Electric Charge and Electric Field

8 Conductors and Electric Fields in Static Equilibrium

Learning Objectives

  • List the three properties of a conductor in electrostatic equilibrium.
  • Explain the effect of an electric field on free charges in a conductor.
  • Explain why no electric field exists inside a conductor in electrostatic equilibrium.
  • Describe Earth's electric field.
  • Explain how an electric field behaves near an irregularly shaped conductor.
  • Describe how a lightning rod works.
  • Explain how a metal car can protect passengers from dangerous external electric fields.

Conductors are materials, such as metals, that contain free charges capable of moving easily throughout the material. In metals, these mobile charges are electrons. Whenever excess charge is placed on a conductor, or when a conductor is exposed to an external electric field, the free electrons immediately begin to move. They continue redistributing until the conductor reaches a stable condition known as electrostatic equilibrium.

Figure 8.1 illustrates how an external electric field influences the free charges inside a conductor. If the applied field has a component parallel to the surface, that component exerts a force on the mobile charges, causing them to move along the conductor. As the charges redistribute, they create their own electric field that opposes the applied field. This process continues until the parallel component has been completely canceled.

At electrostatic equilibrium, the electric field at the surface of a conductor is therefore always perpendicular to the surface. If any parallel component remained, charges would continue moving and equilibrium would not exist.

For simplicity, the figure shows a positive free charge. In real metallic conductors, the mobile charges are electrons, which carry negative charge. The underlying physics is identical—the motion of a positive charge in one direction is equivalent to the motion of a negative charge in the opposite direction.

In part a, an electric field E exists at some angle with the horizontal applied on a conductor. One component of this field E parallel is along x axis represented by a vector arrow and other E perpendicular, is along y axis represented by a vector arrow. Charge inside the conductor moves along x axis so the force acting on it is F parallel, which is equal to q multiplied by E parallel. In part b, a charge is shown inside the conductor and electric field is represented by a vector arrow pointing upward starting from the surface of the conductor.
Figure 8.1: When an electric field [latex]\mathbf{E}[/latex] is applied to a conductor, free charges move until the electric field becomes perpendicular to the surface. (a) The applied field has both parallel and perpendicular components. The parallel component, [latex]\mathbf{E}_{\parallel}[/latex], exerts a force [latex]\mathbf{F}_{\parallel}[/latex] on a charge [latex]q[/latex], causing the charges to move. (b) After the charges redistribute, the parallel component has been eliminated, leaving an electric field that is perpendicular to the surface and a conductor in electrostatic equilibrium.

A neutral conductor placed in an external electric field becomes polarized. The free electrons shift slightly, causing one side of the conductor to become negatively charged while the opposite side becomes positively charged. As shown in Figure 8.2, this redistribution distorts the external field around the conductor. Once electrostatic equilibrium is established, the electric field inside the conductor is zero.

A spherical conductor is placed in the external electric field. The field lines are shown running from left to right. The field lines enter and leave the conductor at right angles. Negative charges accumulate on the left surface of the conductor and positive charges accumulate on the right surface of the conductor.
Figure 8.2: A neutral conducting sphere placed in a uniform external electric field becomes polarized as free charges redistribute over its surface. The electric field lines bend around the conductor and remain perpendicular to its surface. In electrostatic equilibrium, the electric field inside the conductor is zero because the redistributed charges completely cancel the applied field within the conducting material.

Misconception Alert: Is There an Electric Field Inside a Conductor?

A common misconception is that a charged conductor must contain an electric field throughout its interior simply because it carries excess charge. In fact, the opposite is true. In electrostatic equilibrium, the electric field inside the conducting material is zero. If an internal electric field existed, it would exert a force on the free electrons, causing them to continue moving. Since the charges have stopped moving, the internal field must have been completely canceled.

As a result, any excess charge placed on a conductor resides entirely on its outer surface. For a spherical conductor, the charges repel one another and spread out uniformly over the surface, as illustrated in Figure 8.3.

An important consequence of this charge distribution is that, for points outside the sphere, the electric field is identical to the field produced by a point charge located at the center of the sphere with the same total charge. This result greatly simplifies many electrostatic calculations and is widely used in physics, engineering, and biomedical applications involving charged electrodes and conductive objects.

A positively charged sphere is shown and positive charges are distributed all over the surface. Electric field lines emanate from the sphere in the space shown by the vector arrow pointing outward.
Figure 8.3: Excess charges on a spherical conductor repel one another until they are uniformly distributed over the outer surface. The electric field inside the conductor is zero, while the external field is identical to that produced by a point charge at the center carrying the same total charge.

Properties of a Conductor in Electrostatic Equilibrium

Once electrostatic equilibrium has been reached, every conductor obeys three important properties:

  1. The electric field is zero inside the conducting material.
  2. The electric field just outside the surface is perpendicular to the conductor. Electric field lines leave positively charged surfaces and terminate on negatively charged surfaces.
  3. Any excess charge resides entirely on the outer surface of the conductor.

These three properties provide a powerful framework for analyzing electrostatic systems. They explain the behavior of charged conductors ranging from laboratory equipment to biomedical instruments, where metal electrodes and conductive shielding are designed to control electric fields and minimize electrical interference.

One important application is the creation of a nearly uniform electric field. Consider two large conducting plates carrying equal and opposite charges, as shown in Figure 8.4. In electrostatic equilibrium, the excess charge spreads almost uniformly over the facing surfaces of the plates. As a result, the electric field between the plates is nearly uniform: the field lines are straight, equally spaced, and perpendicular to the surfaces, except near the edges where small distortions, called edge effects, occur. These edge effects become less significant when the separation between the plates is much smaller than their dimensions.

Two charged metal plates are shown. The lower plate has negative charge and the upper plate has positive charge. The electric field lines start from positive plate and enter the negative plate represented by arrows.
Figure 8.4: Two large conducting plates carrying equal and opposite charges produce a nearly uniform electric field between them, except near the edges. Uniform electric fields are widely used whenever charged particles must experience a constant force, including particle accelerators, electron-beam devices, and many scientific instruments.

Earth's Electric Field

Earth is surrounded by a naturally occurring electric field. Under fair-weather conditions, this field has a typical magnitude of about 150 N/C and points downward, toward Earth's surface. Although much weaker than the electric fields produced in laboratory experiments, it is present everywhere around us and plays an important role in Earth's global electrical environment.

The source of this field is the difference in charge between Earth's surface and the ionosphere, a region of the upper atmosphere beginning roughly 100 km above the ground that contains large numbers of charged particles. Under fair-weather conditions, the ionosphere is generally at a higher electric potential than Earth's surface, which carries a net negative charge. Together, they behave somewhat like the plates of a gigantic capacitor, producing the electric field illustrated in Figure 8.5(a).

During thunderstorms, however, the situation changes dramatically. Collisions between ice crystals, water droplets, and hailstones inside storm clouds separate electric charge, creating regions of positive and negative charge within the cloud. These charge separations produce electric fields that are much stronger than Earth's normal fair-weather field and may point in different directions, as illustrated in Figure 8.5(b).

If the electric field becomes sufficiently strong, the insulating properties of air break down. For dry air at atmospheric pressure, electrical breakdown occurs at approximately

[latex]E \approx 3\times10^{6}\ \text{N/C}[/latex]

At this point, air molecules become ionized, producing free electrons and ions that can move rapidly through the air. The air, normally an excellent insulator, suddenly becomes conductive, allowing charge to flow. This process produces spectacular electrical discharges such as lightning and, under less extreme conditions, corona discharge.

In part a, a child is flying a kite with two men in an open field on a bright sunny day. In part b, lightning appears over a body of water in stormy weather.
Figure 8.5: Earth's electric field. (a) During fair weather, Earth's negatively charged surface and the positively charged ionosphere create a downward electric field of about 150 N/C. (credit: D. H. Parks) (b) During thunderstorms, charge separation within clouds produces much stronger local electric fields. If these fields exceed the breakdown strength of air, lightning can occur. (credit: Jan-Joost Verhoef)

Electric Fields on Uneven Surfaces

Up to this point, we have focused on conductors with smooth, symmetrical shapes. Real conductors, however, often have sharp edges, corners, or pointed tips. These geometric features have an important effect on how electric charge is distributed. Excess charge tends to accumulate where the surface has the greatest curvature—that is, at the sharpest points. As a result, the electric field is strongest in these regions.

Why does this happen? Like charges repel one another and spread out over the surface of a conductor. On broad, gently curved surfaces, charges have plenty of room to move apart. Near a sharp point, however, the available surface area is much smaller, so the charges cannot spread out as effectively. The result is a greater concentration of charge at the pointed region.

Figure 8.6 illustrates this behavior. Although the electrostatic forces between neighboring charges are similar, the component of the force parallel to the conductor's surface, [latex]\mathbf{F}_{\parallel}[/latex], varies with the local geometry. On flatter portions of the conductor, this component allows charges to continue spreading apart. Near sharp tips, the geometry limits this redistribution, leaving a higher surface charge density.

The same effect occurs when an irregular conductor is placed in an external electric field, as shown in Figure 8.6(c). In electrostatic equilibrium, electric field lines must always meet the surface at right angles. Because the field lines crowd together near sharp points, the electric field is much stronger there. Recall from the previous chapter that a greater density of field lines represents a stronger electric field.

In part a, a conductor is shown with the unsymmetrical shape. The identical pair of charges at opposite ends on the conductor have similar components of forces represented by arrows. In part b, the unsymmetrical object has positive charge on its surface. The electric field lines are shown emerging perpendicular from the surface of the conductor represented by vector arrow. In part c, the field lines in and around the conductor running from left to right is shown. The left surface of the conductor has negative charge and the right surface has positive charge. The field lines enter and leave the conductor at right angles.
Figure 8.6: Electric fields near an irregular conductor. (a) The geometry of the conductor affects how charges redistribute over its surface. (b) Excess charge becomes most concentrated at regions of greatest curvature, producing stronger local electric fields. (c) When placed in an external electric field, an irregular conductor becomes polarized, and the field lines crowd together near sharp points, indicating a larger electric field strength.

Applications of Conductors

One important consequence of charge concentration at sharp points is that the electric field near the surface can become extremely large. As shown in Figure 8.7, the electric field is strongest where the conductor has the greatest curvature. If the field becomes sufficiently strong, it can ionize the surrounding air, allowing charge to leak into or out of the conductor through a process known as corona discharge. This phenomenon has both useful applications and practical consequences.

One familiar application is the lightning rod. Because its pointed tip produces an intense local electric field, a lightning rod can gradually transfer charge between the structure and the surrounding air, reducing the buildup of large electric potential differences. Although a lightning rod cannot prevent lightning, it can reduce the likelihood of a direct strike under some conditions. More importantly, if lightning does strike, the rod provides a low-resistance path that safely carries the current to the ground, protecting the building from serious damage.

In other situations, the opposite goal is desired—we want to prevent charge from escaping into the surrounding air. High-voltage electrical equipment therefore uses smooth, rounded conductors with large radii of curvature. Because the electric field is lower on smooth surfaces, unwanted corona discharge is minimized, allowing the conductor to maintain a much higher voltage. This design principle is used in power transmission systems and electrostatic generators such as the Van de Graaff generator (Figure 8.8).

Another important application of electrostatic equilibrium is the Faraday cage, a conducting enclosure that shields its interior from external electric fields. Since excess charge resides only on the outside surface of a conductor, the electric field inside the enclosure is ideally zero. Faraday cages protect sensitive electronic equipment from electrical interference and are widely used in biomedical instrumentation. For example, electrocardiogram (ECG) and electroencephalogram (EEG) systems measure extremely small electrical signals generated by the body. Conductive shielding helps prevent external electromagnetic noise from overwhelming these signals.

The same principle explains why a metal automobile can protect its occupants during certain electrical hazards. If lightning strikes the vehicle, or if a fallen power line contacts the metal body, the electric current travels primarily over the outside surface of the car. Because the passenger compartment acts as a Faraday cage, the electric field inside remains very small. For this reason, occupants are generally safest remaining inside the vehicle until the electrical hazard has been removed, provided they avoid touching metal components connected to the exterior while simultaneously contacting the ground.

A cone shaped positively charged conductor is shown where most of the positive charges are accumulated at the tip. The field lines represented by arrows emerge at right angles from the surface of the conductor in outward direction. The density of field lines is greater at the tip of the cone than at other surfaces.
Figure 8.7: Charge accumulates most strongly at sharp points on a conductor, producing a much larger electric field than on flatter regions. If the field becomes sufficiently strong, charge can leak into the surrounding air through corona discharge. This principle is used in lightning rods and other high-voltage applications.
In part a, a lightning rod is shown on the roof of a house. In part b, a person is touching the metal sphere of the Van De Graaff and his hair is standing up.
Figure 8.8: (a) A pointed lightning rod produces a strong local electric field that helps dissipate charge and provides a preferred path to ground if lightning strikes. (credit: Romaine, Wikimedia Commons) (b) A Van de Graaff generator uses a smooth spherical conductor to minimize charge leakage, allowing very large voltages to accumulate. The mutual repulsion of like charges causes the person's hair to stand on end. (credit: Jon "ShakataGaNai" Davis/Wikimedia Commons)

Section Summary

  • Conductors contain free charges that can move throughout the material.
  • In electrostatic equilibrium, free charges redistribute until the electric field inside the conductor is zero.
  • Any excess charge resides entirely on the outer surface of a conductor.
  • Just outside a conductor, electric field lines are always perpendicular to the surface.
  • Charge becomes most concentrated at sharp points and edges, where the electric field is strongest.
  • Lightning rods use this concentration of electric field to help reduce charge buildup and provide a safe path to ground if lightning strikes.
  • Earth has a natural electric field that points downward in fair weather. During thunderstorms, much stronger local electric fields can develop, leading to lightning when the electric field exceeds the breakdown strength of air.
  • A Faraday cage is a conducting enclosure that shields its interior from external electric fields, protecting sensitive electronics and helping explain why occupants of a metal vehicle are generally protected during a lightning strike.

Conceptual Questions

  1. Is the object in Figure 8.9 a conductor or an insulator? Justify your answer.Figure 8.9 shows an object placed in an external electric field.
    Electric field lines pass through an object rather than ending perpendicular to its surface, suggesting that the object is not behaving like a conductor in electrostatic equilibrium.
    Figure 8.9
  2. If the electric field lines in the figure above were perpendicular to the object, would it necessarily be a conductor? Explain.
  3. The discussion of the electric field between two parallel conducting plates, in this module states that edge effects are less important if the plates are close together. What does close mean? That is, is the actual plate separation crucial, or is the ratio of plate separation to plate area crucial?
  4. Would the self-created electric field at the end of a pointed conductor, such as a lightning rod, remove positive or negative charge from the conductor? Would the same sign charge be removed from a neutral pointed conductor by the application of a similar externally created electric field? (The answers to both questions have implications for charge transfer utilizing points.)
  5. Why is a golfer with a metal club over her shoulder vulnerable to lightning in an open fairway? Would she be any safer under a tree?
  6. Can the belt of a Van de Graaff accelerator be a conductor? Explain.
  7. Are you relatively safe from lightning inside an automobile? Give two reasons.
  8. Discuss pros and cons of a lightning rod being grounded versus simply being attached to a building.
  9. Using the symmetry of the arrangement, show that the net Coulomb force on the charge [latex]q[/latex] at the center of the square below Figure 8.10 is zero if the charges on the four corners are exactly equal.Figure 8.10 shows four charges at the corners of a square and one charge at the center.
    Four point charges labeled q sub a, q sub b, q sub c, and q sub d are located at the corners of a square, with charge q at the center.
    Figure 8.10: Four point charges [latex]{q}_{a}[/latex], [latex]{q}_{b}[/latex], [latex]{q}_{c}[/latex], and [latex]{q}_{d}[/latex] lie on the corners of a square and [latex]q[/latex] is located at its center.
  10. (a) Using the symmetry of the arrangement, show that the electric field at the center of the square in Figure 8.10 is zero if the charges on the four corners are exactly equal. (b) Show that this is also true for any combination of charges in which [latex]{q}_{a}={q}_{d}[/latex] and [latex]{q}_{b}={q}_{c}[/latex]
  11. (a) What is the direction of the total Coulomb force on [latex]q[/latex] in Figure 8.10 if [latex]q[/latex] is negative, [latex]{q}_{a}={q}_{c}[/latex] and both are negative, and [latex]{q}_{b}={q}_{c}[/latex] and both are positive? (b) What is the direction of the electric field at the center of the square in this situation?
  12. Considering Figure 8.10, suppose that [latex]{q}_{a}={q}_{d}[/latex] and [latex]{q}_{b}={q}_{c}[/latex]. First show that [latex]q[/latex] is in static equilibrium. (You may neglect the gravitational force.) Then discuss whether the equilibrium is stable or unstable, noting that this may depend on the signs of the charges and the direction of displacement of [latex]q[/latex] from the center of the square.
  13. If [latex]{q}_{a}=0[/latex] in Figure 8.10, under what conditions will there be no net Coulomb force on [latex]q[/latex]?
  14. In regions of low humidity, one develops a special “grip” when opening car doors, or touching metal door knobs. This involves placing as much of the hand on the device as possible, not just the ends of one’s fingers. Discuss the induced charge and explain why this is done.
  15. Tollbooth stations on roadways and bridges usually have a piece of wire stuck in the pavement before them that will touch a car as it approaches. Why is this done?
  16. Suppose a woman carries an excess charge. To maintain her charged status can she be standing on ground wearing just any pair of shoes? How would you discharge her? What are the consequences if she simply walks away?

Problems & Exercises

  1. Sketch the electric field lines in the vicinity of the conductor in Figure 8.11 given the field was originally uniform and parallel to the object’s long axis. Is the resulting field small near the long side of the object?Figure 8.11 shows an oblong conductor for this sketching problem.
    Oblong-shaped conductor used for sketching electric field lines near a conductor in an originally uniform electric field.
    Figure 8.11
  2. Sketch the electric field lines in the vicinity of the conductor in Figure 8.12 given the field was originally uniform and parallel to the object’s long axis. Is the resulting field small near the long side of the object?Figure 8.12 shows a second oblong conductor for this sketching problem.
    Oblong-shaped conductor used for sketching electric field lines near a conductor in an originally uniform electric field.
    Figure 8.12
  3. Sketch the electric field between the two conducting plates shown in Figure 8.13, given the top plate is positive and an equal amount of negative charge is on the bottom plate. Be certain to indicate the distribution of charge on the plates.Figure 8.13 shows two conducting plates that are not parallel.
    Two conducting plates, one horizontal and one tilted above it, used for sketching the electric field and charge distribution between oppositely charged plates.
    Figure 8.13
  4. Sketch the electric field lines in the vicinity of the charged insulator in Figure 8.14 noting its nonuniform charge distribution.Figure 8.14 shows a charged insulating rod with a nonuniform charge distribution.
    A positively charged rod with a concentration of positive charges near the top and a few in the middle.
    Figure 8.14 A charged insulating rod such as might be used in a classroom demonstration.
  5. What is the force on the charge located at [latex]x=8.00 cm[/latex] in Figure 8.15 (a) given that [latex]q=1.00\,\mu\text{C}[/latex]?
    Three point charges are shown on the scaling line. First charge plus q is at three point zero, second charge minus two q is at eight point zero, and third charge plus q is eleven point zero centimeters along the x axis. Four charges are placed on a scaling line. First is minus two q at one point zero, second is plus q at five point zero, third is plus three q is at eight point zero, and fourth is minus q placed at fourteen point zero centimeter along the x axis.
    Figure 8.15 (a) Point charges located at 3.00, 8.00, and 11.0 cm along the x-axis. (b) Point charges located at 1.00, 5.00, 8.00, and 14.0 cm along the x-axis.
  6. (a) Find the total electric field at [latex]x=1.00 cm[/latex] in  Figure 8.15 (b) given that [latex]q=5.00\,\text{nC}[/latex]. (b) Find the total electric field at [latex]x=11.00 cm[/latex] in Figure 8.15 (b). (c) If the charges are allowed to move and eventually be brought to rest by friction, what will the final charge configuration be? (That is, will there be a single charge, double charge, etc., and what will its value(s) be?)
  7. (a) Find the electric field at [latex]x=5.00 cm[/latex] in Figure 8.15 (a), given that [latex]q=1.00\phantom{\rule{0.25em}{0ex}}\text{μC}[/latex]. (b) At what position between 3.00 and 8.00 cm is the total electric field the same as that for [latex]–2q[/latex] alone? (c) Can the electric field be zero anywhere between 0.00 and 8.00 cm? (d) At very large positive or negative values of x, the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the right of 11.0 cm is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.)
  8. (a) Find the total Coulomb force on a charge of 2.00 nC located at [latex]x=4.00 cm[/latex] in Figure 8.15 (b), given that [latex]q=1.00\phantom{\rule{0.25em}{0ex}}\text{μC}[/latex]. (b) Find the x-position at which the electric field is zero in Figure 8.15 (b).
  9. Using the symmetry of the arrangement, determine the direction of the force on [latex]q[/latex] in the figure below, given that [latex]q_a=q_b=+7.50\,\mu\text{C}[/latex] and [latex]q_c=q_d=-7.50\,\mu\text{C}[/latex]. (b) Calculate the magnitude of the force on the charge [latex]q[/latex], given that the square is 10.0 cm on a side and [latex]q=2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}[/latex].
    Four point charges labeled q sub a, q sub b, q sub c, and q sub d are located at the corners of a square, with charge q at the center.
    Figure 8.16
  10. (a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in Figure 8.16, given that [latex]{q}_{a}={q}_{b}=-1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}[/latex] and [latex]{q}_{c}={q}_{d}\text{=+}1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}[/latex]. (b) Calculate the magnitude of the electric field at the location of [latex]q[/latex], given that the square is 5.00 cm on a side.
  11. Find the electric field at the location of [latex]{q}_{a}[/latex] in Figure 8.16 given that [latex]{q}_{b}={q}_{c}={q}_{d}\text{=+}2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{nC}[/latex], [latex]q=-1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{nC}[/latex], and the square is 20.0 cm on a side.
  12. Find the total Coulomb force on the charge [latex]q[/latex] in Figure 8.16, given that [latex]q=1.00\,\mu\text{C}[/latex], [latex]{q}_{a}=2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}[/latex], [latex]{q}_{b}=-3\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}[/latex], [latex]{q}_{c}=-4\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}[/latex], and [latex]{q}_{d}\text{=+}1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}[/latex]. The square is 50.0 cm on a side.
  13. (a) Find the electric field at the location of [latex]{q}_{a}[/latex] in Figure 8.16, given that [latex]{q}_{\text{b}}=+10.00\phantom{\rule{0.25em}{0ex}}\mu \text{C}[/latex] and [latex]{q}_{\text{c}}=–5.00\phantom{\rule{0.25em}{0ex}}\mu \text{C}[/latex]. (b) What is the force on [latex]{q}_{a}[/latex], given that [latex]{q}_{\text{a}}=+1.50\phantom{\rule{0.25em}{0ex}}\text{nC}[/latex]?
    Three point charges located at the corners of an equilateral triangle used for electric field calculations.
    Figure 8.17 Point charges located at the corners of an equilateral triangle 25.0 cm on a side.
  14. (a) Find the electric field at the center of the triangular configuration of charges in Figure 8.17, given that [latex]{q}_{a}\text{=+}2\text{.}\text{50}\phantom{\rule{0.25em}{0ex}}\text{nC}[/latex], [latex]{q}_{b}=-8\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{nC}[/latex], and [latex]{q}_{c}\text{=+}1\text{.}\text{50}\phantom{\rule{0.25em}{0ex}}\text{nC}[/latex]. (b) Is there any combination of charges, other than [latex]{q}_{a}={q}_{b}={q}_{c}[/latex], that will produce a zero strength electric field at the center of the triangular configuration?

Glossary

conductor
a material that allows electric charges to move freely through it
free charge
an electric charge that can move freely through a material, such as the conduction electrons in a metal
electrostatic equilibrium
the state of a conductor in which free charges have finished redistributing and no longer move
polarized
a state in which positive and negative charges become separated within an object while the object remains electrically neutral overall
ionosphere
a region of Earth's upper atmosphere containing many charged particles that helps produce Earth's natural electric field
Faraday cage
a conducting enclosure that shields its interior from external electric fields

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