Polarization & Electric Induction: What Is It & How Does It Work? (w/ Examples)

Even if you're new to the discipline in physical science known as electromagnetism, you are likely aware that like charges repel and opposite charges attract; that is, a positive charge will be attracted to a negative charge but will tend to repel another positive charge, with the same simple rule holding in reverse. (This the basis of the everyday saying "opposites attract"; whether this is true in romance is perhaps an open question, but it's certainly the case when it comes to electrical charges on atoms and molecules.)

You may, however, not know that it's possible for a charged object to be attracted to a neutral object – that is, an object with no net charge. This is possible through the phenomenon of charge polarization, which accounts for the fact that molecules that are electrically neutral overall can have an asymmetrical charge distribution within them. By way of analogy, a city might have an equal number of under-40 and over-40 residents, but their distribution within the city's borders is almost certainly asymmetrical.

  • Molecules are collections of two or more atoms representing the smallest chemical unit of a particular compound; these atoms can represent the same element, such as oxygen gas (O2), or include multiple elements, as with carbon dioxide (CO2).  

The transfer of electric charge by induction – meaning without direct touching of the objects that are exchanging charges in the form of free electrons – revolves around the strategic placement of conductors, which are materials through which current readily flows, and insulators, which are materials through which current cannot flow. But more than that, it relies on the polarization of entire objects stemming from the polarization of their constituent molecules, which can be modulated with the use of an electric field.

Point Charges and Electric Fields

Similar to way the linear and rotational equations of motion are analogous to each other, the mathematics underlying the effects of an electric field E acting on point charges strongly resembles that describing the effects of a gravitational field acting on point masses. The force of an electric field is given by FE = qE.

  • The electric field vector points in the same direction as as the electric force vector does when q is positive. The units of E are newtons per coulomb (N/C).

Point charges establish their own electric fields. (Remember that "point" charges can have any magnitude and still not be conceived as taking up any volume.) The expression for this is:

E = kq/r2

where k is the constant 9 ×109 Nm2/C2 and r is the displacement (distance and direction) between the charge and any point at which the field is assessed. Combining the two principal equations above gives:

FE = kq1q2/r2

This relationship is known as Coulomb's law.

Uniform Electric Fields and Polarization

If each point charge establishes its own electric field, is it possible to have a uniform electric field – that is, one in which the magnitude and direction of E is the same? For reasons you'll see, a uniform field is required for the net force on a dipole to be zero.

Placing two infinitely large conducting plates parallel to each other and placing an insulating material, or dielectric material, between them allows for an electric field to be generated if a voltage (electric potential difference) is established between them, such as when the different plates are attached to a battery.

This arrangement is approximated in the manufacture of capacitors, which store electric charge in circuits. The electric field lines are perpendicular to the plates and point toward the negatively plate. But how do charges build up on the surfaces of these units to begin with?

The Polarization of an Insulator

Net electric fields cannot exist inside conductors. This is because, if electrons are free to move, they will do so until they are at equilibrium, where the sum of all forces and torques is zero, and since F = qE, E must be zero. In other words, the movement of free electrons in a conductor obliterates any electric field that would exist by "leveling it out" via a shift in electrons.

The situation inside insulators is quite different. All atoms consist of a positively charged nucleus surrounded by an electron cloud. In the presence of an external electric field (perhaps caused by the presence of a charged object), the electron clouds can shift, resulting in a dipole moment and a net electric force.

Although there is no net charge in an insulator, if any portion of it is sampled, the presence of dipole moments leads to the accumulation of net positive charge on one side of the sample and a net negative charge on the other side. But charges do not actually accumulate on the surface, as with conductors, because of the limited movement of electrons in these materials.

Definition of Polarization

Polarization occurs when the electrons within a neutrally charged object shift their average position relative to the protons, resulting in two "clusters" of electrons (areas of localized increased electron density) per molecule and a dipole moment. The two charges are q equal in magnitude and opposite in sign. In a molecular dipole, the extent of polarization is determined by the material's electric susceptibility (following).

  • p = qd = the dipole moment of a single dipole in an a dielectric material.

To gain a sense of the effect of the electric field E inside the insulator as whole, consider a material with a dipole volume density of N charge dipoles per unit volume. You are now considering a large number of adjacent dipoles, with a slight positive charge at one end of each dipole and a slight negative charge at the other end. (This results in dipole-dipole attractions between + and – charges in end-to-end dipoles.)

The dielectric polarization density P characterizes the concentration of dipoles in the material as a result of the influence of the electric field within it:

P = Np = Nqd

P is proportional to the strength of the electric field, as you would expect. This relationship is given by P = ε0χ0E, where ε0 is the electric constant and χ0 is the electric susceptibility.

Polar Molecules

Some molecules are naturally polarized already. These are called polar molecules. An example of polar molecule is water, which consists of two hydrogen atoms bonded to a single oxygen atom. The H2O molecule itself is symmetrical in that it can be divided into equal halves by a plane placed between them in the correct orientation.

The bonds between hydrogen atoms and oxygen atoms within the same molecule are covalent bonds, but those between these atoms in different water molecules are called hydrogen bonds. The electrons shared in covalent bonds between hydrogen and oxygen lie much closer to the oxygen atom, making the oxygen atom in H2O electronegative and the hydrogen atoms electropositive. The resultant formation of hydrogen bonds between adjacent molecules is thus a consequence of the polarity of molecules, which propagates through the entire water sample.

If you hold a charged object near a thin stream of water from a faucet (which is a conductor owing only to the presence of ions and other impurities), you can see the water stream move ever so slightly toward the object due to this effect. This is because the molecules orient themselves so that the end of the molecule with the opposite charge points toward the charged object.

Electric Induction

The phenomenon of charge separation happens a little differently in conductors than in dielectrics. Instead of molecules becoming dipoles, free electrons are induced to move to one side of the material.

A glass rod, which is an insulator, can collect free electrons and become charged if swiped across a surface such as wool. (This is an example of the other kind of charge transfer, con_duction, or direct contact.) If a negatively charged rod is brought near the ball of an _electroscope without touching it, electrons will be "pushed away," and they will freely move along the conducting surfaces of the ball toward the pair of aluminum leaves hanging inside. You will see the leaves repel each other.

Note that the electroscope is still electrically neutral in total, but the charge is distributed differently. The "fleeing" of the electrons toward the leaves inside is balanced by the settling of positive charges where the rod is close to the sphere.

If you were to actually touch the charged rod to the ball, electrons will be transferred from the rod because of the positive charges nearby. When you pull the rod away, the electroscope will remain charged, but the negative charges will distribute themselves evenly throughout the ball.

Examples of Induction

Now, you're in a position to put all of this together and observe what happens when you place a charged rod close to a conductor that may also be connected to something else. (Bringing a charged rod close to a conducting sphere and yanking it away to make the sphere's own electrons "dance" in response might get boring after a time.)

Assume you have a charged insulating rod, and you bring it close to a solid conducting sphere connected to the ground by an insulating post. Although previous sections have described dipoles in terms of individual molecules in dielectrics, the same phenomenon is induced "en masse" in a conductor via induction. If the conductor is a sphere (ball), the conductor's electrons will flow to the surface of the hemisphere opposite the tip of the rod.

Twin Spheres

Imagine what happens if, while a friend holds the rod from above in place, you slide a second, also neutral conducting ball up against the first, directly opposite the rod placement. The electrons gathered there will seize the opportunity to get even farther away from the rod and its repellent electrons, and will move to the far side of this sphere.

Now you can get creative. If you want the second ball to remain charged, simply pull the two balls apart while the rod is still in place (and thus "distracting" positive charges). Electrons will have been transferred ultimately from the rod to the second sphere, where they distribute themselves evenly across its surface. The first ball returns to its initial neutral and uniform state.

  • Non-symmetrical objects play by the same physical rules, but it's not as easy to figure out the "exact" behavior of electrons as it is in the case of spheres.

Ground Wires

Have you ever pondered what ground wires do, or how they work? Earth is considered electrically neutral, but it is vast enough to absorb local perturbations in charge without consequence. Because of this, Earth can act as a vast reservoir or charge buffer, supplying electrons as needed through ground wires to neutralize positively charged objects, or accepting them from negatively charged objects through the wire in the opposite direction.

So, in order to prevent unwanted voltage thanks to the sizable accumulation of net charges on large conducting objects, ground wires offer a safety feature in a highly electrical modern world.

References

About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.