Location: Ch 14: Electric Fields and Potential
|
Location: Ch 14: Electric Fields and Potential
|
 |
ELECTROSTATICS
IN THIS CHAPTER:
FEATURES: |
pace around a strong magnet is different from how it would be if the
magnet were not there. The space around a black hole is different from
how it would be if it were not there. Similarly, the space around a concentration
of electric charge is different from how it would be if the charge were
not there. If you walked past a charged Van de Graaff generator, the hair
on your head would stand out. The space that surrounds a magnet, a black
hole, or an electric charge is altered. The space contains a force field.
The force field that surrounds a mass is a gravitational field. If you throw a ball into the air, it follows a curved path. Earlier chapters showed that it curves because there is an interaction between the ball and the earth—between their centers of gravity, to be exact. Their centers of gravity are far apart, so this is action at a distance.
The fact that things not in contact could exert forces on each other puzzled some scientists. Force fields eliminate the distance factor. The thrown ball is in contact with the field all the time and thus it is "interacting" with the gravitational field of the earth. We usually thing of rockets and space probes as interacting with gravitational fields, rather than the huge masses of planets that are actually responsible for the fields.
Just as the space around the earth and every other mass is filled with a gravitational field, the space around electrical charges is filled with an electrical field. The gravitational field between a planet and a satellite is comparable to the electrical field between a proton and an electron. Thus, the force that one electric charge exerts on another can be described as the interaction between one charge and the electric field set up by the other.
An electric field, like a vector, has both magnitude and direction. Its magnitude (strength) can be measured by its effect on charges within the field. Where the force is greatest on the test charge, the field is strongest. Where the force on the test charge is weak, the field is at its weakest.
The strength of an electric field is a measure of the force exerted
on a small test charge placed in the field. This test charge MUST be small
enough as to not disturb the original charge. If a test charge q
experiences a force F at some point, the electric field E
is defined as: 
.
Field strengths can be measured in newtons per coulomb N/C
or volts per meter V/M. The direction of the electric
field is the direction of the electrical force on this small positive test
charge. If the charge that sets up the field is negative, the field points
towards the test charge. If the charge that sets the field up is positive,
then the field points away from the test charge.
Since an electrical field has both magnitude and
direction, it is a vector and can be represented by vectors. A negatively
charged particle is represented by vectors that point towards the particle.
A positively charged particle is represented by vectors that point away
from the particle. The length of the vectors indicates the magnitude of
the field. The electric field is greater where the vectors are longer than
where the vectors are short. To represent a complete electric field by
vectors, you would have to show a vector at ever point in the space around
the charge. Such a diagram would be unreadable (and would show up as a
big red blob.) A more useful (and readable) way to describe an electric
filed is with electric field lines, which are also known as lines of force.
Where the lines are farther apart, the field is weaker. For an isolated
charge, the lines extend to infinity, while for two or more opposite charges,
the lines emanate from a positive charge and terminate on a negative charge.
Following are diagrams of electric field configurations.
One interesting thing about electric fields involves
conductors. Electric fields created outside of a conductor are unable to
penetrate inside the conductor. Since the conductor shields the space from
the field outside, any electric conductor can create a good way to eliminate
electric fields. Most major computers (like my big tan tower case) shield
the outside from the fields produced inside. Bad shielding results in interference
and static on nearby radios and computer monitors. Charges are most often
spread out over a wide variety of surfaces. Charges also move. The motion
is communicated to neighboring electrical fields by changes in the electric
field.
While visiting the Science Museum in Boston, they had a rather dramatic display. Using a 60(?)-foot high Van de Graaff generator, the operator proceeded to create lightning snaps between the two spheres. Later, he pointed the large sphere towards the metal cage he was housed in, and turned it on. He was simulating a car being struck by lightning, yet he was completely safe. He even went as far as to touch his finger along a metal ring that was attached to his "birdcage", and was perfectly safe. The electrons that showered onto the birdcage repelled each other and spread out over the metal surface, eventually reaching the grounding source. Inside the birdcage, the configuration of electrons canceled each other to practically no charge. In fact, if the charge on a conductor is not moving, the electric field inside the conductor is exactly zero.
This absence of electric field within a conductor holding static charge does not arise from the inability of an electric field to penetrate metals. It comes about because free electrons within the conductor can "settle down" and stop moving only when there is no electric field. Then the charges arrange themselves to ensure zero field within the material.
Consider the charged metal sphere at right. Because of mutual repulsion,
the electrons have spread as far apart from one another as possible. Thus
they are distributed uniformly over the surface of the sphere. A positive
test charge located exactly in the middle would feel no force. The electrons
on all sides would be pulling on the charge, completely canceling each
other out. Thus, the electric field is zero.
However, if the conductor is not spherical in shape, then the charge distribution will not be uniform. If it is a cube, then most of the charge is located near the corner. The remarkable thing, however, is the fact that the exact charge distribution over the surfaces and corners of a conducting cube is such that the electric field inside the cube is zero.
Since gravity only attracts (and there is no repelling force), there is no way to shield the effects of gravitational force. There is, however, a way to shield electric fields. All you have to do is surround the object with a conductor, and you are shielded. The free charges in the conducting surface will arrange themselves on the surface of the conductor so that all field contributions inside cancel each other out. That is why electronics are often cased in metal boxes.
Work is done when a force moves something in the direction of the force. Thus objects can have potential energy by virtue of its location, say in a force field. If you lift an object, you apply a force equal to its weight. You are also increasing its gravitational potential energy. The greater the object is raised, the greater is the amount of potential energy. Doing work increases gravitational potential energy.
In a similar way, a charged object can have potential energy by virtue of its location in an electric field. Just as work is required to lift an object against the gravitational field of the earth, work is required to push a charged particle against the electric field of a charged body. The electric potential energy of a charged particle is increased when work is done to push it against the electric field of something else that is charged.
The figure at left shows a small positive charge located some distance
from a positively charged sphere. If we push the small charge close to
the sphere, we will expend energy to overcome electrical repulsion. Just
as work is done in compressing a spring, work is done in pushing the charge
against the electric field of the sphere. This work is equal to the energy
gained by the charge. The energy that charge now possesses by virtue of
its location is called electric potential energy. If the charge is released,
it will accelerate in a direction away from the sphere, and its electric
potential energy will transform into kinetic energy.
If we pushed two charges instead of one, we do twice as much work. The two charges in the same location will have twice the electric potential energy as one; three charges will have three times the electric potential energy; a group of ten charges will have ten times the electric potential energy. Rather than deal with the total potential energy of a group of charges, in is convenient when working with electricity to consider the electric potential energy per charge. The electric potential energy per charge is the total electric potential energy divided by the amount of charge. At any location, the potential energy per charge—whatever the amount of charge—will be the same. For example, an object with ten units of charge at a specific location has ten times as much energy as an object with a single unit of charge. However, it also has ten times as much charge, so the potential energy per charge is the same. The concept of electric potential energy is called electric potential. Thus, electric potential = electric potential energy/charge. The SI unit of measurement for electric potential is the volt, named after Allesandro Volta. Since potential energy is measured in joules and charge is measured in coulombs, 1 volt = 1 J/C. Thus, a potential of 1 volt is 1 joule of energy per coulomb of charge; 1,000 volts is 1,000 joules per coulomb. If a conductor has a potential of 1,000 volts, it would take 1,000 joules of energy per coulomb to bring a small charge from far away and add it to the charge on the conductor.
Since electric potential is measured in volts, it makes sense to refer to it as voltage. Once the location of zero voltage has been specified, a definite value for voltage can be assigned to a location whether or not a charge exists at that location. We can speak about voltages at different locations in an electric field whether or not there is an electric charge.
If you rubbed a balloon on your hair, the balloon will become negatively charged, perhaps to several thousand volts! If the charge on the balloon were 1 coulomb, it would require several thousand joules to give the balloon that voltage. However, 1 coulomb, as stated in the last chapter, is a very large amount of charge. Thus the amount of energy associated with the charged balloon is very small—about a thousandth of a joule. A high voltage requires great amounts of energy only if a great amount of charge is involved. This is one of the major differences between electric potential energy and electric potential.
Electrical energy can be stored in a device called a capacitor. Capacitors are found in nearly all electronics. Computers use low-energy capacitors as on-off switches (and memory). Keyboards have capacitors below each key. Capacitors in photoflash units store loge amounts of energy slowly and release it rapidly during the short duration of the flash. On a much larger scale, massive amounts of energy are stored in banks of capacitors that power giant lasers in laboratories.
The simplest capacitor is a pair of conducting plates separated by a small
distance, but not touching each other. When the plates are connected to
a charging device such as a battery, charges are transferred from one plate
to the other. This charging occurs as the positive battery terminal pulls
electrons from the positive plate. These electrons in effect are pumped
through the battery and through the negative terminal to the opposite plate.
The capacitor plates then have equal and opposite charges—the positive
plate is connected to the positive battery terminal, and vice versa. The
charging process is complete when the potential difference between the
plates is the potential difference between the battery terminals—the battery’s
voltage. The greater the battery voltage and the larger and closer the
plates, the greater the charge that is stored. In practice, the plates
may be thin metallic foils separated by a thin piece of paper. This "paper
sandwich" is rolled up for compactness, and canned. A charged capacitor
is discharged when a conducting path is provided between the plates.
Discharging a capacitor is a shock experience if you are the conducting
path. The energy transfer that occurs can be fatal where high voltages
are present, such as in the power supply of a TV set.
The energy stored in a capacitor comes from the work
required to charge it. The energy is in the form of the electric field
between its plates. Between parallel plates the electric field is uniform,
and thus the energy stored in a capacitor is energy stored in the electric
field. Electric fields are storehouses of energy. Energy can be transported
over long distances by electric fields, which can be directed through and
guided by metal wires or directed through empty space. In fact, energy
from the sun is radiated in the form of electric and magnetic fields.
|
|
|
 |
A common laboratory (and sci-fi flick) device for building
up high voltages is the Van de Graaff generator. A simple model of the
Van de Graaff generator is show to the left. A large hollow metal sphere
is supported by a cylindrical insulating stand. A motor driven rubber belt
inside the support stand moves past a comb-like set of metal needles that
are maintained at a high electric potential. A continuous supply of electrons
is deposited on the belt through electric discharge by the points of the
needles and is carried up the hollow metal sphere. These electrons leak
onto metal points attached to the inner surface of the sphere. Because
of mutual repulsion, the electrons move o the outer surface of the conducting
sphere. This leaves the inside surface uncharged and able to receive more
electrons as they are brought up the belt. The process is continuous, and
the charge builds up to a very high electric potential—about several million
volts.
A sphere with a radius of 1m can be raised to a potential of 3 million volts before electric discharge occurs through the air because breakdown occurs in air when the electric field strength is about 3×106 V/m. The voltage can be further increase by increasing the radius of the sphere or by placing the entire system in a container filled with high pressure gas. Van de Graaff generators can produce as much as 20 million volts. These devices accelerate charged particles used as projectiles for penetrating the nuclei of atoms. |
|
|
| The print head of an inkjet printer typically ejects a thin, steady stream of thousands of tiny kink droplets each second as it shuttles back and forth across the paper. As the steam flows between electrodes that are controlled by the printer’s logic, selective droplets are charged. The uncharged droplets then pass undeflected in the electric field of a parallel plate capacitor and form the image on the page; the charged droplets are deflected and do not reach the page. Therefore, the image produced on the paper is made from ink droplets that are not charged. The blank spaces correspond to deflected ink that never makes it to the page. |
In conclusion, an electric field fills the space around every electric charge. The field is strongest where it would exert the greatest electrical force on a test charge. The direction of the field at any point is the direction of the electrical force on a positive test charge. Field lines are a representation of an electric field. Static charge occupies only the outer surface of a conductor; inside the conductor the electric field is zero. An electric filed is a storehouse of energy. A charged object has electric potential energy by virtue of its location in an electric filed. The electric potential, or voltage, at any point in a electric field is the electric potential energy per charge for a charged object at that point. A zero of potential must be specified; it is often at infinite distance from charges. Lastly, a capacitor is a device for storing charge and energy.