# Charging electroscope

In above picture. When near positive rod to the electroscope, electrons go to top of electroscope. then connect electroscope to ground. Why electrons go from ground to electroscope? in top of electroscope exist electrons and those electrons should repel electrons that is coming up from ground.

Consider the free electrons in the ground wire. The attractive force due to the continued presence of the positive rod is greater than the repulsive force due to the electrons gathered at the top of the electroscope in diagram 2. [This because only a finite number of electrons moved up the stem of the electroscope between diagrams 1 and 2. Electrons stopped moving up the stem when the field in the stem due to the separation of charge in the electroscope was equal and opposite to that due to the positive rod.]

We gain greater insight by considering potentials. When free electrons have stopped moving in the electroscope stem, the leaves, stem and top cap are all at the same potential. This potential is positive because of the proximity of the positively charged rod. Hence electrons flow from ground to the electroscope when the ground connection is made.

The knob and the leafs, together, are a single conductor. I think it is clearer to consider only the electrical potential of a conductor, not the induced charges within the conductor. Draw the setup as two capacitors in a conventional circuit diagram, and leave induced charges within conductors out of the circuit diagram. The rod and the knob of the electroscope, separated by a variable gap, are modeled as a variable capacitor, Cvar. The electroscope is represented by a fixed capacitor, Ce. Initially the gap is large and Cvar=0. In situation 1 and 2, the gap is minimal and Cvar=Cvar,max. The electric potential of the knob, V', is variable. In situation 1, V' is somewhere between 0 and V0. In situation 2, V'=0. The charge that flowed through the switch, between situation 1 and 2, is Q=V0/Cvar,max.

• I tell, why electrons go up from ground. there is electrons in top of electroscope and those repel each other. – user3728644 Jul 19 '19 at 6:12
• Before the ground wire is connected, the knob is at a positive electrostatic potential. Although there is negative induced charge at the knob, and positive induced charge at the leafs, the knob and the leafs are at the same positive potential, because they are part of a single conductor. When the ground wire is connected to the knob, electrons in the wire are attracted by the knob because of its positive potential. The induced negative charge in the knob does not repel electrons in the ground wire. – jkien Jul 19 '19 at 17:17

To understand this you need to consider the following things:

1. When you are bringing the positively charged rod near the electroscope, we express that electrons will gather near the charged rod leaving a net positive charge on the electroscope leaves, as you have shown in the diagram. This doesn't mean that there aren't any electrons on the ball, it actually means that there is a net negative charge on the ball due to attraction caused by bringing a rod which has a net positive charge (due to the deficit of free electrons). In all these cases, we are talking about only 'free electrons' and not the electrons that are orbiting in the inner shells around the nucleus.

2. The amount of polarization of charge that will happen on the electroscope will depend on how much net positive charge does the rod contain. A rod with charge $$q_1$$ will cause more electrons to get accumulated on the ball as oppose to $$q_2$$ charge, where $$q_1>q_2$$. Now, why does this polarization of charges on the electroscope stops, why doesn't all the free-electron get accumulated on the ball leaving the leaves of the electroscope completely deficient in electrons? Well, that is because, while net free electrons increase on the ball they also create a net positive charge on the electroscope leaves (due to the absence of electrons). So, in a way you reach a state of equilibrium when a certain amount of net negative charge is existing on the ball.

3. By grounding the ball of the electroscope now you are disturbing this balance. The act of grounding the ball is enabling more free electrons to get accumulated (these extra free electrons come from the Earth's surface) thereby reducing the amount of polarization. As an effect, you will observe that the leaves of the electroscope will move slightly closer at the instance you ground the ball.

Now, coming to your query, are those free electron, which were originally present on the ball before grounding, not repelling the free electrons moving up from the Earth's surface? Well, yes, they are. And that's the precise reason why a further re-distribution of charges happen causing the lowering of leaves by a small amount, as the net positive charge on the leaves also reduces.

We generally imagine a static picture, but in the actual case, the free electrons are not stationary in the metal. They are constantly drifting, it is just that at a given instance the net charge on the ball would be more negative. I hope this helps in clarifying your query.

• in 3 part of your answer, I don't understand why electrons on top of electroscope don't prevent from coming electrons from ground. – user3728644 Jul 19 '19 at 20:35
• I think power of positive rod stronger than those negative charges. Correct? – user3728644 Jul 19 '19 at 20:36
• @user3728644 I have mentioned the reason below point 3. Also, you need to think this as a dynamic situation where the motion of particles is decided by the resultant forces acting on them. The forces (repulsion due to electrons on the ball and attraction due to rod's positive charge) are both acting, but charges will not experience them separately, they will experience a resultant force which if is pulling the electrons from Earth's surface (in this case) will move the electrons up the ball. – orion Jul 20 '19 at 3:48