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Electricity and Magnetism


Electricity and Magnetism: Introduction

Despite its use in many different forms of matter, electricity itself is not composed of matter. Instead, physicists refer to electricity as an event. To understand this distinction, it is important to remember that matter is composed of charged particles. The simplest form of matter is the atom. The atom consists of a nucleus containing protons and neutrons which is surrounded by an electron cloud. Protons are positively charged particles, electrons are negatively charged particles, and neutrons are particles that carry no charge at all. When atoms are neutral they have a net charge of 0. Therefore, all uncharged atoms have equal numbers of protons and electrons. However, when an atom gains or loses electrons it develops a negative or positive charge, respectively. This makes the atom attractive to other atoms that bear an opposite charge; i.e., positively charged atoms are attracted to negatively charged atoms and vice versa.

This attraction provides the basis for electricity and resulted in the formulation of Coulomb’s Law in 1785 by Charles Augustin de Coulomb. Through experimentation with tiny charged balls, Coulomb was able to apply Newton’s Third Law of Motion and show that the balls not only were attracted to one another with equal but opposite forces but also carried opposite charges (Figure 1). The international, or SI, unit for charge is the coulomb (C).

Coulomb’s experiments led him to demonstrate mathematically that the forces which attracted the spheres to one another were proportional to the product of the charges on the spheres as well as inversely proportional to the square of the distance separating their centers. For example, Coulomb showed that doubling the charge on a single sphere resulted in a doubling of the force. Further, he discovered that if he doubled the charge on both spheres the force quadrupled. This led to the development of Coulomb’s Law, which is written mathematically as:

The proportionality constant, k, is equal to 9.0 x 109 N x m2/C2. Coulomb’s work led to the determination that an electron has a charge of 1.60219 x 10-19 C. To put the charge of a single electron in perspective, a charge of 1 C would exert a force of 9 billion N. Charges of this magnitude are not normally encountered.

In its normal state, an atom typically has a net charge of 0. However, losing electrons creates a positive charge because protons now outnumber the electrons. Similarly, if an atom gains an electron it develops a negative charge because the electrons now outnumber the protons. The willingness to accept or donate electrons is a property of matter. Some types of matter are more willing to accept or donate electrons than others. Unlike materials are more likely to undergo electron transfer when rubbed together than like materials. Thus, rubbing a glass rod with a wool swatch is more likely to result in a transfer of electrons than rubbing two glass rods or two wool swatches together.

Greater surface area of materials means a greater likelihood that electron transfer will occur. The amount of contact between the two objects also plays a role in electron transfer. For example, scuffing the sole of one foot against a carpet one time before touching a metal doorknob is unlikely to result in a shock, but scuffing both feet across the same carpet over several meters is likely to result in a tangible discharge of electricity upon contact between a person’s fingers and the doorknob. Even the simple act of sliding across seat upholstery when exiting a car can generate significant electron transfer. This is why signs at gasoline pumps advise touching a metal surface before refueling to discharge any built-up electrons. Otherwise, a static discharge could ignite fumes released when gasoline flows from the pump into the vehicle’s tank.


Static Versus Current Electricity

Up to this point, we have been discussing static electricity. What is the relationship between static electricity and the electricity which powers appliances, known as current electricity? Electricity is electrons in motion.

  • In static electricity, electrons are moving between materials.
  • In current electricity, electrons are moving through materials.

In other words, electrons flow in a path just as water flows through a pipe (below).

The flow of electrons in one direction in a material generates an apparent flow of positive charge in the opposite direction of the flow of electrons (green in the above diagram). In the late 1700s, electrons had not yet been discovered. Thus, the assignment of charge was arbitrary. Benjamin Franklin proposed that objects with an excess of charge were positively charged, and objects that were deficient in charge were negatively charged. In reality, the objects that Franklin determined to be positively charged had lost electrons so were technically deficient in electrons rather than having an excess of charge. Similarly, objects termed negatively charged by Franklin did not have a deficiency of positive charge. Instead, they had an excess of electrons. However, by the time electrons were discovered and determined to be the factor that actually flowed in an electric current Franklin’s terminology was firmly entrenched. Thus, current is still frequently referred to as a flow of positive charge. It should be remembered, however, that this is an apparent flow of positive charge, and it is the electrons that are actually in motion. The atomic nuclei, where the positive charges are located (in the form of protons), are stationary within the material.

Electricity flows through a circuit. A circuit is an uninterrupted path between the terminals of a power source. The diagram below illustrates a very simple circuit consisting of a battery and a light bulb. In this circuit, the direction of current flow (apparent flow of positive charge) is designated (in green) in a clockwise direction from the positive terminal, through the base and filament of the bulb, and then back to the negative terminal through the tip of the bulb. Electrons, however, flow in the counterclockwise direction from the negative terminal through the circuit and back to the positive terminal.



A battery is a source of chemical potential energy. The most popular batteries are alkaline batteries because they are long-lasting. Alkaline batteries consist of a steel can lined with a compressed mixture of manganese oxide, graphite, and an electrolyte (see diagram below). The manganese mixture plus the steel can serve as the battery’s cathode (negative terminal). Inside the manganese oxide is a center core of zinc powder in a potassium hydroxide liquid. This zinc core is the anode (positive terminal) and is separated from the manganese by a paper filter soaked in an electrolyte solution. A brass nail inserted into the zinc mixture from the top collects the current and creates the raised area on the positive end of the battery.


The two chemicals each have a different electrical potential. Electrical potential is defined as the energy per unit charge. This potential difference (difference in potential energy) provides the impetus for current flow. As illustrated in the simple battery/light bulb circuit above), the direction of current flow is designated from areas of high potential (positively charged regions) to areas of low potential (negatively charged regions), even though electrons flow from the negatively charged regions to the positively charged regions. Current will not flow in a circuit unless there is a difference in potential. Only differences in potential energy can be measured. In electricity, this potential difference is measured in volts (V). Energy is measured in Joules (J), so 1 V = 1J/C. The volt is named after Alessandro Volta, who developed the first electric battery. Potential difference is also known as voltage, and the two terms are used interchangeably. Voltage is measured using a voltmeter.

Voltage is additive. Alkaline batteries all are rated at 1.5 V, as the potential difference between zinc metal and manganese metal is 1.5 V. However, some forms of alkaline battery, such as a transistor battery, are rated at higher voltages. A transistor battery shares the same chemical make-up as the D cell battery shown in the diagrams above. However, the transistor battery is actually a series of six batteries, or cells, with positive and negative terminals touching inside a single case (see diagram). The potential difference across the cells is six times the individual potential differences of the cells, or 9 V.

The current that is generated by differences in potential in a battery or other electrical circuits can be measured. Current is determined quantitatively by measuring the net amount of charge that passes a given cross-section of wire in a specified period of time. Current is abbreviated with the letter “I” and is defined mathematically as:

where ΔQ equals the net amount of charge passing the specified cross-sectional area of the wire and Δt equals the given time period. Current is measured in amperes (A or amp) and 1 A = 1 C/s, named after 19th-century French physicist André Ampère, who determined the relationship between current and the magnetic field around a wire. Current may also be called amperage and is measured using an ammeter.

The amount of current which flows through a circuit is dependent upon the potential difference in the circuit as well as the type of wire in the circuit. Current flows more easily through some metals than others. This is dependent upon the atomic structure of the atoms of the substances which make up the wire in the circuit. Some atoms, such as those of tungsten, are more reluctant to allow the passage of electrons than others such as copper and aluminum. This property is known as resistance.



Resistance is a function of both the type of material that makes up the wire and the wire’s dimensions. Long wires provide greater resistance than short wires, while wires with large cross-sectional areas provide less resistance than those with small cross-sectional areas. An excellent example of a wire with a very high resistance is the filament in an incandescent (lamp) bulb.

The filament is made of a very thin tungsten wire that is two meters or more in length. The wire is coiled and then coiled back on itself in order to fit into the light bulb. The tremendous resistance provided by this combination of great length and tiny cross-sectional area generates a white-hot heat that provides the light produced by the bulb.

As resistance increases, the amount of current for a given voltage decreases proportionally. This can be demonstrated mathematically as:

where V equals voltage, I equals current, and R equals resistance. This relationship is known as Ohm’s Law, as it was determined by one of Ampère’s contemporaries, Georg Simon Ohm. Manipulation of this equation yields the definition of resistance as the ratio of voltage to current:

Resistance is measured in ohms, abbreviated by the Greek letter omega (Ω); 1 ” = 1V/A. It should be pointed out that not all materials and devices adhere to Ohm’s Law; it is specific to metals which conduct electricity. A conductor of electricity is a substance that has electrons that can move freely. Substances in which the atoms hold tightly to their electrons, thus preventing electron flow, are called insulators, or nonconductors. Some substances are intermediate in their abilities to conduct electricity. These are classified as semiconductors.



The concept that opposite charges attract one another in electricity bears a strong resemblance to the same concept in magnetism. However, until 1820, scientists were unable to demonstrate any attraction between isolated electric charges and magnets. In 1820, Hans Christian Oersted demonstrated that while placing a compass next to a stationary charge such as that generated by rubbing wool on glass did not affect the compass, placing it next to a wire carrying an electric current caused the needle to deflect. Oersted had discovered that current moving through a wire generates a magnetic field in concentric circular paths around the wire (see Straight Wire diagram). The direction of the magnetic field can be determined easily by using the right-hand rule: wrap the right hand around the wire with the thumb pointing in the same direction as the flow of current. The fingers will curve around the wire in the same direction as the magnetic field.
The same effect is seen if the wire is made into a circular loop. The current generates a magnetic field that flows through the loop (see Circular Loop of Wire diagram). As can be seen, the right-hand rule still applies to a loop of wire. The direction of the magnetic field follows the direction of the fingers again so that in the diagram the direction of the magnetic field is toward the palm of the hand. Notice that as in the case of the straight wire, the thumb still points in the same direction as the current.

If wire is coiled into a series of evenly spaced loops called a solenoid and electrified (a current is passed through it), a magnetic field is generated around and through the coil. If a metal bar such as a nail is placed in the center of the coil, the magnetic field generated by the current flowing through the coil turns the metal bar into an electromagnet. The bar loses its magnetic ability if the current is disconnected. The magnitude of the magnetic field (B) generated by the solenoid is determined by the number of loops of wire in the coil, the length of the coil, the amount of current present in the circuit, and a proportionality constant known as the permeability of free space. Magnetic field can be calculated using the following equation:


  • B = magnitude of the magnetic field in tesla (T)
  • μ0 = 4π x 10-7 T-m/A
  • N = number of loops of wire in the coil
  • L = length of the coil in meters (m)
  • I = current in amperes (A)

The quantity N/L represents the number of loops per length of the coil, and can be represented by “n”. Thus, the equation can be rewritten as:

As the magnitude of the magnetic field of the coil increases, the strength of the electromagnet increases, so that its ability to attract and hold objects made of materials with magnetic properties also increases. B can be increased by increasing the number of loops in a coil of a given length, decreasing the length of the coil without changing the number of loops, increasing the current, or by some combination of these factors. However, if the number of loops and the length of the coil are both increased, the ratio of loops to length must be greater than the starting ratio or B will not increase.

This CELL is designed to introduce you to the relationship between voltage, current, and resistance in ohmic devices by first demonstrating that voltage and current are proportional. You will then discover that this proportional relationship is due to the resistance provided by the ohmic device (a resistor) and that in a circuit with constant voltage current will change in proportion to the amount of resistance present in the circuit.

In the lab, you will place resistors in series to explore how resistance increases as resistor length increases. You will also place resistors in parallel to generate the effect of increasing the diameter (and thus cross-sectional area) and discover that increasing the cross-sectional area decreases the amount of resistance in a circuit. Manipulation of resistor dimension using series and parallel circuits will reinforce for you the concept that resistance determines the rate at which electrons can flow through a circuit. Finally, you will explore the connection between electricity and magnetism by creating an electromagnet and testing the effects of changing the number of loops as well as the amount of current. You will then have an opportunity to apply the concepts you have learned by using your gained knowledge of resistance and magnetic field to design a series of electromagnets of varying strengths.


The Focus Questions in each Investigation are designed to help teachers and students focus on the important concepts. By the end of the CELL, you should be able to answer the following questions:


Investigation 1:
  • What is the relationship between voltage, current, and resistance? 


Investigation 2:
  • What is the relationship between voltage, current, and resistance? 
  • How do the dimensions of a resistor affect current? 
Investigation 3:
  • What is the relationship between electricity and magnetism? 
  • What factors affect the strength of an electromagnet? 

Note: Some questions may be revisited as the CELL progresses. As students acquire additional knowledge, their responses should reflect this.


  • Fun Facts: Making Electricity
  • More Fun Facts: Static Electricity
  • Learn the Lingo
  • Get Focused



Making Electricity

Everyone knows that the gas, water vapor, that is formed from boiling water can create enormous pressure. Take the simple whistle of a teapot for example. Sparking what would become known as the industrial revolution, inventors, engineers, scientists, and entrepreneurs learned that the pressure from steam escaping from boiling water could be harnessed to do work. The first trains and tractors were powered by steam engines. Soon, factories were harnessing the same steam power to turn the mega-machines that gave birth to large-scale manufacturing, and the world was changed forever. All from boiling water, the most abundant molecule on Earth!


Fossil Fuel

One of the most important uses found for steam power was the turbine. Turbines are devices that are capable of turning the pressure of boiling water vapor, steam, into electricity. Below is a schematic illustration of a fossil-fuel power station from the Tennessee Valley Authority.

Fossil-Fuel Power Station (click on image to enlarge)

In this illustration, coal is being used to stoke the fires that boil the water and generate steam to turn the turbine and produce electricity. However, anything that burns, typically other fossil fuels like oil or natural gas or even firewood, can do the same job.

While fossil-fuel supplied the energy to drive the industrial revolution and usher humanity into the modern age, it has the unfortunate sideproduct of causing pollution of both air, land, and water. In addition, burning fossil fuels release “greenhouse gases” into the atmosphere that can contribute to large-scale weather changes. We will discuss this aspect of the issue of fossil fuels elsewhere. In any case, the development of cleaner ways to produce electricity in the future has become a major challenge and will, in all likelihood, remain so for future scientists and engineers like yourself perhaps.

Fossil-Fuel Power Station

Nuclear Reactors

Keeping in mind that a turbine can make electricity regardless of how the water is boiled, alternatives to fossil-fuels have largely focused on alternative ways to heat the water and turn the turbines. One such method is nuclear power (below).


Nuclear Power Station (click on image to enlarge)

Nuclear Power Plants capture heat energy caused by controlled nuclear fission reactions to heat water and generate steam to turn turbines. As can be seen in the schematic diagram above, outside of replacing coal fires with nuclear reactions, fossil-fuel and nuclear power stations operate in a very similar manner.

Unfortunately, nuclear power has its own environmental issues. While the cooling towers seen in the video above are spewing steam, not smoke, nuclear plants can impact local water supplies by heating them in the cooling process. In addition, nuclear power plants are a constant potential disaster should the nuclear reactor core, where the fission reaction takes place, meltdown. Such meltdowns can and have lead to catastrophic releases of radiation into the environment.


Hydroelectric Power

Running water has been used to turn small and sometimes rather large waterwheels for centuries. The video below depicts just how simple such technology can be.

The shaft of the turning wheel can be used to do mechanical work, grinding flour, for example. However, with the invention of the turbine, hydro-electric power generation has taken the amount of electricity that can be produced from water power to incredible levels.

To increase the amount of power that can be generated by water, massive dams have been constructed across major waterways and rivers. Dams prevent water from naturally flowing downstream, building up reservoirs of water. As seen in the example below, the water level of the reservoir can be many, many meters higher than the outlet on the other side of the dam. As you can imagine, this difference in water level brings gravitational force into play. The potential energy of the high water level on the upstream side of the dam is converted to kinetic energy as it moves to the other side of the dam. In a hydroelectric power plant, turbines are placed in the path of the flowing water to convert the mechanical kinetic energy into electric energy.

The placement of turbines in the path of falling and dammed water has been used to produce electricity since before the turn of the last century. In the 1890s, the brilliant engineer, Nicola Tesla, working with the Westinghouse Corporation, used turbines he designed at the Adams Power Station to harness the power of Niagra Falls to produce electricity for the city of Buffalo, New York.

While hydroelectric power plants do not release greenhouse gases, they are not without their own environmental impacts. Also, their construction is costly and limited, of course, to specific geographical locations. Large dams convert thousands of square kilometers into submerged reservoirs. In addition, dams are a direct physical impediment to the upstream migration of anadromous fish like the salmon shown below.


Wind Power

Wind Power is actually a form of solar power (more below). Think about it. This is because, as we have learned (or will learn) in the Atmosphere CELL, wind is caused by the uneven heating of the Earth’s surface by the Sun. Rising, low-density hot air is replaced with cooler, high-density air masses, thus causing the movement of tremendous volumes of air across the planet’s surface. The kinetic energy of moving air masses (wind) can be harnessed by turbines attached to huge blades to generate electricity. This is an exciting new way to generate electricity that does not release greenhouse gases.

Nonetheless, while wind-powered windmills are an exciting new form of electricity production, they are not without technical problems and their own environmental impact. For example, windmills do not work at all when there is no wind to turn the turbines and they are known to kill birds at a significant rate.


Solar Energy

Perhaps the most exciting energy technology is direct solar power (as opposed to indirect solar-induced wind power). The heart of solar energy production is the solar panel. An entire “farm” of thousands of solar panels is shown below.

Nuclear Power Station

An individual solar panel is shown being carried onto a construction site for installation in the picture below. Thus, solar panels and solar energy can be used to produce electricity on an industrial scale on the one hand, and for private, residential use on the other. 

Individual Solar Panel


A simplified overview of the way solar panels produce electricity from sunlight is shown in the schematic below. In essence, photons are produced in the interior of the Sun. After leaving from the Sun’s surface and traveling for about 8 and a half minutes, the photon strikes the surface of the solar panel where it releases its energy as an electron (e). The electrons then move through the solar panel silicon layers, creating an electrical current.

Solar panels do not emit greenhouses gases as they produce electricity. However, steps in the manufacturing of solar panels do produce greenhouse gases and involve some toxic chemicals. In addition, this form of solar power involves an obvious drawback to its use as a sole source of electricity production – solar panels do not work well on overcast days or at night. The key to the use of solar panels as a long-term solution to clean, renewable electricity production will likely revolve around technological developments that detoxify manufacturing, low costs, increase efficiency at low light levels, and storage of electricity produced at peak solar hours for use at other times. These are all technical problems that engineers and scientists will hopefully soon solve.



Static Electricity

Electricity was first identified as a property of amber by the ancient Greeks. The term electricity is derived from the Greek word for amber, elektron. The Greeks chose this term because rubbing an amber rod with a piece of cloth caused the rod to attract dust. This was called the “amber effect”, and is now recognized to be the form of electricity known as static electricity.


Static electricity can be very powerful. For example, lightning is caused by a buildup of static electricity in storm clouds. This was one of the major scientific accomplishments of the American scientist and statesman, Benjamin Franklin. The famous experiment of flying a kite in a thunderstorm with a metal key attached represents this discovery.

Nonetheless, even though there is a tremendous amount of power in lightning, it is not an easy source of electricity to use. One of the most notorious (and fantastical) direct uses of electrical power harnessed from lightning is in the story of the Frankenstein monster from 1930 Hollywood horror films. While old fashioned today, at the time the novel Frankenstein was written by the then 17-year old English novelist Mary Shelley in 1817, widespread fascination with the mysterious power of electricity captivated both lay and scientific thinkers alike.

Colorized image from the 1974 movie Young Frankenstein



The following list includes Key Terms that are introduced within the Backgrounds of the CELL. These terms should be used, as appropriate, by teachers and students during everyday classroom discourse.

Note: Additional words may be bolded within the Background(s). These words are not Key Terms and are strictly emphasized for exposure at this time.


Investigation 1:
  • Current: the amount of charge that passes a given point in a specified period of time, measured in amperes (amps, A). The direction designated for current flow is opposite from the direction of the flow of electrons in a circuit. In a closed circuit powered by a battery, the direction of current flow is from the positive terminal to the negative terminal of the battery.
  • Current Electricity: Current electricity is an electrical charge in motion. It is the flow of electrons through a complete circuit of conductors.
  • Electric potential: the potential energy per unit of positive charge. Measured in volts.
  • Multimeter: an instrument used to measure current, voltage, and resistance.
  • Ohm’s Law: the ratio of voltage to current is resistance and is represented by the equation R = V/I, where R = resistance, V = voltage, and I = current.
  • Potential difference: the difference in electric potential between point A and point B. In a circuit, point A and point B represent the positive and negative terminals of a power source such as a battery. Also known as voltage. Measured in volts (V).
  • Resistance: the decrease in the flow of electrons and current due to a change in the diameter or material of a wire. Resistance is measured in ohms (Ω).
  • Resistor: any wire in a circuit which causes a decrease in the flow of current due to its diameter or material. An example would be the filament in a light bulb. Also, any wire placed into a circuit specifically to maintain the flow of electrons and current at a specific level.
  • Static Electricity: Static electricity results from an imbalance between negative and positive charges in objects.


Investigation 2:
  • There are no new Key Terms introduced in Investigation 2.
Investigation 3:
  • Tesla (T): Unit of measure for the magnitude of a magnetic field.