**Electromagnetism**

May 17 2018

- electric charge is a fundamental property of matter that comes in two states, is conserved, and is indivisible
- electric force an universal force much stronger than gravity that attracts and repulses depending on the charge
**Coulomb's Law**
- the force between two charges varies directly with quantity of the charges and inversely with the square of their distance
- the electric field is the aura around an electric charge that results in a force upon a charge if it is placed there
- electric forces and fields are follow the superposition principle and can be added vectorially
**Gauss' Law**
- an expression of Coulomb's law about the global behaviour of the electric field over any close surface
- electrical flux is the flow of an electric field through an area, as calculated through a surface integral
- the electrical flux through any closed surface is proportional to the net charge enclosed in that surface
- we can solve for the electric field of symmetric charge distributions using the surface integral
- for conductors where the charges can move in response to an electric field
- the field is zero anywhere inside a conductor in electrostatic equilibrium
- any net charge resides on the conductor's surface and has a magnitude proportional to the local surface charge density
**Electrical Energy**
- electric energy is conservative
- work is done in moving a charge in an electric field and results in stored potential energy
- the electric potential difference between two points is the change in potential energy per unit charge in moving between the points
- it is calculated by the line integral of the electric field over the distance
- this is the change in energy per unit charge and is denoted the by the volt
- even though a system of charges may have zero net charge
- it takes work to assemble the particular distribution of internal charges
- this energy is released when we burn gasoline or metabolize food
- whereby we rearrange the charge distributions of molecules into new configurations that contain less energy
- where is the energy stored in such a system of charges?
- it is literally stored in the electric field created by the distribution of charges
- so all electric fields represent stored energy
- the energy density of an electric field in a volume of space is proportional to the strength of the field squared
- the total energy stored in a field can be calculated by integrating the energy density over the volume
- a capacitor is a pair of insulated conductors used to store electric energy
- capacitance is the amount of stored charge per unit of electric potential difference
**Electric Current**
- electric current is the flow of electric charge
- with current we do not have electrostatic equilibrium
- and there is usually an electric field inside a current-carrying conductor
- microscopically, current density is the current per unit area
- the current depends on the density of charge carriers, their charge, and the drift velocity
- the charge carriers lose energy as they collide with the conducting material
- so it takes an electric field to sustain a steady current
- the current density is linearly proportional to the electric field by a factor of the material's conductivity
- this Ohm's law relation is an empirical statement, not a fundamental law of physics
- the macroscopic version relates current, voltage, and the material's resistance
- electric power is energy gained across a conductor per time
**Magnetism**
- magnetism is an interaction that fundamentally involves moving electric charge
- moving charge produces magnetic fields
- moving charges respond to magnetic fields by experience a magnetic force
- the magnetic force experienced by a moving charge is given by the right-hand rule
- similar to Coulomb's law for electric fields of a single charge
- Biot-Savart law describes the magnetic field arising from a small element of steady current
- similar to Gauss' law for electric fields charge distributions
- Ampere's law describes the magnetic field arising from an entire steady current
- we can solve for the magnetic field of symmetric steady currents using the line integral
**Electromagnetic Induction**
- a changing magnetic field produces an electric field
- unlike the static electric fields that begin and end on charges
- the induced electric field form closed loops
- the induced electric field is nonconservative
- the work done in moving a charge through the field depends on the path taken
- traversing around a closed loop takes net work, unlike for a conservative electrostatic field
- for a closed loop containing a changing magnetic flux
- the changing flux is proportional to the work per unit charge gained as current goes around the loop
- Faraday's law relates the line integral of the induced electric field to the changing magnetic flux
- it can be used to calculate the induced electric field for symmetric field distributions
- Lenz's law shows the induced effects act to oppose the changes that give rise to them
- it uses the concept of the conservation of energy to help determine the direction of the induced electric field
- magnetic fields contain stored energy, just as electric fields
- an inductor is a self inducing current loop used to store magnetic energy
- inductance is the amount of magnetic flux stored per unit of electric current
**Electromagnetic Waves**
- Faraday's law suggests changing magnetic fields induce electric fields
- Ampere's law with Maxwell's modification suggests changing electric fields induce magnetic fields
- these electric and magnetic fields together form self-regenerating structures that propagate through space as electromagnetic waves
- the source of these waves are accelerating electric charge
- the speed of these waves is the speed of light, regardless of wavelength and frequency
- visible light are electromagnetic waves, making up a tiny fraction of the electromagnetic spectrum