Electromagnetism

The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them: $F = k_e \frac{|q_1 q_2|}{r^2}$.

The net electric flux through any hypothetical closed surface is equal to $\frac{1}{\varepsilon_0}$ times the net electric charge enclosed within that surface: $\oint_S \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{enc}}{\varepsilon_0}$.

The magnetic flux through any closed surface is zero, implying that magnetic monopoles do not exist: $\oint_S \mathbf{B} \cdot d\mathbf{A} = 0$.

The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux enclosed by the circuit: $\mathcal{E} = -\frac{d\Phi_B}{dt}$.

The magnetic field integrated around a closed loop is proportional to the electric current passing through the loop: $\oint_C \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enc}$.

The direction of an induced current is such that it creates a magnetic field that opposes the change in magnetic flux that produced it.

The current passing through a conductor between two points is directly proportional to the voltage across the two points: $I = \frac{V}{R}$.

Describes the magnetic field generated by a constant electric current, relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.

The force on a point charge due to electromagnetic fields is given by the equation $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$.

The net electric charge of an isolated system will always remain constant.

The space-charge-limited current in a vacuum diode varies as the three-halves power of the anode voltage: $I \propto V^{3/2}$.