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5.1 Electric charge

5.1.1

There are two types of charge, positive and negative...and they are opposite. Positive charges are attracted to negative charges, but like charges repel. Conductors are capable of moving charge in the form of electricity, while insulators will not allow charge to flow through them. Insulators are capable of storing charge on their surface...Perspex or ebonite rods can become charged by rubbing them against fur, though they acquire opposite charges (as I recall).

5.1.2

Electric charge will be conserved, always...if one thing gains a positive charge, then something else must become negative...fairly obvious.

5.1.3

Electrostatic induction...This is why uncharged pieces of paper will 'jump' up to a charged rod...because by holding a negative charge above it, the negative charges in the paper are pushed down, while the positive charges are pulled up. This creates an effective opposite charge on the paper (the same thing happens with positive charged rods), which creates a force of attraction, and pulls the paper up. The same principle can be applied to an electroscope. When a negatively charged rod is brought close to the top, negative charges in it are pushed down. This creates a negative charge in both the gold leaf and the center shaft, and since the like charges repel, the leaf jumps up. If the electroscope is then earthed, negative charges will neutralize the top of the electroscope, giving it a total negative charge, and thus the leaf stays up even once the rod is taken away.

5.1.4

Inductively charge a metal ring attached to an insulated handle. Then use a charge detector (sort of like a compass only in 3D) to see if there's any charge changing it's direction...it doesn't ? good. This basically means that the inside of a hollow charged surface will not have any net charge (and thus field).

5.1.5 : Realistic applications

Lightning rods - they conduct lightning more easily than a building, so it goes down them instead.

Fires in airplanes - if static charges build up during flight, then it could cause sparks as the plan is being fueled...so we earth the first...the same goes for oil tankers.

5.2 Electric force, field and potential=

5.2.1 :Coulomb's law

The force is proportional to both the charges, and there is an inverse square relationship between force and the distance between them (which means it's only really a short range force). Charge is measured is coulomb, which is a derived unit (and a hell of a lot of charge...electrons are 1.6 x 10<aup>-19</sup>C)

5.2.2 : Electric field

If an electric charge experiences an electric force then it is in an electric field. The equation allows the strength of an electric field, in NC^-1, to be found based on the force experienced by a given charge.

5.2.3

Electric field lines go from positive to negative (it's like the old days of conventional current, before the knew about electrons). These are relatively simple, but really need diagrams to explain (anyone want to draw them ?). One important point is that field lines always strike a surface at 90 degrees, so make sure to get that right...in brief...

Isolated point charge...Lines go towards, or away from the point. Moving further away, the lines are further apart, representing a weaker field than when they are closer together.

Two like point charges...the two charges repel each other's field, and so on the far side, it is like a single point charge, but in the center, there is an area of no charge.

Two opposite point charges...there is a line straight from one charge to another, then the others come out as normal, but are bent towards the other point charge.

Pair of charged plates...I think we only have to deal with oppositely charged plates...the lines run straight down or up as appropriate, but at the end, some curve is introduced to account for the 90 degree thing as mentioned above.

These are field lines...equipotential lines run perpendicular to these, and mark areas of equal potential.

5.2.4

Potential difference () is defined as the work done by moving a positive charge from one point to another in an electric field. The equation , allows the potential difference to be calculated.

5.3 Electric current

5.3.1

Electric current is defined as the amount of charged passed divided by time. It's unit is the ampere...It is usually used in relation to electric charge, where electrons are flowing, often through a wire, though also through a vacuum (cathode rays), or in relation to positive ions flowing through something.

5.3.2

In a metal...electrons are free to move, although the atoms are held in a reasonably strong, though mobile lattice. As electrons flow through a metal, they 'bump' into the metal atoms, explaining resistance, and the fact that metals may heat up when electricity flows through them.

5.3.3 : emf -- electromotive force

The voltage produced by a reaction in a battery is called it's emf (it applies to any electrical current source, ie induced by a magnet etc.). Some of the energy produced is wasted inside, and so a battery with an emf of 3V may only have a potential difference between it's terminals of 2.5V.

5.3.4

Potential difference is defined as the energy dissipated per unit current (measured in volts)...ie if the potential difference across a battery is 12v, this means that each coulomb of charge will 'spend' 12 joules of energy going around the circuit.

5.3.5

Resistance is defined based on potential difference and current as ...so you can sub in any two values and get a third...resistance is measured in ohms.

5.3.6 : Factors affecting resistance

Length: resistance increases with the length of the conductor.

Cross sectional area...resistance decreases as cross sectional area increases.

Type of conducting material...well it's just going to vary isn't it...metals tend to be good conductors.

Temperature...as the temperature increases, the resistance also increases.

5.4 Electric circuits

5.4.1

The circuit symbols are in the front of the data book, though I don't see where transistors or logic gates come into things...still, it's all fairly obvious. Drawing them is basically a matter of practice, not something I can really explain.

5.4.2

Non ohmic conductors are those which don't follow ohm's law () when the temperature is not kept at a constant (and relatively low) degree.

5.4.3

Electrons flow from the negative terminal to the positive, conventional current flows from the positive to the negative. They go in opposite direction, because conventional current was invented before they knew about electrons...Which one you use doesn't really have any major effect on simple circuits.

5.4.4

A resistor is something which turns electric energy into heat when electricity runs through it (due to electrons 'bumping' into metal ions. Internal resistance refers to the resistance inside the source (like the difference between emf and potential diff).

5.4.5

Circuits should first be divided into separate 'branches'...The total resistance of each parallel branch is

etc ... This then creates a simple series circuit which can be solved with . In a series circuit, the current is constant throughout the circuit, but the voltage is shared between the resistors. In parallel, the current is split between each branch (relative to it's resistance) and the voltage in each branch is equal to the voltage across the whole parallel branch. Once each parallel bit has been calculated, and then the whole circuit has been done in series, the information can be put back to calculate the current or voltage in each bit of the parallel branch.

5.4.6

work = charge x potential difference and charge = current x time. Thus, subbing the second into the first, we get

.

Divide by , and since power equals work/time:

We can then sub in , giving . or rearranging to , we get .

These can all be applied as appropriate ... Power is measured in watts (or joules per second), work in joules, time in sec, PD in volts, current in amps and charge in coulomb.

5.4.7

Ammeters should be used in series with the part of circuit you want the current in, voltmeters in parallel, branched over the part you want the PD between.

5.4.8

Electricity is generally sold in kilowatt-hours, which have a particular price...Different devices draw different amounts of power, generally given as kilowatts...If it runs for 1 hour, then it uses kilowatt-hours...if it runs for 2 hours and so on...

When current flows through an appliance, heat is produced, some appliances (kettles, heaters) use this fact (I don't know why this is hare, but the syllabus points it out...so now I did to).

5.4.9

Fuses are short pieces of low melting point wire. There are place in a fuse box, and complete the circuit, but if the current rises over a certain point, the heat produced in the fuse (due to it's resistance) melts the fuse, and breaks the circuit. Circuit breakers work on a similar principle, except they act much faster...Fuses are used to prevent overheating in other areas, causing fires, while circuit breakers (aka overload cut-out systems) are designed to prevent electrocution. Earth-leakage detectors are designed to detect current escaping from the circuitry, and so also help prevent electrocution.

5.5 Magnetic fields

5.5.1

Magnetic fields flow in circles around a current carrying wire. If you point you RIGHT HAND thumb in the direction the current is going, your fingers curl in the direction of the field rotation...Nb, in diagrams, the symbol X is commonly used for a current going into the page, and a dot for current coming out of the page...the same convention is used for fields going into or out of the page.

5.5.2

The magnetic field around a solenoid (coil of wire) runs through the center and loops around and back to the other end (Diagram anyone ?). The polarity of each end can be found by drawing the letter N (for north) and putting arrows on the ends...thus, if the current is going around anticlockwise looking down from one end, then a north pole will be at that end...otherwise it's a south pole. Field lines go from the north pole to the south.

5.5.3

Moving further away from a current-carrying wire, the equipotential lines get further apart, because the field is getting weaker...when they are close together, the field is stronger.

5.5.4

The magnetic field produced by a solenoid depends on the current running through it (increases with increases current), The number of turns of wire (increased turns -> increased B field strength). The substance at the core of the field also has an effect, though it depends on the core's nature.

5.5.5

The force on a current carrying wire in a magnetic field can be found by again using your RIGHT HAND...the palm is force, thumb is current and fingers (at right angles to thumb) are field direction...You'll look like an idiot while working it out, but who'll be laughing when you get a 7 :)

5.5.6

When we have two long wires, the fields are just like single wires...this allows us to work out which way the field from each wire is acting on the other, and so the force...if you want to just remember it, when the current is running in the same direction, attraction occurs and when it's opposite, repulsion occurs.

5.5.7

The ampere is defined as the current which produces a force of 2 x 10^-7 N of force per meter of wire between two infinitely long wires 1 meter apart.

5.5.8

or force = length x current x magnetic field strength...This is used to calculate the strength of the force on a wire of length l (meters) carrying current I (amps) in a field of force B (teslas).

or Force = charge (Coulomb) x velocity (m/s) x Field strength...This applies to a single point charge moving through a magnetic field...To work out the direction, we need to remember that we are working with conventional current here, and so for a positive charge, the current will be in the direction it's moving, but a negative one will be backwards. Other than that, the right hand thing still applies.

5.5.9

A d.c. motor works basically on the principle that a force will be exerted on a current carrying wire in a magnetic field. A coil of wire (sort of a square) is places in a magnetic field, and allowed to rotate on it's axis so the coil can rotate in the field. If a current is passed through, the coil will make one quarter turn, but then the force will push it back, because the current is running in the opposite sense. As a result, the ends of the coil are connected to brushes which run around the edge of a commutator, reversing the current every half turn. (A commutator is sort of a ring, where one half is the negative terminal, and the other is positive, so at it turns, the current is reversed). The direction the coil turns can be found in the same way as for a normal wire, remembering that conventional current runs from positive to negative.

5.6 Electromagnetic induction

5.6.1

First, a definition of magnetic flux ... , or magnetic flux = magnetic field strength x area (in m2). is measured in webbers.

When a conductor is moved through a magnetic field, it cuts through a given amount of magnetic flux in a given time. The induced emf in the conductor . Thus EMF .

This equation is in the data book, only they have a for emf. It should also be noted that this assume that the conductor is perpendicular to the filed...only HL has to deal with when it's not.

The direction of this emf can be found using the left hand thing, if we know that the force will be in the opposite direction to the motion, and the emf is in the same direction as current.

5.6.2

When a conductor is moved through a magnetic field, a current is induced in it so as to produce a force to oppose the motion, this in known as Lenz's law....for example, if a wire is moving to the left, then a force to the right will be produced. Based on this, and the known field direction, we can find the direction of the current

5.6.3

When a coil is rotated in a magnetic field (like the motor described above) an emf will be produced...this will be an alternating current, as no commutator will be used. The emf will be at a maximum when the coil is horizontal, and zero when it's vertical (assuming the field goes horizontally), and so the graph will follow a sort of sine curve...the initial direction can be found as above, and it reverses every time the coil turns through vertical.

5.6.4

Transformers operate based on this principle of induced current, but placing to wire coils close together. On has an alternating current running through it, and so this produces an alternating magnetic field. This causes a current to be induced in the other coil, again an alternating current. The amount of power (P = VI) remains constant, but the voltage and current change related to the number of turns in each coil. The primary coil is the one with the current running through it, the secondary coil is the one with the induced current. It needs to be noted that this works because the alternating current causes a continual flux change, and thus induces an alternating current.

5.6.5

The current and voltage can be calculated using the equation:

This relates the number of loops (n) in the coils to the voltage and current in both the primary and secondary. A step-up transformer is one which increases the voltage (and do decreases current) while a step-down transformer is one which decreases the voltage, and increases the current. Most transformers are around 99% efficient, and this can be calculated with the equation efficiency . (or ).

5.6.6

Power is generally transmitted through power lines at high voltage and low current. This is because the power loss is related to current, not voltage in the equation . Since we can't easily reduce the resistance in the wires, reducing the current can reduce the power loss. Since , using a big current, with a set power, will reduce the current, and so everything works out nicely...if you have to work it out, sub the power and voltage into the above equation, then sub the resulting current.

Comments

Section 5.1.3 EDITED

While explaining the concept of electroscope, the wrong charge of the rod was used. It should be that if a NEGATIVE charged rod is brought close to the top of the electroscope, THEN the negative charges in the ELECTROSCOPE will be pushed down and thus the gold leaf will jump. Nothing major, just a typo i think.