Trivia

[`Maxwell's first equation of classical electromagnetism in integral form: ∯E·dA = q/ϵ | This states that the electric flux through a closed surface, thought of as the flow of the electric field through that surface, is proportional to the magnitude of the net electric charge enclosed within the surface.`,
`Maxwell's first equation in differential form: ∇·E = ρ/ϵ | This states states that the divergence of the electric field at a point in space, thought of the measure of how the field is "spreading" throughout space, is proportional to the electric charge density at that point.`,
`Maxwell's second equation in integral form: ∯B·dA = 0 | This states that the net magnetic flux through any closed surface is 0. In other words, a magnetic field has no start and end, therefore magnetic monopoles do not exist.`,
`Maxwell's third equation in integral form: ∮E·dL = -∬(dB/dt)·dA | This states that a changing magnetic field produces an electric field. A practical application of this is to generate electricity; spinning a magnet inside a metal coil will generate an electric current through the coil.`,
`Maxwell's fourth equation in integral form: ∮B·dL = μ∬(J+ϵ*dE/dt)·dA | This states that both an electric current and changing electric field produce a magnetic field.`,
`Maxwell's equation in differential form, while not as easier to interpret as their integral counterparts, are easier to read. ∇·E = ρ/ϵ | ∇·B = 0 | ∇×E = -dB/dt | ∇×B = μ(J+ϵ*dE/dt)`,
`Coulomb's law states that the electric force between two electric charges is proportional to the charge quantities and inversely proportional to the square of the distance between the charges.`,
`A restatement of Maxwell's third equation: The magnitude of the induced electromotive force/electric potential difference (in volts) in a loop wire subjected to a changing magnetic field is equal to the change of the magnetic flux (the flow of the magnetic field through the wire loop) over time.`,
`A restatement of Maxwell's second equation: The net flow of a magnetic field through a surface is always 0. This is widely interpreted to mean that magnetic monopoles do not exist. Magnetic field lines do not start and end in different places; rather, they loop into themselves.`,
`Half of a restatement of Maxwell's fourth equation: A current passing through a conducting wire forms a magnetic field in the shape of concentric circles looping around the wire.`,
`Electric fields are conservative. In other words, the total work required to move a charged particle from one point in the field to another is independent of the path taken.`,
`The potential energy (in joules) stored in a parallel plate capacitor is equal to 0.5CV^2 where C is its capacitance (in farads) and V is the potential difference (in volts) across the plates.`,
`The potential energy (in joules) stored in a spring is equal to 0.5kx^2 where k is the spring constant (in newtons/meter) and x is the distance stretched/compressed (in meters).`,
`The acceleration of objects near the surface of the Earth is approximately 9.80665 m/s^2`,
`The kinetic energy (in joules) of an object is equal to 0.5mv^2 where m is its mass (in kilograms) and v is its velocity (in meters/second).`,
`The famous mass-energy equivalence equation E = mc^2 is incomplete. The equation giving the total amount of energy contained in an object is E^2 = (mc^2)^2 + (pc)^2 where m is the mass (in kilograms), p is the momentum of the object (in kilogram*meters/second), and c is the speed of light in a vacuum (300 million meters/second). This means E = mc^2 only holds true for objects at rest.`,
`The energy contained in a single photon of light is given by E = hf where E is the energy of the photon (in joules), h is Planck's constant (in joule-seconds), and f is the photon's frequency (in hertz).`]