# Polarization

Neutral objects are attracted to charged objects. You've seen this effect if you've ever rubbed a balloon on your head (which charges the balloon) and stuck it to a (neutral) wall. Or if you've removed a piece of plastic wrap from the roll and had it stick to your (neutral) hand. We know that like charges repel and opposite charges attract, but why would a neutral object react to a charge?

## Polarization of a Conductor

Suppose you place a positively charged rod next to a conductor, as shown. The negative charge carriers inside the conductor will be attracted to the positive charge, and because they are free to move where they like, negative charge will start to build up on the surface facing the positive charge. Positive charge carriers inside the conductor, on the other hand, are repelled by the external charge, and so will build up on the surface away from it. (Or, if you prefer, the negative charge carriers abandon the far side of the conductor, leaving it with a net positive charge.) The conductor has become polarized: positive charge on one side, negative charge on the other.

Now the negative charge isn't satisfied with sitting on the surface. It is still attracted to the rod, and so will try to pull the conductor closer to the rod. The positive charge on the other side, meanwhile, will try to push the conductor farther away. But the negative charges are closer to the rod, and so experience a greater electric force. They win, and the neutral conductor as a whole is attracted to the positive charge.

If we bring a negative charge towards the conductor instead, the conductor polarizes in the opposite direction, but the same result occurs: the nearby positive charges drag the conductor towards the negative charge.

## Polarization of an Insulator

But wait, you say. This process requires charge carriers to flow from one side of the material to the other, and insulators (such as the walls and hands I mentioned earlier) don't have charge carriers. Are they attracted to charges too? Can they polarize?

Interactive 8.2.1

To answer that question, we first have to consider what happens to an atom in the presence of another charge. Atoms, as you'll recall, are made up of a positive nucleus and a negative "electron cloud", bound to each other by electrostatic attraction. When an atom comes close to a positive charge, the nucleus is repelled by the charge and the cloud is attracted to the charge. The figure shows the result: the atom itself becomes polarized.

When a positive rod comes close to an insulator, all of its atoms polarize in this way, with the electron clouds leaning towards the rod and the nuclei leaning away. In some materials (like water), the molecules themselves are naturally polar: they don't have to stretch, they just rotate their negative end towards the positive rod. In either case, the side of the insulator closest to the positive charge develops a layer of negative charge, while the opposite side develops a positive layer. Insulators polarize just as conductors do, though the mechanism is different. The difference is one of degree: conductors are much better at polarizing. The polarized layers in a conductor are made up of charge carriers from the entire material, while an insulator's layers only include the charges that were already at the surface to begin with.

I place an insulator into an electric field that points to the left. How does it polarize?
Remember that positive charges are pushed with the field, and negative charges are pushed against the field. The insulator will develop a layer of positive charge on the left, and a layer of negative charge on the right.

## Electric Breakdown

While an atom will stretch a little bit in an electric field, it holds together because the positive nucleus and the negative cloud attract to each other. If the electric field is strong enough, however, it can overpower the force binding the electrons to the atom, and one or more of the valence electrons may be torn free from the atom, turning the atoms into ions. This is called electric breakdown, or we say that the material is ionized.

When this occurs in an insulator, those free electrons and ions can act as charge carriers, and the insulator becomes a temporary conductor. For example, clouds often develop a positive charge in their upper layers and a negative charge in their lower layers, creating a dipole field inside the cloud. (Part (a) in the figure.) When this field gets strong enough, the air inside the cloud ionizes (b), becoming a conductor. Positive charge begins to flow downward from the upper layer to the lower layer, and negative charge in the opposite direction. As the charge imbalance shrinks, the electric field between the clouds shrinks as well, and eventually the conditions for electric breakdown no longer apply. The free electrons reunite with their ions, and when they collide energy is released in the form of heat, light, and sound (c). This release of energy is what we call lightning and thunder. Note that the lightning we see is not the motion of charge itself, but the aftereffect, the un-ionizing of the air. This same thing occurs at a much smaller scale whenever a charged object (say, your finger after you've shuffled across a carpet) comes too close to another object (like a doorknob): that spark and crackle is just very, very tiny lightning.

Every insulator has its own threshold for electric breakdown. Air, for example, undergoes partial ionization when the electric field is around $$3\ten6\u{N/C}$$.

A large charged plate (surface charge density $$\sigma$$ is placed above a neutral metal plate; the gap between them is filled with air. What is the maximum value of $$\sigma$$ which won't result in a spark jumping between the plates?
The electric field created by the charged plate is $$E=2\pi k\sigma$$. To prevent any sparks from jumping, we need this field to be smaller than $$3\ten6\u{N/C}$$, and so $$2\pi k\sigma<3\ten6 \implies \sigma<\frac{3\ten6}{2\pi(9\ten9)}=5.3\ten{-5}\u{C/m^2}$$ or $$53\u{\mu C/m^2}$$. Remember our discussion of how large a coulomb of charge is (Example 3.1.1)? This result suggests that it would be hard to store even a millicoulomb of charge on a relatively small object, without that charge bleeding away through the ionized air surrounding it.