrons flow from Earth to positively charged end as soon as it's earthed, but then the leaves and top part end up becoming negatively charged as the electrons on the leaves redistribute to the neutral top plate and the leaves (leaves + top part form one conducting assembly). Since now the top plate is negatively charged so the electrons will flow from top plate to Earth till the leaves + plate assembly finally become neutral in charge.

 

[kuruman]

Think of the electrons in the plate and leaves that are free to move. In step 1 they move as far away from the negatively- charged rod as possible, into the leaves. When the plate is earthed, they are repelled even farther away, into the Earth.

 

[vcsharp2003]

Think of the electrons in the plate and leaves that are free to move. In step 1 they move as far away from the negatively- charged rod as possible, into the leaves. When the plate is earthed, they are repelled even farther away, into the Earth.

Is the explanation that I attempted in the last paragraph of my original post not correct?

 

[kuruman]

Is the explanation that I attempted in the last paragraph of my original post not correct?

It doesn't make sense. You start by saying

Perhaps, the electrons flow from Earth to positively charged end as soon as it's earthed, $\dots$

There is also the negative charge on the rod that repels them. If you enclose the electroscope and the rod by a closed (Gaussian) surface, the total charge inside is negative. Why would the electrons from the Earth that are outside this volume be attracted to the net negative charge within the volume? It's the earthing in step 2 that expels the excess negative charge within the volume. In step 3 the Earth connection is removed prevening further exchange of electrons with the Earth. In step 4 the rod is removed to infinity and only then are the electrons redistributed on the electroscope which now has a deficit of electrons, i.e. a net positive charge. That's how charging by induction works.

 

[vcsharp2003]

It doesn't make sense. You start by saying

There is also the negative charge on the rod that repels them. If you enclose the electroscope and the rod by a closed (Gaussian) surface, the total charge inside is negative. Why would the electrons from the Earth that are outside this volume be attracted to the net negative charge within the volume? It's the earthing in step 2 that expels the excess negative charge within the volume. In step 3 the Earth connection is removed prevening further exchange of electrons with the Earth. In step 4 the rod is removed to infinity and only then are the electrons redistributed on the electroscope which now has a deficit of electrons, i.e. a net positive charge. That's how charging by induction works.

Also, we could say that due to the negatively charged rod, the plate leaf assembly will have a negative potential since this assembly is in the immediate vicinity of the negatively charged rod. Now a conductor in electrostatic equilibrium will have the same potential at all points on its surface, so all points on the plate leaf assembly are at the same potential and this potential is negative. Now, when the plate is earthed then the Earth will be at a higher potential of 0 compared to negative potential of plate. As a result, free electrons will flow from lower potential to higher potential i.e. from plate to earth.

Is above also a correct explanation of electron transfer in this case?

 

[kuruman]

It works.