Topic 4: Electricity and magnetism

Electricity and magnetism are two faces of the same fundamental force. This topic builds from simple magnets and static charge up to working circuits, generators, transformers and motors, with the core relationships V = I x R, P = I x V and Vp/Vs = Np/Ns tying the calculations together.

Magnetism and magnetic fields

A magnet has two poles, north and south. Like poles repel and unlike poles attract, and this attraction or repulsion is the only sure test of magnetism, because a plain piece of magnetic material will be attracted to a magnet whether it is itself magnetised or not. Magnetic materials such as iron, steel, cobalt and nickel can be magnetised; non-magnetic materials such as copper and aluminium cannot. A magnetic field is the region around a magnet where another magnet or magnetic material feels a force. Field lines run from north to south outside the magnet, never cross, and sit closer together where the field is stronger. Soft iron is easy to magnetise and demagnetise, making it ideal for temporary magnets, while hard steel keeps its magnetism and is used for permanent magnets.

Electromagnets

When current flows through a wire it produces a magnetic field around the wire in circles. Winding the wire into a coil, called a solenoid, concentrates the field so the coil behaves like a bar magnet, with a north and south pole at its ends. Placing a soft iron core inside the coil greatly strengthens the field, giving an electromagnet. The strength of an electromagnet is increased by increasing the current, adding more turns to the coil, or using a soft iron core. A key advantage over a permanent magnet is that the electromagnet can be switched on and off and its strength varied, which is why it is used in devices such as the relay, the electric bell, the loudspeaker and the scrapyard crane.

Electric charge and static electricity

There are two kinds of charge, positive and negative. Like charges repel and unlike charges attract. Insulating materials can be charged by rubbing, which transfers electrons from one surface to the other. The object that gains electrons becomes negatively charged and the one that loses electrons is left positively charged; the protons do not move. For example, rubbing a polythene rod with a cloth gives the rod a negative charge. Charge is measured in coulombs (C). A conductor allows charge to flow through it, while an insulator does not. Static charges can be detected with a gold-leaf electroscope, and charged objects attract small uncharged pieces of paper because the charge induces an opposite charge on the near side of the paper.

Electric fields

An electric field is a region in which an electric charge experiences a force. The direction of the field at a point is the direction of the force on a small positive test charge placed there. Field lines point away from a positive charge and towards a negative charge. Around an isolated point charge the lines are radial; between two parallel charged plates the field is uniform, shown by evenly spaced parallel lines running from the positive plate to the negative plate. The field is stronger where the lines are closer together. A charged particle placed in a field is pushed along a field line, which is how electrons are deflected inside many electrical devices.

Electric current

Electric current is the rate of flow of electric charge. In a metal the moving charges are free electrons. Current is measured in amperes (A) with an ammeter connected in series. The relationship between charge, current and time is Q = I x t, where Q is in coulombs, I in amperes and t in seconds. Conventional current is taken to flow from the positive terminal to the negative terminal of a supply, which is opposite to the actual direction in which the electrons drift. Worked example: if a current of 3 A flows for 20 s, the charge transferred is Q = I x t = 3 x 20 = 60 C. Current is the same at every point in a simple series loop because charge is not used up.

EMF and potential difference

Electromotive force (emf) is the electrical work done by a source in driving unit charge around a complete circuit, and potential difference (p.d.) is the work done in moving unit charge between two points in a circuit. Both are measured in volts (V), where one volt is one joule per coulomb. The emf describes the energy a cell or generator gives to the charges, while the p.d. across a component describes the energy those charges transfer to it. Potential difference is measured with a voltmeter connected in parallel across the component. A higher p.d. across a component means more energy is delivered to it for each coulomb of charge that passes.

Resistance and the resistance of a wire

Resistance opposes the flow of current and is measured in ohms (W, written as the ohm). It is defined by R = V / I, where V is the p.d. in volts and I the current in amperes. Worked example: a lamp has 6 V across it and carries a current of 0.5 A, so its resistance is R = V / I = 6 / 0.5 = 12 ohm. For a metal wire at constant temperature, current is proportional to p.d., which is Ohm's law, giving a straight-line graph through the origin. The resistance of a wire increases as its length increases and decreases as its cross-sectional area increases, so a long thin wire has a high resistance and a short thick wire a low resistance. Resistance also tends to rise as the wire gets hotter.

Series and parallel circuits

In a series circuit components are joined one after another in a single loop. The current is the same everywhere, the p.d. of the supply is shared between the components, and the total resistance is the sum of the individual resistances, R = R1 + R2 + ... In a parallel circuit components are connected across each other on separate branches. The p.d. across each branch is the same and equal to the supply, the current divides between the branches and recombines, and the total resistance is less than the smallest single resistance. Worked example: two 6 ohm resistors in series give 6 + 6 = 12 ohm; the same two in parallel give a combined resistance of 3 ohm because 1/R = 1/6 + 1/6 = 2/6. Household lighting uses parallel connection so each lamp works independently and gets the full mains voltage.

Electrical energy and power

Electrical power is the rate at which electrical energy is transferred, measured in watts (W). It is given by P = I x V, where I is in amperes and V in volts. The energy transferred is E = I x V x t, with t in seconds and E in joules. Worked example: a heater draws 4 A from a 230 V supply, so its power is P = I x V = 4 x 230 = 920 W, and in 60 s it transfers E = I x V x t = 4 x 230 x 60 = 55 200 J. Power can also be written P = I squared x R or P = V squared / R by substituting V = I x R. These relationships explain why thick supply cables waste less energy as heat than thin ones carrying the same current.

Electromagnetic induction and the a.c. generator

When a conductor cuts through magnetic field lines, or the field through a coil changes, a voltage is induced across the conductor, an effect called electromagnetic induction. If the circuit is complete an induced current flows. The induced voltage is larger when the magnet moves faster, the magnet is stronger, or the coil has more turns. The direction of the induced current always opposes the change producing it. An a.c. generator uses this effect: a coil is spun in a magnetic field so that it repeatedly cuts the field lines, inducing an alternating voltage that reverses each half turn. The ends of the coil connect to slip rings and brushes, and the output is alternating current whose frequency equals the rotation rate of the coil.

Transformers

A transformer changes the size of an alternating voltage. It has a primary coil and a secondary coil wound on a soft iron core. Alternating current in the primary creates a changing magnetic field in the core, which induces an alternating voltage in the secondary. For an ideal transformer the voltages and turns are linked by Vp / Vs = Np / Ns. A step-up transformer has more turns on the secondary and increases the voltage; a step-down transformer has fewer and decreases it. Worked example: a transformer with 100 primary turns and 500 secondary turns supplied at 12 V gives Vs = Vp x (Ns / Np) = 12 x (500 / 100) = 60 V. For an ideal transformer power is conserved, so Vp x Ip = Vs x Is. Transformers raise voltage for efficient transmission in the National Grid, reducing current and therefore energy lost as heat in the cables.

The motor effect and the d.c. motor

When a current-carrying conductor is placed in a magnetic field it experiences a force. This is the motor effect, and the force is at right angles to both the current and the field. The force is larger if the current is increased, the magnetic field is stronger, or the length of wire in the field is increased, and it reverses if either the current or the field is reversed. Fleming's left-hand rule gives the direction: the thumb shows the force (motion), the first finger the field and the second finger the current. A d.c. motor uses this effect on a coil placed in a magnetic field, so the two sides of the coil feel forces in opposite directions and the coil turns. A split-ring commutator reverses the current in the coil every half turn, keeping it spinning in the same direction.