Electricity and magnetism


Resources to support AS 90937 Physics 1.3
Demonstrate understanding of aspects of electricity and magnetism

Note that this corresponds to the expired standard 90185 and you can use past papers from that standard for revision without too many problems.
Achieved = understanding; Merit = in depth understanding; Excellence = comprehensive understanding
understanding: how simple facets of phenomena, concepts or principles relate to given situations. This may include using methods for solving problems involving aspects of electricity and magnetism.
in-depth understanding: involves providing evidence that shows how or why phenomena, concepts or principles relate to given situations.
comprehensive understanding: how or why phenomena, concepts, or principles are connected in the context of given situations. Statements must demonstrate understanding of connections between concepts.

Evidence may be written, mathematical, graphical, or diagrammatic.
Aspects of electricity and magnetism will be selected from the following:
• Static Electricity: positive and negative charge, conductors and insulators, uniform and non-uniform charge distributions, earthing, electrical discharge in air, separation of charge by friction, charging by contact.
• DC Electricity: voltage, current, resistance, power, series circuits and simple parallel circuits, circuit diagrams, the relationships:
V = IR, P = VI, P = E/t, RT = R1 + R2 + R3 ...
•Magnetism: magnetic field directions, interactions and the result of interactions (including magnetic field of bar magnets, the earth’s magnetic field, magnetic fields due to currents in straight wires and solenoids), right-hand grip rule, electromagnet, the relationship B = kI/d


Specific Learning Outcomes
By the end of this unit you should be able to:
Electrostatics
  • understand that "static" electricity results from the build up of electric charge
  • know that static charge arises because of the removal or addition of electrons to an insulator as a result of friction (insulators rubbing together)
  • know that charge can be negative, due to excess (added) electrons, or positive - due to a deficit (shortage, or removal) of electrons, or neutral where electrons and protons are balanced
  • be aware that electrostatic charge only form from the movement of electrons i.e. negative charges
  • know that similar (like) charges repel and different (unlike) charges attract each other; relate this to observations about the way electrically charged objects behave.
  • be aware that charged objects can attract (but not repel) uncharged (neutral) ones; explain this in terms of charge movement in an imperfect insulator
  • describe conductors as substances where charges can easily move and insulators as substances that make it very difficult for charges to move; classify some common substances as conductors, insulators or in-between (resistors) based on general knowledge or on information supplied.
  • Explain the behaviour of charged objects, including those charged by induction
  • Describe and explain the operation of an electroscope
  • Describe and explain the operation of a van de Graaf generator

Current electricity
  • describe an electric current as a flow of electric charge; distinguish between conventional current and electron flow in a metallic conductor
  • know that the units of current are amperes (or amps), symbol A; be aware that this refers to a certain amount of charge per unit time
  • Describe ‘voltage’ in as thethe electric potential energy carried by the electrons around a circuit’; define(V) in terms of this
  • Describe the role of a cell, batteries or power supply in a circuit as a source of electrical energy
  • Describe resistance as anything that limits the flow of electrons around a circuit; relate this to a "resistor" as a device that converts electrical energy to some other energy form
  • State that the units of resistance are ohms (Ω); give the derivation of this in terms of volts and amps
  • give examples of substances which make good conductors and good insulators
  • use the correct symbols to draw circuits using these components: bulb, cell/ battery, power source, wire, ammeter, voltmeter, fuse, resistor, variable resistor, switch (open and closed). Note: students are expected to use rulers to draw all straight lines for circuit components and wires, and to follow circuit conventions in component placement.
  • be able to tell the difference between a series and parallel circuit range: two devices in series or parallel
  • Apply the formula for resistors in series to calculate the total resistance of two or more resistances in series with each other
  • Be aware that if two or more resistors are in parallel the total resistance will be less than the smallest resistance; relate this to the role of resistors as ‘gatekeepers’ of current calculation of resistance value in parallel is not required
  • Explain the rules for finding current and voltage values in a simple series or parallel circuit containing a power source and a combination of switches and resisting devices; apply these rules to find unknown voltages, resistances or currents
  • Apply the formula V=IR (where V=voltage; I=current and R= resistance) to find one of the three values where the other two are supplied in problems given as circuits or word problems
  • State that electric power is the product of voltage and current; apply the formula P= VI to solve
  • Solve problems involving power and or energy in situations where known variables may include resistance or other values not directly in the formula these may be multi step and may require prior calculation of voltage or current from other data such as resistance etc.

Magnetism and electromagnetism
  • Describe a magnetic field as something that can exert a force on a magnet or magnetic material, or current-carrying wire
  • explain that permanent magnets have a magnetic field around them
  • Describe the north end of a magnet as the “north-seeking” end; explain that it is the end that points approximately geographic north in most parts of the world; draw magnetic field lines around a variety of differently shaped magnets or poles of magnets (magnetic field lines from north to south) range: one bar magnet, two bar magnets with similar or opposite poles towards each other; horseshoe magnet
  • Explain that a freely moving bar magnet or compass will align itself along magnetic field lines i.e. with the north end of one magnet pointing to the south end of another; be aware that this implies that the magnetic pole at the north end of the Earth is equivalent to the south end of a bar magnet inside the Earth; draw simple magnetic field lines on an outline of the Earth note: including the fact that the magnetic poles are offset from the rotational poles
  • Be aware that a current-carrying wire has a magnetic field around it; draw the shape of that field (applying the right hand grip rule with respect to conventional current) and be able to predict the orientation of a compass needle placed near a current carrying wire or infer the direction of current given the needle direction
  • Apply the formula: B = kI/d to calculate the strength of the magnetic field near a current carrying wire; use tesla as the unit for magnetic field strength
  • Apply rules about the geometry of magnetic fields around a wire to predict the direction and geometry of the field around and through a coil/electromagnet; explain why the coil has a stronger field than a single wire and apply this to problems involving electromagnets in circuits




Electrostatics
You have probably heard of "static electricity". You may not have thought about the term 'static'. It means not moving. Static electricity is the term we used to describe electrical phenomena (things that happen) in substances that are insulators. Insulators are substances that make it very hard for electric current to travel e.g. glass, ceramics, rubber, some plastics, dry air.

In an atom, the negative electrons are on the outside. Below is an illustration of the electron arrangement in a phosphorus atom. You should be familiar with this from the chemistry unit.

phosphorus configuration.png


Phosphorus is a non-metal. It has five valence electrons. Phosphorus as "white phosphorus" is covalently bound in a giant network with other atoms If it were rubbed against another non-metallic element, such as carbon (diamond), the valence electron from some atoms in the network could be transferred to a carbon atom (in its own network). This does not involve a chemical reaction, as both atoms are still bound in their original networks.
Because both substances are non-conductors, the extra electron is stuck where it is, One substance has an overall one extra electron, which gives it a negative charge. The other atom has a deficit of one electron and thus has an overall positive charge (as there is now one more proton than electrons). Repeat this process sufficiently often, and one substance becomes negatively charged and the other positive.
Note that there are two requirements:
  • both substances must be insulators, as otherwise charges will move around to try to minimise the potential energy represented by the unequal charge distribution
  • friction is required for electrons to be rubbed from one substance to the other

Only electrons can move. Thus a positive charge is ALWAYS a deficit of electrons, and cannot itself move (though it could cause a positive charge in something else by drawing away some electrons to make up its own deficit).
(Note: this explanation is an oversimplification but is what the NZQA expect; for a more detailed explanation go here)

In practice, compounds rather than elements are usually used e.g. silk is rubbed against glass.
These compounds must be good insulators and involve some sort of giant covalent network. Substances such as glass, plastics and ceramics are good candidates (silk is a natural plastic).
Electrons get rubbed off one substance, and onto the other. Which way round depends on which substance holds on to electrons more strongly. You are not expected to be able to work out which substance would become positive and which negative, but you are expected to use information given to work this out.
external image chargingbyfriction.png
In the case of silk and glass, silk is more able to attract electrons than glass, so the electrons get rubbed from the glass to the silk. The silk becomes negative and the glass becomes positive. as shown above.

Opposite charges attract each other with a force called electrostatic force i.e. a positive charge and a negative charge attract each other. the closer together they are, or the bigger the size of the charge, the more force there is.

Two of the same charge i.e. positive and positive or negative and negative, repel each other (exert a 'push' force). Once again, the size of the force is bigger for a bigger sized charge and at a closer distance.

water_bending.jpg
Either a positive or a negatively charged object can exert an attractive force on some types of uncharged object e.g.rubbed pen can attract bits of paper. It can also attract water as shown in the picture.

Something that has an electrical contact with the ground is said to be earthed.

Remember that electrons are negative.
  • objects that have a surplus of electrons will be negatively charged
  • objects that have a shortage of electrons will be positively charged
  • objects that have a balance of electrons and protons will be neutral
Remember that only electrons can be transferred from one object to another.


The Electroscope
An electroscope is a device for detecting electric charge and doing experiments with it. There are a number of designs. A common one is the gold leaf electroscope.
electroscope.png


The gold leaf is very thin, light and flexible. Because both the gold and the plate are conductors, if they become charged the charge will distribute itself equally between the leaf and the plate. This will cause the leaf and plate to repel each other and the leaf will move upwards. The size of the charge can be estimated by how far the gold leaf moves.
Touching an uncharged, electrically isolated (non-earthed) electroscope with a charged object will cause the leaves to move apart:
external image 7198daf9-e4f6-40c1-8542-b95188baa848.gif


Note the way that the leaves have moved apart in the second drawing BEFORE the rod is touched to the top. This is because the electrons are attracted to the top, leaving an overall positive charge (electron deficit) at the leaves. This is called an induced charge.



Static electricity simulation
Note that this PhET simulation runs in HTML5 so should run on iPad. The PhET site has others which will only run on platforms that support Java or Flash..

Current Electricity

Conductors and insulators
external image Power-transmission-line1.jpgMaterials that allow electricity to flow easily are call conductors. When we do problems related to electric circuits, we assume that the metal wires conduct electricity perfectly. In practice they don't, but the error in our calculations caused by this is not noticeable under most circumstances.
Good conductors include:
  • most metals,
  • graphite,
  • water with dissolved ions,
  • melted substances made from ions (e.g. molten salts).
  • molten metals

Parts of the core of the Earth conduct electric currents and this is what causes the Earth's magnetic field. This allows us to make inferences about the material from which the core is made.
Materials that are very good at stopping electric current are called insulators. Good insulators include:
Insulator
Insulator


  • dry nitrogen gas,
  • dry air (not as good as pure dry nitrogen)
  • dry glass,
  • dry ceramics,
  • some oils and waxes,
  • rubber,
  • most plastics,
  • many minerals.

Note that many insulators are less effective if damp, because water is NOT a good insulator and salt water is a fair conductor. The shape of the insulators on power lines (illustrated above right) is designed to shed water from rain so as to improve insulation.

A lot of materials fall somewhere in-between being good conductors and good insulaters
Humans, for example, are not good conductors - if you connect yourself between a power socket and a light bulb, it won't light up. However, you might get a shock because of a small current passing through you - you are not a perfect insulator either. An electric shock occurs when an electric current large enough to be felt flows through the body (the minimum to feel is about 10 milliamps).

Objects the fall in-between conductors and insulators are called o resistors. Most resistors change some electrical energy into heat energy; this is why electrical accidents often cause burns.
bar heater.jpg

The glowing bars in the heater are made of resistance wire, wound around an insulating rod of baked clay. Resistance wire is made to be able to get hot without damage.

Ordinary wire will also get hot if too much current goes through it. The amount of resistance depends on the length and thickness of the wire:
  • thinner wires have more resistance
  • longer wires have more resistance
This means that you need thick wires to carry large currents e.g. jumper leads for starting a car:
external image 1375533_130930205233_1000_Amp_Jumper_LEads_Booster_Cable.jpg
If you use leads with wires that are too thin, they will get hot and potentially melt the insulation (causing a hazard). This is particularly a risk if you use leads designed for a small car on an large diesel vehicle such as an off-roader.
The wiring in your house can get hot if too much current passes through it. This could set your house on fire.
To prevent this, all the wires pass through a fuse. This is a thin piece of wire protected inside a small fireproof box. If excess current occurs (e.g. by plugging too many devices into one power point) the wire gets hot enough to melt. This causes a break in the circuit, and stops the wires in dangerous places like the walls from overheating.
external image 3593899.jpg

One of the difficulties with renewable power generation is that suitable sources of energy, such as wind or hydro, can be a long way from where the electricity is used. Longer wires have more resistance so more energy is lost. Using very high voltage transmission and economies of scale (lots of wind turbines in one place) can reduce this problem, but not completely eliminate it.


Circuit Electricity
Electricity flows in a circuit like runners around a race track. The electrons flow from the negative terminal to the positive terminal of the battery or the power supply:

external image 37_nogapincircuit.jpg



external image electron-flow.gif

When we draw a circuit, we don't actually draw pictures of the devices. Instead, we use symbols. The messy layout of the wires is simplified into straight line. This is similar to the way a map of Auckland's rail lines doesn't show the actual arrangement in space of the stations:
external image auckland-rail-map.jpg

Wires are drawn as straight lines, joining or bending at right angles whenever possible. Symbols are used for various components:

circuit symbols key.png


Some rules when drawing circuits:
  • use a ruler (straight lines)
  • use right angles (not skewed lines)
  • lines for wires attach to the middle of other lines and the middle of circuit components
  • only two wires should attach to each component


A circuit in which a complete path can be traced without a break or an open (off) switch is called an unbroken circuit:
external image simple-circuit-diagram-300x2741-300x274.jpg

The circuit above contains an ammeter in series with a resistor and a cell; a voltmeter is in parallel with the resistor.

If there is a break in the circuit - a gap or an open switch, the circuit is broken. Devices which are in series with the broken part of the circuit will not work:
external image cub_electricity_lesson05_figure1.jpg
If you trace your finger around the circuit above, you come to the gap caused by the open switch. The circuit is broken and the light won't go.

Series and parallel
If you run your finger around the circuit and can only take one path, without anywhere reaching a junction with more than one possible direction to go, that is a series circuit.
If there is more than one possible path for the electrons to take, that is a parallel circuit.
external image circt.gif
(note the diagrams above use an old fashioned symbol for a lamp)
To use the analogy of the Auckland train lines -
  • Glen Innes station and Ellerslie station are in parallel. A train can pass through one or the other of them but not through both
  • Papatoetoe station and Middlemore station are in series. A train must pass through one of them to get to the other
You can see that the same number of trains must pass through Middlemore as through Papatoetoe.
You can see that the total of trains through Glen Innes plus trains through Ellerslie must add up to trains through Middlemore (or it did before the Onehunga Branch was opened).

In a series circuit
  • the current through all things in series must be the same
  • the voltage across things in series adds up to the total voltage
In a parallel circuit
  • the voltage of the things that are in parallel with each other must be the same
  • the current in the different branches of the circuit adds up

Exercises and practicals: Drawing and interpreting circuits

Exercise 1
Exercise 2
Practical: arrangements of three bulbs

YouTube video on drawing circuits (from Mr K)
YouTube video on series and parallel, and other concepts (makemegenius)

Voltage, current and resistance

Current
The electric current is an indication of how many electrons per second are passing. A current of one ampere is about 6.25 x 1018 electrons per second. This number of electrons is called a coulomb . A coulomb (by definition) is an amp-seconds worth of electrons i.e. the number of electrons that passes a point in one second if a current of one amper is flowing.The symbol for coulomb is capital C, and the derivation is 1 C = 1 A s

The ampere (the unit of current) is a SI base unit with its own definition (it is defined in terms of the force two current carrying wires would exert on each other due to magnetic effects).

Small currents are often given in milliamps, mA. One milliamp is a thousanth of an amp. For example, a small LED lamp would draw a current of around 40 mA.

Voltage
The amount of potential energy the electrons have is their voltage. One joule of energy per coulomb of electrons is called a volt, symbol capital V. A volt is one joule of energy per coulomb of electric charge.
i.e.

1 V = 1 J C


Strictly speaking, this is the difference in potential energy between two points. For this reason, a more accurate term for voltage is potential difference, often abbreviated pd. The units of pd are volts.
You could think of electricity as being like water flowing in a garden hose. The amount of water (litres per second) is the current and the pressure (how far it squirts) is the voltage.

A better analogy for voltage is to think of gravity. In Earth's gravity field, if you lift up a 1 kg object by 1 metre you must do 10 J of work. If you place the 1 kg object on a shelf at a height of one metre, it has 10 J of gravitational potential energy with respect to the floor. You could then generalise that to say that, for a height of one metre in Earth's gravity, objects have a gravitational potential difference of 10 joules per kilogram.
This number would differ for different heights and different gravities. The differences in voltage around an electric circuit are analagous to the different heights, and the different power supplies can be thought of as being like stronger or weaker gravity.

All the potential energy must be used up between the two terminals of the power supply - you can't have any left over. Thus all the potential differences around a circuit must add up to the total voltage. Back to our gravity analogy, it is like having a set of steps at different heights, but the sum of the height of the steps must be equal to the height of the stairway.
You can apply this rule to work out missing voltages:

(diagrams and examples to follow)



Resistance
Perfect conductors are rare. Most substances cause some electrical energy to change into heat, a bit like friction causes some kinetic energy to change into heat. This “electrical friction” is called resistance.
The amount of resistance can be worked out by how many volts it takes to make 1 ampere of current flow. For example, a pencil lead may need 20 volts to make 1 amp of current flow. We write this as 20 ohms, symbol Ω.
The equation relating resistance (R) to voltage (V) and current (I) is
V = I R
voltage = current in amps x resistance in ohms.

This is sometimes called Ohm's Law.
This rearranges as R = V/I or I = V/R
Here is a PhET simulation on Ohm's Law.


Exercises: Voltage, current and resistance
Simple exercises (Year 10 level)
Textbook - Circuits - requires SHC logon


Power

Electrical power is given by
P = V I
where P is the power in watts, V the voltage in volts and I the current in amps.
This also rearranges into: I = P/V and V = P/I

Example 1:
A 12 V starter motor for a car draws 100 A of current. What is its electrical power?
Solution: P = V I

12 V x 100 A

1200 W (or 1200 V A)The unit "V A" or "volts-amps" is often used for the power output of generators, and is equivalent to watts.
50 kV A diesel generator
50 kV A diesel generator


Since power in the more general sense (recall from the Mechanics unit) is work (energy) per time, you can work out the energy can be calculated from E = P t.
The formula you will be given in the exam is P = E/t
A lot of students tend to think the E stands for something electrical. It is energy in joules. Note that time must be in seconds.

Example: a 500 W heater runs for 5 minutes. How much electrical energy is used?
E = P t = 500 W x 300 s = 150,000 J or 150 kJ
Note that since a watt (by definition) is a joule per second, the units of the answer work out correctly.


Simple power problems - Year 10 level
Textbook examples Circuits2
Textbook examples Circuits3


Magnetism and electromagnetism

external image Magnet-Paperclip.jpg
We all know that magnets can pick up certain objects, such as pins or nails. These substances are termed ferromagnetic, and are attracted towards magnets;
Iron is the best known magnetic substance, but nickel, cobalt, various alloys and the oxide of iron known as ferrite or magnetite are all capable of being attracted to magnets or made into magnets.
The attractive force produced by a magnet is due to a magnetic force field we will discuss in more detail later.

external image water-compass400.jpg
A long thin magnet is called a bar magnet. If you float a magnet on water, or allow it to rotate (e,g, by suspending it balanced on string), the magnet will slowly turn around until one end is pointing roughly north. This 'north seeking' end of the magnet is termed the north end of the magnet:

Experimenting with two bar magnets will quickly show you that the north end of one magnet repels the north end of another. The north and south end of two magnets attract each other, and two south ends will also repel. This can be summarised as
- like ends of a magnet repel
- unlike ends attract.


The magnetic force field around a bar magnet can be 'seen' if you sprinkle ironsand or iron filings on a piece of paper with a magnet underneath:
external image 3902825.jpg?500

(notes in preparation, use text in the interim)

right_hand_grip_rule.png


Electromagnetism
A wire carrying an electric current has a magnetic field around it. The direction of the field is shown in the picture: The field lines are circles that run anticlockwise if the current is coming towards you. The other way to think of it is that the field lines go in the direction that your fingers curl if you hold the wire with your right hand and your thumb pointing in the direction of the current. This is called the "right hand grip rule".
wire_compasses.png
A compass placed on the piece of paper illustrated would have its needle pointing in the directions of the field lines at that point.
The magnetic field is strongest close to the wire and reduces in direct proportion to the linear distance.
Magnetic field strength is given in units called tesla. The symbol for tesla is T. A field of one tesla is extremely strong; even a rare earth magnet has a field of only a few millitesla at the strongest.
The magnetic field strength is calculated using the formula
tesla_formula.png
In this formula, B is the magnetic field strength in tesla; I is the current in amps and d is the perpendicular distance from the wire in metres.

The "k" in this formula is a constant Constants are things that are needed in formulas to make the answer come out in the right size and units for a particular situation. For example,. you have used the formula F = mg to calculate the force on an an object of mass m due to gravity. The value of g we use is 9.8 N kg-1. This value is approximate and is only true for Earth; it would be different on Mars. The units for g (of ) are needed to make the answer come out in newtons.

In the magnetic field formula the constant k stands for a constant that only applies in air or a vacuum; it would have a different value in different situations. The value of the constant is k = 2 x 10-7 T m A-1. The units of this are the units needed to make the answer come out in tesla if you use current in amps and distance in metres. Note that an alternative way of writing this is k -2 x 10-7 T N A-2.; this would give you an answer in N A-1 m-1 (which is actually another way of writing tesla). This is similar to the way that the constant "g" can be written as g = 9.8 N kg-1 or g = 9.8 m s-2 , They are mathematically equivalent but written in different ways.


Review of this unit

Electricity workbook: note you must be logged into your SHC Google account for this link to work. Can I suggest you download the PDF and load it up either into your own Google Drive folder or into an external application you can use to write on it e.g. Notability (Apple)

Private workspace: You must be logged into your SHC Google account to view the following documents:
Electrostatics -
Circuits -
Circuits2
Circuits3
Energy and power
Magnetism
Answers to questions


Old fashioned stuff
Electrostatics
Lightning
Magnets 1

Old School Cert exercises: Part 1 Part 2 Answers

Electronics in colour

Drawing circuits exercise 1
Drawing circuits exercise 2
Problem sheet - bike lamp


Past NCEA papers - in my Google Drive folder; you must be logged onto SHC Google to view these

Cloze exercise for vocab


Lifting electromagnets question