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