This paragraph contains no physics. I have placed all the electric current and circuit topics into 5.2 (which I call ‘circuits’ instead of ‘heating effect of electric currents’, which I believe does not capture the essence of the topic particularly well)

5.1 Electric fields

There are two types of charges. Like charges repel, unlike chargers attract. We call one type of charges ‘positive’, and the other ‘negative’. This choice was made in the early days of the scientific study of electricity, and in our modern view, is pretty arbitrary.

To visualise electric fields, we make use of field lines. These lines are directional. The direction of a field line at a point shows the direction of the electric force a positive charge placed at that point will experience. The density of field lines shows the strength of the electric field. Since like-charges repel, the field lines from a positive charge point away from it. Since unlike-charges attract, the field lines from a negative charge point towards it.

More formally, we can calculate the electrostatic force with Coloumb’s law, which states that the force between two charges is proportional to the magnitude of their charges, and inversely proportional to the square of the distance between them

F = (4πε₀)^-1 q₁ q₂ r^-2,

where ε₀ is the permitivity of free space. The electric field strength is the force a unit test charge would experience

E = (4πε₀)^-1 q₁ r^-2.

The potential energy of the electric field is the work done by an external agent to bring a positive charge q₂ from infinity to a distance r from charge q₁, without changing the electric field.

U = – (4πε₀)^-1 q₁ q₂ r^-1.

The electric potential is the potential energy per q_2,

V = – (4πε₀)^-1 q₁ r^-1.

There is a unit of energy called electronvolts, which is convenient to use in certain cases. It is the energy gained by an electron when it is accelerated by a potential difference of 1 volt.

5.2 Electric circuits

For the most part, in everyday materials, it is the electrons which conduct electricity. When we speak of currents through wires, we are referring to a net movement of electrons in a particular direction. Specifically, the current is the flow of charge. Since the electron has a negative charge, when an electron moves to the left, the current moves to the right. Let’s take the analogy of money. The money current goes in the opposite direction of IOU notes.

These electrons jiggle about at the thermal velocity. However, this motion is random and does not produce any net current. The directed motion which gives rise to current is from the drift velocity of the electrons, their net overall movement.

With this understanding of electricity, we can now see why metals are good electrical conductors. Metals have a sea of delocalised electrons around a lattice of positively-charged ions. These delocalised electrons are free to move when an external electric field is applied to them, creating a current.

Instead of thinking of electric fields and forces on the electrons, it is more conventional to think of the potential difference between two points. This causes electrons to move, like balls rolling down a slope.

So let’s say we apply a potential difference between two points. How much current will we get? This is dependent on what is between the two points. We call this property, this ratio between potential difference and current, the resistance. The resistance is affected by material properties, the material’s cross sectional area, and its length. Moreover, the material properties change with physical quantities, like temperature.

Resistivity circuit diagrams

To analyse complicated circuits, we can make use of Kirchoff’s circuit laws. The first law states that the current going into a junction must equal the current coming out. This is simply a restatement of the conservation of charge. The second law states that when going around a circuit and returning to the same point, all the potential differences must add to zero. This is like when you go for a jog and get back to the same point you started, the upward slopes and downward slopes must add together to get zero. This is a result of potential being a function of state, not path.

The power dissipated through a circuit is P

P = IV,

and using the formula for resistance, this can also be expressed as

P = I2R = V2/R.

When doing questions which require explaining what happens to the power when something in the circuit changes, it is expedient to choose the form of power such that one of the quantities is constant, and only the other changes, such that the effect on power is obvious.

effects of power dissipation

Electric cells, internal resistance, and emf

5.3 Magnetism

A current generates a magnetic field in loops around it. The direction of the field is given by the right hand grip rule.

Direction of the force on a particle moving in the field (F = q (v x B)) and on a current carrying wire in the field (F = Bqv, F = BIL).