SPH 3UElectricity and Magnetism
Review of Matter
1. All matter is composed of atoms.
Our ideas about the nature of atoms have progressed over the last two centuries (and continue to develop today).
John Dalton introduced a new form of the ancient Greek idea of atoms at the beginning of the nineteenth century.
In 1897, J.J. Thomson discovered the electron and suggested the 'plum pudding' model of the atom.
In 1911, Rutherford suggested that electrons orbit the atomic nucleus like planets round the Sun.
In 1914, Bohr modified Rutherford's model by introducing the idea of energy levels.
2.Atoms contain protons, neutrons and electrons. Of these three subatomic particles, only the proton (positively charged) and the electron (negatively charged) are considered charged particles. A neutral object has an equal number of protons. A charged object has an unequal number of electrons and protons.
(see hyperlink for more information)
Electrostatics
Static: still
Electrostatics: is the study of the phenomena arising from what seems to be stationary electric charges.
Three themes – charge difference, medium, distance run through our study of electrostatics and electricity
1. Charge Difference
- An object becomes charged if it gains or loses electrons. A neutral object has an equal number of positive and negative charges! Charged objects obey the law of opposites as follows
Fundamental Law of Electric Charges
- Like charges repel.
- Opposite charges attract.
- Charged objects can attract some neutral objects, (depending on the level of conductivity)
- A historical look at charges
The choice of which type of electricity is called "positive" and which "negative" was made around 1750 by Ben Franklin, early American scientist and man of many talents (the stamp on the left commemorates his role as first US postmaster--and colonial postmaster before that). Franklin studied static electricity, produced by rubbing glass, amber, sulfur etc. with fur or dry cloth. Among his many discoveries was proof that lightning was a discharge of electricity, by the foolhardy experiment (he claimed) of flying a kite in a thunderstorm. The kite string produced large sparks but luckily no lightning, which could have killed Franklin.
Franklin knew of two types of electric charge, depending on the material one rubbed. He thought that one kind signified a little excess of the "electric fluid" over the usual amount, and he called that "positive" electricity (marked by +), while the other kind was "negative" (marked -), signifying a slight deficiency. It is not known whether he tossed a coin before deciding to call the kind produced by rubbing glass "positive" and the other "resinous" type "negative" (rather than the other way around), but he might just as well have.
Later, when electric batteries were discovered, scientists naturally assigned the direction of the flow of current to be from (+) to (-). A century after that, electrons were discovered and it was suddenly realized that in metal wires the electrons were the ones that carried the current, moving in exactly the opposite direction. Also, it was an excess of electrons which produced a negative electric charge. However, it was much too late to change Franklin's naming convention
In 1896 Joseph John Thomson discovered the electron. However he didn't manage to define its mass neither its charge. He only calculated the proportion of the charge to the mass of the electron (q/m). He believed that the newly discovered particle was a part of an atom. But he didn't give enough evidence for that hypothesis. Defining the charge and the mass could be the final proof.
Many scientists tried to solve this problem. The first who managed to measure what was the elementary charge was one of Thomson's students- J.S. Townsend. Unfortunately the final result he got had a big measurement error. The first scientist who quite precisely defined that charge was Robert Andrews Millikana. It must be said that he didn't measure the charge of the electron. He only showed that there is some indivisible amount of charge in nature- the elementary charge. All other charges are exact multiples of that elementary one. Later it emerged that the elementary charge was the the charge of the electron.
Since protons are fixed in the nucleus of an atom, electrons are the charge which become influenced and move. {electron flow} But, because charges obey the law of opposites, we can analyze charges through the movement of either positive or negative charges, ignoring their connection to the atom. {Current flow} The grade 11 curriculum encourages the use of the current flow convention which assume that positive charges flow.
- Charging an object
- Friction
Whenever two different objects are rubbed together, electron transfer will occur due to their electron affinity. Electron affinity refers to how much hold a substance has on its electrons.
More information can be found at
including the triboelectric series
- Arcing/Contact
If a charged object is brought near another charged object or a conductor, electrons might jump through space due to their attraction. This is called arcing. Lightning is an example of an arc – a large transfer of charge.
- Induced Charge Separation / Grounding / Charging by grounding
As the diagram indicates the following explains another method of charging an object
In the first picture, the charges are uniformly distributed.
When a negative rod is brought near, the charges realign – called INDUCED CHARGE SEPARATION
If the neutrally charged ball (same number of positive and negatively charged objects despite the new alignment) is then connected to ground, the charge will flow to even out the local excess of charge.
If the ground is removed, the once neutrally charged ball is charged.
- Q=Ne
Robert Millikan hypothesized that all charges were based on some multiple of an elementary charge – the electron. His claim was verified by his famous oil drop experiment in August 1913. For more reading – see
Q stands for the charge - units are Coulombs
N stands for a the number of electrons in excess or deficit
e stands for the charge of the elementary charge – the electron
e = 1.6021892 1019 Coulombs
2. Medium
Definition - the surrounding environment, substance. Examples include air, metals, etc..
Conductors vs. Insulators
More on conductivity....
The bonding nature (structure) of a material affects its ability to be influenced by a charge.
A conductor allows a charge (electrons) to move within the material rather easily where an insulator restricts any internal movement of charge (electrons). An insulator restricts the movement of particles including electrons.
Humidity
Humidity is a measure of the amount of water vapour in the air. Water is a better conductor then air and Lightning is more likely to happen when the humidity is high or when there is rain.
3. Distance
Coulomb(1736-1806) mathematically analyzed the law of opposites.
More information -
Coulomb’s law describes the force that one electric charge will exert on another:
- The magnitude of the electric force between any two charged objectsis directly proportional to the product of the charges on the objects andinversely proportional to the square of the distance between their centers.
k is the Coulomb's law constant, for air the value is approximately
Summary
- The smallest charge freely occurring in nature is the elementary charge.
- The elementary charge is equal to about 1,602x10-19Coulombs.
- An electron is of the negative, elementary charge.
- The first one to define the quantity of the elementary charge was Robert Andrews Millikan.
- positive charge comes from having more protons than electrons. i.e. +e
- negative charge comes from having more electrons than protons. i.e. –e
- charge is quantized, meaning that charge comes in integer multiples of the elementary charge e
Q = N ∙ e
Q - the symbol used to represent charge
N - a positive or negative integer
e - the electronic charge, 1.60 x 10-19 Coulombs (C).
4. Movement
Stephen Gray , in 1707-8, determined that charge can flow through conductors and that this flow could be controlled.Gray’s discovery marked the first step of the journey from electrostatics to the control of electric current.
The second more crucial step occurred in 1800, Alessandro Volta (1745-1827) invented the electrochemical cell.
Discovered that if you place salt water soaked paper between two different metals, such as silver and zinc, an electric charge appeared on each of the metal disks and became known as a voltaic cell.
When he made a pile of these cells the electric strength increased. This pile became known as a battery or voltaic pile.
Question:
Suppose that two point charges, each with a charge of +1.00 Coulomb are separated by a distance of 1.00m. Determine the magnitude of the electrical force of repulsion between them in (N), then in units we can better make sense of.
Objects do not acquire charges on the order of 1.00 Coulomb.
Q values are on the order of 10-9 (nano, nC) or possibly 10-6 (micro, μC).
Question:
Two balloons are charged with an identical quantity and type of charge: -6.25 nC. They are held apart at a separation distance of 61.7 cm. Determine magnitude of the electrical force of repulsion between them. 9.2x10-7 N
Electric Current
The number of electrons flowing past a single point per second is referred to as electric current. The SI unit for current is the ampere (A). We measure electric current with an ammeter.
When a current of 1A flows through a conductor for 1s, 1C of charge passes any point in the conductor. 1C of charge is equal to electrons.
Question: A typical lightning flash lasts a quarter of a second and the peak current is about 15kA. Determine the quantity of charge in coulombs transferred by this lightning strike. Approximately how many electrons is this?
WHICH WAY DO ELECTRONS FLOW? DO WE KNOW?
2 THEORIES
Conventional Current
Today, the term current (I) means the flow of positive charge from the anode to cathode in a circuit. (positive terminal to negative terminal) This was the convention chosen during the discovery of electricity.
Electron Flow
The flow of negative charge from cathode to anode is called electron flow. (negative to positive terminal)
Both Conventional Current and Electron Flow are used by industry. In fact, it makes no difference which way current is flowing as long as it is used consistently. The direction of current flow does not affect what the current does.
We will use the conventional current theory since a wealth of theory was based on this convention.
Potential Difference
Imagine skiers on an electric hill, they represent the charges.
The chemical action inside a battery takes negative charges from the cathode (bottom of the electric hill) to the anode (top of the electric hill), giving them electric potential energy.
The difference in electric potential energy (∆EQ) per unit of charge (Q) is defined as the potential difference(V).
(V) is sometimes called the voltage of the cell, battery or power supply.
The SI unit for potential difference is the volt. We measure potential difference with a voltmeter.
Question: A battery has a potential difference of 18.0V. How much work is done when a charge of 64.0 C moves from the anode to the cathode?
Producing Electric Potential Energy
Electrochemical Cells
- Different metals hold onto their electrons differently.
- In a solution, the solute disassociates into ions. Thus possible charge carriers.
- When these 2 conditions are present, electrons will move due to the potential difference caused by the 2 metals. The current depends on the pull of the electrodes and the freedom of electron movement.
Voltaic Cell
2 metals in an acidic solution.
Dry Cell
2 metals in a paste
safer because the acidic cannot leak
Piezoelectric Cell
by squeezing a crystal, a current can be created.
Secondary Cell
the electrons, through electrical energy, can be moved back to their origin causing the cell to recharge.
Thermocouples
2 metals coupled together can indicate temperature difference.
Photoelectric
light comes down to free an electron.
The Simple Circuit
Whatever current leaves the source must also return to the source. Because the charge carriers must lose their energy during their trip & the resistance in the loop is predetermined, the rate at which they travel through the loop adjust accordingly. This law is represented mathematically as V = I R.
Kirchoff’s Voltage Law
The algebraic sum of the potential differences around any closed pathway or loop must equal zero.
VT = V1 + V2 +…
Via the conservation of energy, electrons gain as much energy at the source as they lose at each load. (must spend all their energy). As a result the potential difference across the components in a parallel circuit must be equal.
VT = V1 = V2 = V3
Kirchoff’s Current Law
At any junction in an electric circuit the total current flowing into the junction is equal to the total current flowing out of the junction.
Electric charge is neither created nor destroyed in any electric circuit. (same current returns) Since charge can only flow through one pathway in a series circuit, the electric current at all points is the same.
IT = I1 = I2 = I3
At a parallel connection the total current flowing into the connection must be equal to the sum of the currents flowing out.
IT = I1 + I2 + …
Ohm’s Law
The potential difference across a load is equal to the product of the current flowing though the load and the loads resistance.
V = I R
Ohm’s Law is limited to metal conductors at stable temperatures. Therefore, does not explain resistance in all circuits.
Some loads will not obey Ohm’s Law and are referred to as non-omhic. (i.e. light bulb)
As the current increases through the load the resistance increases.
Question:
Solve the following circuit. Find the unknown values.
Mixed Circuits
Your house is wired in parallel. One branch goes to your dryer, one to the kitchen, one to the basement, etc.
Within each path we can further divide it and setup series sections.
The net effect is you end up with a parallel circuit with a series section. To solve the circuit, you must first simplify all subsections to 1 main type of circuit.
Resistance
The wire’s resistant nature is referred to as resistivity and depends upon:
the type of metal (gold is the best conductor)
the length of the loop
the cross sectional path (thickness)
the temperature (higher the temperature of the wire the higher the resistance)
If you combine the relationship of the resistance of a conductor to it’s length and cross-sectional area, the result is
Temperature affects the resistivity values for different conducting materials.
Question:
Calculate the resistance of 15m length of copper wire at 20°C that has a diameter of 0.050cm. (copper 1.7 x 10-8 Ωm)
Resistance in Circuits
The total resistance in the circuit dictates the voltage and current based on the limits of the power supply.
The greater the resistance, the greater the need for energy to pull one electron around the loop. This results in less electrons completing the loop (I ↓). (and vice versa)
We look to the total Resistance in the circuit at the power supply because of this adjustment of V and I, at the source.
The variation in resistance calculation changes with the type of circuit (parallel, series), due to the number of loads each electron must travel through.
In Series:
at the power supply or
RT = R1+R2+R3+…()
In Parallel:
at the source or
()
Summary note on Current electricity.
Review of Equations
Circuits – a complete path for electrons to follow getting energy from a power source and spending this energy at one or several loads. This energy is transferred to the load and is used to do work on the load.
Laws / Series Circuit- only one path for the electron / Parallel Circuit
- multiple paths for the electron / Mixed Circuit
- a parallel and a series combination
Ohm’s Law
(at each load) / R = V/I / R = V/I / R = V/I
Total Resistance / RT = R1+ R2+… Rn / / the circuit must be simplified to properly solve – two loads can be replaced with an equivalent load
Kirchoff’s Voltage Law / VT = V1+ V2+… Vn / VT = V1= V2=… Vn
Kirchoff’s Current Law / IT = I1= I2=… In / IT = I1+ I2+… In
I = current (Amps, A), R = resistance (Ohms, Ω ), V = voltage or potential difference (Volts, V)
Other equations
Power P = VI Work = Energy change = VQCurrent I = Q/t
(Watts, W = V∙A)(Joules, J = Joules, J = V∙C)(Amperes, A = C/s)
Resistance
Resistivity
The wire’s resistant nature is referred to as resistivity and depends upon:
the type of metal (gold is the best conductor)
the length of the loop
the cross sectional path (thickness)
the temperature (higher the temperature of the wire the higher the resistance)
If you combine the relationship of the resistance of a conductor to it’s length and cross-sectional area, the result is
The coefficient “ ρ” depends upon the material. Values can be found in Table 13.1 of your PRACTICE PROBLEMS sheet.
Practice problems 16-20
Resistance in Circuits
The total resistance in the circuit dictates the voltage and current based on the limits of the power supply.
The greater the resistance, the greater the need for energy to pull one electron around the loop. This results in less electrons completing the loop (I ↓). (and vice versa)
We look to the total Resistance in the circuit at the power supply because of this adjustment of V and I, at the source.