Coulomb s Law. F = k q 1q 2. k = x 10 9 N m 2 /C 2

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1 Electricity Electricityisaforcemuchlikegravitybutmillionsoftimemorepowerful. Unlike gravity, electricity can be attractive and repulsive. There are two types of electric charge which are labeled positive and negative. Like charges (two positive or two negative charges) repel one another. Unlike charges (one positive and one negative) attract one another. Allcommonmatterismadeupofatoms. Atthecenterofanatom is the positive nucleus consisting of protons with a positive charge and neutrons without a charge. Orbiting around the nucleus are electrons which have a negative charge. The amount of charge on the proton is exactly equal to the charge on the electron. The electric attraction between the positive nucleus and negative electrons hold the atom together. For example, Helium has two positive protons in the nucleus and two negative electrons in orbit around the nucleus. Electrons have a very small mass (9.1 x kg). A proton is much more massive (1.67 x ) or about 1800 times the mass of the electron. Because the nucleus is so much more massive than the the electron, it is normally the electrons that move around. If an atom loses or gains one or more electrons, it is called an ion. If you walk across a carpet on a day with low humidity, you can rub some of the electrons off of your shoes.

2 You build up a charge and when you touch something, electrons are attracted to your lack of electrons in the form of a spark. This also happens when you dry your clothes. As the clothes (especially synthetic fabrics) tumble after they are dry, they acquire a charge. You can then get a static discharge when you touch them. Charge is measured in a unit called a Coulomb (C). The electron (or proton) has a charge of magnitude 1.6 x C. Said another way, a Coulomb is the charge of 6.25 x electrons. The origins of the Coulomb unit go back to chemistry and the early study of electricity before the atomic nature of matter was understood. The Coulomb is a SI (metric) unit but there is no English unit of charge. For things electrical, the entire world uses metric units. Coulomb s Law Coulomb s Law tells us the force between two charges. It very much resembles Newton s law of gravity but the masses are replaced by charges and the proportionality constant is different. Coulomb s law is: F = k q 1q 2 r 2 Theforce,F,isinNewtonsandthechargesq 1 andq 2 areincoulombs. The distance, r, is in meters. The proportionality constant is: k = x 10 9 N m 2 /C 2 k is sometimes called Coulomb s constant. It is very big compared to G. Two like charges, each of charge 1 C, placed 1 meter apart will repel each other with a force of about 9 x 10 9 Newtons.

3 Charge Polarization If a charged object, say with a positive charge, is placed near an uncharged object, the positive charge attracts some of the electrons in the uncharged object to the side of the object nearer to the charged object. This is called charge induction. While the uncharged object has not total charge (we have not added or removed charge from the uncharged object) we have rearranged the charge on the object. Such an object is said to be electrically polarized. There are many things in nature e.g. a water molecule, that exhibit this type of charge arrangement. If the humidity is low and your laundry becomes charged with static electricity, you may have seen a statically charged piece of clothing like a sock jump to an uncharged object like a wall or you. If the sock has a negative charge, it pulls a positive charge to the side of the uncharged object. In fact, the pull is actually a pushing of some of the electrons away from the part of the object near the negatively charged sock. Making a Static charge Building up a static charge is more complicated than simply rubbing electrons off of one object to another. This does occur but the effect is normally very small. The materials that are in contact determine how much charge can be accumulated.

4 The chemical potential of the material determines how strong the material s atoms hold on to their electrons. (Some elements like chlorine hold on very tightly to their electrons and will even steal them from other atoms. Other elements like many metals only loosely hold on to some of their electrons and will give up or trade them freely). Depending on the material being in contact, free electrons can be transferred from one material to the other. The rubbing gives many opportunities for this transfer to take place. The process is selflimiting. Once one surface becomes charged with an excess of electrons, the accumulated negative charge repeals other electrons trying to add to the negative charge. Photo copies Photocopiers use static electricity to make copies. The key to the processis abelt or cylinder ofamaterialwhichis aphotoconductor. A photoconductor is normally an insulator but becomes conducting when exposed to light. The process starts when the photoconductor is charged by a negative corona discharge (a uniform spray of charge frommanyfinewires). Anopticalimageofthedocumenttobecopied is projected on the charged photoconductor. Where the light (white part of the image) hits the photoconductor, the photoconductor becomes a conductor and the charge is neutralized.

5 The remaining part of the process is transferring the (black) image to the plain paper. Since the black part of the image on the photoconductor is still charged, fine positive toner particles are attracted to the negatively charged areas. At this point, a lamp discharges the photoconductor and the image is transferred to plain paper. The fine toner particles are then bonded to the paper by heat (or chemicals). Electric Fields Like gravity, a charge fields the influence of another charge at a distance. We can use the idea of an electric field to visualize the force field around a charge, group of charges or even a charge distribution. The field lines at a given point in space tell us the direction a very small positive charge would move if placed at that point. Thus the lines always point away from a positive charge and towards a negative charge. The electric field is defined by: E = F q The units of the electric field is Newton per Coulomb (N/C). From Coulomb s Law and the definition of the electric field, the magnitude of the electric field for a point charge is given by E = k q r 2 The Corona discharge for the photocopier utilizes this feature of a point charge electric field. As you approach a small point at the end of a wire or surface, the electric field lines concentrate creating a region of strong electric fields near the point. This allows for a discharge because the electric field is strong enough to ionize the air and create a discharge.

6 Other charge distributions have more complicated electric fields which depend on the geometry of the charge distribution. For a single positive charge, the electric field lines point radially away from the point charge. For a positive and negative charge, the pattern is called a dipole. For two sheets of charge, the pattern is a series of uniformly spaced lines. Gravity and electricity are examples of a field. A field is just a wayofthinkingabouttheforce. Theforcepervadesallofspace. The earth does not touch the moon but we know it pulls (exerts a force) onthe moon. Thisis calledforce or action at a distance. Even if there is not a charged object at a point in space, we know there would be a force on a charge object from the electrostatic attraction. The direction and magnitude of this imaginary pull at any point is how we think of the field. Actually, this idea of action at a distance has some problems. How do we really know the charged object (or massive object for gravity) is really there? What if it moved very quickly to another location.

7 Although they are called quantum field theories, in modern (quantum) physics every force is transmitted by sending a force particle (boson) between the two particles feeling the force. In this way, modern physics avoids the problems of action at a distance. Electric Potential Just as we spoke of a mass having gravitational potential energy in a gravitational field, an electric charge in an electric field also has potential energy. Because the energy depends on position (and not motion) this is potential energy. A larger charge at the same position asasmallerchargeinanelectricfieldwillhavemorepotentialenergy. To avoid dealing with total energy depending on the charge, we define the electric potential as: electric potential = electric potential energy amount of charge The unit of electric potential is the Volt (V). It is defined as: 1 volt = 1 Joule Coulomb Electric potential gives us a way to determine the electrical effects at a location in space even if there is not a charge present at that location. Often we speak of potential difference. This is just the difference in electrical potential between two given points. Electric potential can be related to the electric field by: electric field magnitude = V r The direction of the electric field is given by the direction which has the largest change in the voltage change (gradient).

8 There are many ways to produce a potential difference between two points. A battery produces a potential difference between the two terminals of the battery by chemical means. A power station produces a (varying) potential difference between the wires on the power grid. A power station produces the electrical potential by induction which we will discuss when we talk about magnets and magnetic fields. Electric Current When a potential difference is applied across a conducting wire, the electrons move towards the positive terminal and way from the negative terminal. In conductors (normally a metal) there are electrons which can move freely inside the conductor. (A bad conductor is called an insulator analogous to heat flow). A flowing of electric charge is called a current. The wire does not become charged since the electrons are simply moving around the closed circuit under the influence of the potential difference supplied by the voltage source. battery current electrons By convention we say the current is flowing from the positive terminal to the negative terminal of the battery. This is backwards to the electron flow. This convention was defined before people knew about free electrons in metals or even understood atoms.

9 You can think of the flow of charge much like the flowing of water in a pipe. In this analogy the battery is a pump, the pump pressure is the potential difference, the wires are the pipes and the flow rate is the current. This current (flow rate of charge) is measured in amperes. An ampere is a Coulomb of charge flowing past a point in the circuit (through the crosssection of the wire) in one second. Resistance Some conductors provide an good path of the charge to flow (a big pipe in our water analogy), others obstruct the flow to some extent (a narrow pipe). Electrical resistance is how well a current can flow through something. A wire which will allow only a small current to pass through it is said to have a high resistance. Resistance is measured in Ohms (Ω). If a large potential difference is applied to given conductor, more current will flow. In our water analogy this is like increasing the water pressure. More water will flow through the same pipe if youup the pressure. This is embodied in Ohm s Law: current = voltage resistance or V = IR where V is the voltage (potential difference), I is the current and R is the resistance (Ω). In terms of units: amperes = volts Ω Ohm s law lets us find current, voltage or resistance when we know two two of these values.

10 switch battery battery bulb We can analyze a common flashlight using Ohm s law. The filament is a thin tungsten wire as we discussed earlier. The filament is very thin and tungsten is not an excellent conductor like copper or aluminum. The resistance of the filament in the bulb is 20Ω. When the switch is closed current can flow in a closed circuit around the batteries and through the bulb. Each battery is 1.5 volts. The two batteries in series give 3 volts. From Ohm s law, the current is 3 volts/20ω or 0.15 amperes. Electrical Power Power (energy or work per time) is normally expressed in watts. With an electrical circuit, the power output of the voltage source is given by: or said in terms of the units: Power = current x voltage Watt = ampere x volt A 60 Watt electrical bulb operating at 120 volts draws 1/2 ampere of current from the electrical outlet. For our flashlight, the power is 3 volts times 0.15 amperes or 0.45 watts. This should not be too much of a surprise since current is Coulombs/second and volts are Joules/Coulomb. Multiplied together you get Joules/second which is, of course, a watt.