The Physics of Polarization and Charge Rearrangement of Charges

The lesson begins with a physical demonstration involving a rubber balloon and fur.
Rubbing the balloon against fur transfers charges, resulting in the balloon having an excess of electrons. This gives the balloon a net negative charge (q < 0).
When the negatively charged balloon is placed against a whiteboard (an insulator), it sticks to the surface.
The central question posed is: why does the balloon stick to the whiteboard?

The behavior of the balloon on the whiteboard is not an example of charging by conduction or induction.
Students initially hypothesize that charges transfer to or from the whiteboard, but this is dismissed because the whiteboard is an insulator.
In conduction, there is a transfer of charge between objects. In this scenario, no charges are transferred to or from the whiteboard.
The interaction is caused by the rearrangement of existing charges within the material, rather than a change in the net charge of the wall.

The ability of charges to move depends entirely on the nature of the material.
Conductors: - Examples include metals, such as an aluminum can or the metal used in an electroscope. - Conductors possess at least one electron per atom that is free to move throughout the entire object. - This mobility allows for charging through conduction and induction.
Insulators: - Examples include the whiteboard, a wall, or paper. - Insulators do not have many free electrons; electrons are restricted to their orbits around the nucleus of the atom. - Because electrons cannot flow freely across the material, insulators react to external charges through local displacement within the atom.

"Polarization" is defined as the rearrangement of charges within an object such that one side becomes more positive or negative than the opposite side, without changing the object's net charge.
The wall remains electrically neutral during the process, but its charge distribution is altered.
Mechanism in the Wall (Insulator): 1. The balloon is negatively charged (excess electrons). 2. Protons in the wall are fixed in the nucleus and do not move. 3. According to the Law of Charges, like charges repel. Therefore, the electrons in the wall atoms are repelled by the electrons in the balloon. 4. Because the wall is an insulator, the electrons do not leave the atoms but instead shift in their orbits to the side of the atom furthest from the balloon. 5. This results in the protons in the wall atoms being closer to the balloon than the electrons in those same atoms.

The attraction between the balloon and the wall is governed by Coulomb's Law: - $F_e = \frac{k q_1 q_2}{r^2}$ - where $F_e$ is the electric force. - $k$ is the Coulomb constant. - $q_1$ and $q_2$ are the charges. - $r$ is the distance between the centers of charge.
The law demonstrates that the electric force is inversely proportional to the square of the distance ( $r$ ).
Force Analysis: - There is an attractive force between the positive protons in the wall and the negative electrons in the balloon. - There is a repulsive force between the negative electrons in the wall and the negative electrons in the balloon. - Because the protons (opposite charges) are physically closer to the balloon than the electrons (like charges), the distance ( $r$ ) for the attractive force is smaller. - A smaller $r$ leads to a larger electric force ( $F_e$ ). - Consequently, the attractive electric force is larger than the repulsive electric force, resulting in a net attractive force that holds the balloon against the wall.

Small Pieces of Paper: - A negatively charged balloon can pick up small fragments of paper because it polarizes the paper exactly like it polarizes the wall. - The balloon repels electrons in the paper, making the side closest to the balloon relatively positive, which creates attraction.
Aluminum Can (Conductor): - An empty aluminum can on a table can be moved by a negatively charged balloon without contact. - Because aluminum is a conductor, the electrons are not just pushed to the other side of an atom; they flow to the opposite side of the entire can. - This results in a larger separation between the repelled negative charge and the balloon, leading to a larger net attractive force compared to an insulator.

The electric forces produced by polarization are generally quite small.
The balloon and bits of paper are able to be manipulated because their masses are small; the electric force only needs to be strong enough to overcome their weight ( $F_g$ ).
The instructor observes that the balloon cannot pick up a whole piece of paper off the table. While it can move the whole sheet slightly, the polarization-induced electric force is not strong enough to overcome the force of gravity acting on the larger mass of the entire sheet.
Conductor vs. Insulator Magnitude: - A conductor will experience a larger net attractive force from polarization than an insulator. - In the insulator (wall), electrons only move to the opposite side of the atom. - In the conductor (aluminum can), electrons move to the opposite side of the whole object, creating a larger disparity between attractive and repulsive distances and thus a stronger net force.

Question: Is the balloon sticking to the wall caused by conduction or induction?
Answer: No. The wall is an insulator and cannot transfer charges freely. This is a separate phenomenon called polarization where charges rearrange locally.
Question: In the wall, are both protons and electrons moving?
Answer: No. The protons in the wall stay fixed. However, the electrons can move in their orbits around the nucleus to shift away from the balloon.
Question: Why does the aluminum can roll toward the balloon?
Answer (Billy): The aluminum can polarizes like the wall. The negatively charged balloon repels the electrons in the can. In the metal, these electrons flow to the opposite side of the can, which causes a net attractive electric force that makes the can roll toward the rubber balloon.
Question: Why can't the balloon lift a whole sheet of paper?
Answer: The electric force generated by polarization is small. While it is enough to lift small pieces with low mass, it is not large enough to overcome the force of gravity on a full sheet of paper.