Materials; 4th Maxwell equation pending

Magnetic Field Energy pending

Self-inductance; RL circuit The ability of a circuit to fight the electric flux that is produced by the circuit itself.

Levitation Describes the three forms of magnetic levitation: using superconductors, movement, or alternating current.

Aurora Borealis The Auroras are a result of these electrons and protons from the solar wind colliding with the our atmosphere. This causes a breathtaking display of light near the Earth's poles.

Heart The polarization waves of the heart produce an electric field around our body. This can be measure in an ECG.

Maxwell’s addition to Ampère’s law Maxwell suggested that we add a term to Ampere's law, which contains the derivative of the electric flux. This is called the displacement current.

Motional EMF; AC Motors To create an induced EMF, and must change the change in the magnetic flux by either changing the magnetic field in time; changing the area in time, or changing the angle θ in time.

Electromagnetic induction; Faraday’s law A current, therefore an electric field, can be produced by a changing magnetic field. This current wants to oppose the change in the magnetic field.

Ampère’s law Ampère's law relates the magnetic field of a closed loop to the electric current passing through that loop.

Biot-Savart law; Gauss’s law for magnetism The Biot-Savart law describing the magnetic field generated by a constant electric current. Gauss's law for magnetism says that magnetic monopoles do not exist.

Moving charge; Cyclotron A magnetic field changes the direction of a moving charged particle, but it doesn't do work.

Magnets; Charges in motion; Lorenz force The magnetic force acting on a moving charge can be expressed in terms of a magnetic field. Similar to how the electric force can be expressed in terms of an electric field.

Batteries; Kirchhoff’s rules pending

Current; Ohm’s law Ohm's law is the linear relation between the potential and the current.

Capacitors The capacitance of two conductors to store energy only depends on their geometry. Adding a dielectric increases the capacitance.

Energy density Another way to find electrostatic potential energy.

Gradient field; Faraday cage The gradient relates the electric potential with the electric field.

Potential The work per unit charge required to go from infinity to point P.

Gauss’ law Gauss' law relates the electric field through a closed surface with the charge contained within that surface.

Electric field The electric field is defined as the force per unit charge in space.

Coulomb’s law The electric force between two particles decreases with the inverse square of the distance, just as the gravitational force.

Overview Triple integrals, surface integrals and contour integrals, and bridges between them.

Stokes’ for work (in space) The work done by a vector field along a closed curve, can be replaced with a double integral.

Curl (in space) The curl measures the value of the vector field to be conservative. For a velocity field, curl measures the rotation component of the motion.

Gradient Field (in space) Test for gradient field. Find the potential of a gradient field.

Diffusion/heat (in space) The Diffusion equation governs motion of e.g. smoke in unmovable air, or dye in a solution.

Divergence (in space) Divergence measures how much the flow is expanding. It singles out the stretching component of motion.

Work (in space) Whenever a force is applied to an object, causing the object to move, work is done by the force.