# Electromagnetism

Three rules

• Static Electric field does not exist inside of a conductor.
• Surplus electric charge will spread uniformly on the surface of a conductor.
• Electric charge cannot be created or destroyed.
• Voltage will normalize across a conductor.
• Electric charge on a sphere will mimic the same charge at the center.

$V = Ed$ where $E$ is electric field in Newtons per Coulomb, $V$ is potential difference (voltage) in Joules per Coulomb.

### Maxwell's Equations

$\PhiE = \oint\vec{E}\cdot\vec{dA} = \frac{q{enc}}{\epsilon_0}$

where $q_{enc}$ is the enclosed charge. Electric field lines only begin or end at electric charges, otherwise they extend to infinity. The net flux through a closed surface is only dependent on the charge inside the surface.

$\Phi_B = \oint\vec{B}\cdot\vec{dA} = 0$

All magnetic fields are loops. Any closed surface will have no net magnetic flux.

$V = \oint\vec{E}\cdot\vec{d\ell} = -\frac{d\Phi_B}{dt}$

where $V$ is voltage. The voltage over an enclosed loop is linearly related to the change in magnetic flux through that loop. This change could come in the form of the magnetic field changing strength. Or the loop could move laterally in relation to the field, resulting in the loop moving into an area of the field with a different strength. Or the loop could rotate inside the magnetic field, changing the angle of the loop in relation to the field vector.

$\oint\vec{B}\cdot\vec{d\ell} = \mu_0I + \mu_0\epsilon_0\frac{d\Phi_E}{dt}$

where $I$ is the enclosed current in Coulomb's per second.

### Superposition of fields

Two electromagnetic forces overlap perfectly, such that the electric (or magnetic) force at a location is the vector sum of all electric forces at that location. Therefor, the effect of all electric charges in the universe on a particular point in space can be described with a single vector, $\vec{E}$. And the effect of all magnetic forces with a single vector, $\vec{B}$. The force on a particle of charge $q$ is then

$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$

where $\vec{v}$ is the velocity of the particle.

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