IB Physics/Electric Currents

5.1 Electric charge

5.1.1

There are two types of charge, positive and negative, and they are the opposite of each other. Positive charges are attracted to negative charges and vice versa, 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. This means that when drawing an arrow diagram of the charges, the arrows will go to the center of a conductor, but only to the surface of an insulator.

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.

5.1.2

Electric charge will be conserved, always. If one thing gains a positive charge, then something else must have become negative as a result.

5.1.3

Electrostatic induction is what causes uncharged pieces of paper to 'jump' up to a charged rod. By holding a negative charge above it, the negative charges in the paper are repelled (pushed down), while the positive charges are pulled up. This creates an effective opposite charge on the paper (the reverse 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 positively charged rod is brought close to the top, positive charges in the electroscope are repelled away from the rod. This creates a positive charge at the bottom 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 its direction. We should find that it doesn't, illustrating that the inside of a hollow charged surface will not have any net charge (and thus field).

5.1.5

Lightning rods: They conduct lightning more easily than a building, so it goes down the rod rather than the building.

Fires in air-planes: If static charges build up during flight, then it could cause sparks as the plane is being fueled, so the plane is earthed first. The same thing goes for oil tankers.

5.2 Electric force, field and potential

5.2.1

Coulomb's law: $F={\frac {1}{4\pi \varepsilon _{0}}}\cdot {\frac {Q_{1}Q_{2}}{r^{2}}}$

The force is proportional to both the charges, and there is an inverse square relationship between force and the distance between them (so the force gets weaker as the distance, or radius, increases). Charge is measured in coulombs, which is a derived unit describing a flow of 1 Ampere per second (and a lot of charge, a since electron's charge is 1.6 x 10^-19C). $\varepsilon _{0}$ is the permitivity of the free space, and is equal to 8.85 × 10⁻¹² Farad per metre.

5.2.2

If an electric charge experiences an electric force then it is in an electric field. The equation E = ^F/_q allows the strength of an electric field, in NC^-1 (Newtons per Coulomb), 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 they knew about electrons). They describe the effect on a hypothetical positive test charge placed anywhere around the object. These are relatively simple, but really need diagrams to explain (any volunteers 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. The following features are common on these sorts of diagrams.

Isolated point charge : Lines go towards, or away from the point. Moving further away, the lines are further apart, representing a weaker field.

Two like point charges: The two charges repel each other's field, and so near each point charge, 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.

Equipotential lines : These lines run perpendicular to these field lines, and mark areas of equal potential.

5.2.4

Potential difference (V) is defined as the work done by moving a positive charge from one point to another in an electric field without acceleration. The equation ΔV = ^ΔW/_q, allows the potential difference to be calculated.

5.3 Electric current

5.3.1

Electric current is defined as the amount of charge passed divided by time, and its unit is the ampere. It is usually used in relation to electric charge, where electrons are flowing, often through a wire, which also applies 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

Electromotive force (emf) : The voltage produced by a reaction in a battery is called its emf (it also applies to any electrical current source, i.e. induced by a magnet etc.). Some of the energy produced is wasted inside, and so a battery with an emf of 3 V may only have a potential difference between its terminals of 2.5 V. The electromotive force is usually referred to as just emf in order to not cause confusion since the emf is not an actual force.

5.3.4

Potential difference : The energy dissipated per unit charge (measured in volts). 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 external circuit.

5.3.5

Resistance is defined based on potential difference and current as R = ^V/_I, so you can sub in any two values and get the 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. Metals tend to be good conductors.
• Temperature : As the temperature increases, the resistance also increases for ohmic materials. On the increase of temperature, resistance of semi-conductors decrease.

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 we can really explain here. Volunteers to draw up some examples?

5.4.2

Non ohmic conductors are those which don't follow ohm's law ( V = IR ) when the temperature is not kept at a constant (and relatively low) degree. An example of a non-ohmic conductor is an ordinary light bulb. As the filament in the bulb is heated up the resistance increases, giving a non-linear relationship between voltage (V) and current (I).

5.4.3

Electrons flow from the negative terminal to the positive, where as conventional current flows from the positive to the negative. They go in opposite directions because conventional current was invented before anyone 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

If resistors are in series, then the total resistance is given by

$R_{t}=R_{1}+R_{2}+...+R_{n}$

If resistors are in parallel, then the total resistance is given by

${\frac {1}{R_{t}}}={\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+...+{\frac {1}{R_{n}}}$

This then creates a simple series circuit which can be solved with V = IR.

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 its resistance) and the voltage in each branch is equal to the voltage across the whole parallel branch.

Once each parallel section 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 section 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 W = ItV.

Divide by t, and since power equals work/time, we get P = VI

Substitute in V = IR, giving P = I²R.

Alternately, substitute in I=^V/_R and we get P = V² / R

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

5.4.7

Ammeters should be used in series with the part of circuit for which you want to find the current. An ideal ammeter would have an infinitely small resistance, as to not change the circuit.

Voltmeters should be used in parallel, branched over the part you want to find the potential difference between. An ideal voltmeter would have an infinitely large resistance, as to not change the circuit.

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 X kilowatts. If the device runs for 1 hour, then it uses X kilowatt-hours. If it runs for 2 hours then it uses 2X 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 here, but the syllabus points it out).

5.4.9

Fuses are short pieces of low melting point wire. They are placed 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 of the circuit, which could otherwise cause 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 through & around a current carrying wire. If you point your RIGHT HAND thumb in the direction the current is going, your fingers curl in the direction of the field rotation. This "RIGHT HAND RULE" is based on "Electron Flow"; negative to positive.

Note that, 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 recalled 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 increased current), The number of turns of wire (an increased number of turns gives an increased magnetic field strength). The substance at the core of the field can also have 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.

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

An 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

F = $IlB$ 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).

F = qvB or Force = charge (Coulombs) 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 from above still applies.

5.5.9

A d.c. (direct current) motor works 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 placed in a magnetic field, and allowed to rotate on its 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.

To overcome this, 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. Ø = BA, or magnetic flux = magnetic field strength x area (in m²). Ø 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 = -^ΔØ/_Δt. Thus EMF = -^ΔØ/_Δt. This equation is in the data book, only they have a curly E (Like this perhaps? ξ I can't remember anymore) for emf. It should also be noted that this assumes that the conductor is perpendicular to the field. Only HL students have to deal with situations where 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 the principle of induced current, by placing two wire coils close together. One has an alternating current running through it, and so this produces an alternating magnetic field. The magnetic field 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 only 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

^V_p/_Vs = ^n_p/_ns = ^I_s/_Ip.

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 so 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 following equation.

efficiency = ^V_sI_s/_VpIp. (or ^P_s/_Pp).

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 P_L = I²R. Since we can't easily reduce the resistance in the wires, reducing the current can reduce the power loss.

Since current = ^power/_voltage, using a big voltage, with a set power, will reduce the current, and so everything works out nicely. If you have to work it out, substitute the power and voltage into the above equation, then substitute the resulting current.