Electric fields

Electric Charge

We now use electricity to power many devices but the idea of charge was originally developed to explain static electricity.

Electric force

The electric force is the force that occurs due to charges interacting. For example, the attraction between a proton and an electron. The formula for this force is almost identical to the formula for gravity. This attraction or repulsion between two charges is equal to

$F_{e} = k \frac{q_{1} q_{2}}{r^{2}}$

q₁ and q₂ are the magnitudes of the charges. k is a constant, and r is the distance between both charges.

Electric field constant (k)

K is easily calculatable, but it depends on the medium. Precisely, it depends on the permittivity of the medium through which the charges are interacting. It is calculated by

$k = \frac{1}{4 πε}$

Permittivity of free space

Epsilon represents the permittivity of space in the medium. So the formula for electric force becomes

$F_{e} = \frac{q_{1} q_{2}}{4 {πεr}^{2}}$

Permittivity is the amount of charge needed to create 1 single unit of electric flux in a given medium. A charge will yield more electric flux in a medium with high permittivity. Electric flux is the rate of flow of electric field a given area. It is calculated as the integral of the dot product of the perpendicular electric field vectors and the perpendicular vector of an infinitely small area dA.

Charge & Power

Charge: a fundamental property of all particles. A particle can have a positive charge, negative, or no charge. Like charges will repel while opposite charges will attract.

Coulomb's law

Current

Definition: The time rate (△t) at which the charge (△q) moves past a particular point in a circuit.

Conversion from electrons per second to amps

Inorder to convert from electrons per second to amps, multiply by the charge of an electron in coulombs ( $1.6 \times 10^{-19} C/1e$ )

$I=\frac{\Delta q}{\Delta t}(1.6\times10^{-19})$

Direct Current vs Alternating current

Direct current: A circuit where the current flows in one direction. Used for short distance circuits because it is safer.

Alternating current: A circuit where the current flows alternate directions over time. Used for long distance circuits because of its higher voltage capacity.

Potential difference

Potential difference is the difference in electric potential between two parts of a circuit. It is this difference which causes current to move through the circuit.

Units: Voltage (V)

Heating effect of electric currents

Circuit diagrams

Some important circuit diagrams to remember are:

Name	What it does	Diagram
Cell	A component which pushes the electric current (Voltage) from positive to negative.
Battery	A component which consists of several cells.
Resistor	A component which reduces the current flow.(Almost every component is technically a resistor)
Variable resistor	A components which controls the current flow.
Light bulb	A component which emits light, by heating up filament inside the bulb.

Kirchhoff’s circuit laws

Ohms law

Resistance and resistivity

resistivity

Factors that affect resistance

There are five things which can affect resistance, also as current is inversely proportional to resistance these five things will also change current but inversely.

Factor	Explanation	Equation
Length of wire	The longer, the wire, the more times the electrons hit the sides slowing down.	R∝L
Material	The lower the conductivity of the material(σ) the higher the resistance.	R∝1/σ
Wire thickness	The smaller the diameter(⌀) of, the wire, the more times the electrons bump into each other	R∝1/⌀
Temperature	Heating a wire makes the atoms in the wire vibrate increasing the number of collisions.	R∝T

Resistance formula: $R = ρ \frac{L}{A}$ (resistance = resistivity * (length/current)

Series vs parallel circuits overview

Series

Current: Is the same all around the circuit.
Voltage: Shared across each component. Components with higher resistance get more voltage
Resistance: $R_{t} = R_{1} + R_{2} + R_{3} . . .$

Parallel

Current: Split across each component
Voltage: The same for all components
Resistance: $\frac{1}{R_{t}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} . . .$

Voltmeters and Ammeters

Type of meter	What it measures	How it is connected	Ideal resistance
Voltmeter	Voltage	In parallel	Very high resistance, so electricity does not flow through it.
Ammeter	Current	In series	Very low resistance, so electricity flows easily through it.

Potential Dividers

A potential divider is a circuit made of two or more resistors that allow us to tap off any voltage we want that is less than the battery voltage. You can imagine as using resistors to create a ratio of the voltages.

Formula: $V_{out} = \frac{V_{in} R_1}{R_1+R_2} $

The input voltage (Vin) is the emf of the battery.
The output voltage (VOut) is the voltage taken after the resistor
R1 is a large resistor which takes the majority of the resistance
R2 is a small resistor which takes the small amount of resistance.

Power and power dissipation

Power: The rate of energy required to drive electrical current through a circuit. It proportional to the potential difference and to the electrical current that flows through the circuit.

Electricity and magnetism

Electric fields

Electric Charge

Electric force

Electric field constant (k)

Permittivity of free space

Charge & Power

Coulomb's law

Current

Conversion from electrons per second to amps

Direct Current vs Alternating current

Potential difference

Heating effect of electric currents

Circuit diagrams

Kirchhoff’s circuit laws

Ohms law

Resistance and resistivity

resistivity

Factors that affect resistance

Series vs parallel circuits overview

Series

Parallel

Voltmeters and Ammeters

Potential Dividers

Power and power dissipation

Power dissipation

Electric cells

Cells

Internal resistance

Secondary cells

Terminal potential difference

Electromotive force (EMF)

Magnetic effects of electric currents

Magnetic fields

Magnetic force

Editors