Electrostatics

• Electric field due to a point charge

  • To find the electric field, use Coulomb’s law, which states that the electric field strength (E) at a point is directly proportional to the charge (q) of the point charge and inversely proportional to the square of the distance (r) from the charge.
  • Shortcut method: $$E \propto \frac{q}{r^2}$$

• Electric potential due to a point charge

  • To find the electric potential, use the formula that the electric potential (V) at a point is directly proportional to the charge (q) of the point charge and inversely proportional to the distance (r) from the charge.
  • Shortcut method: $$V \propto \frac{q}{r}$$

• Gauss’s law

• To apply Gauss’s law, calculate the surface integral of the electric field over a closed surface, and set it equal to the total charge (Q_{inside}) divided by the permittivity of free space (\epsilon_0).

• Shortcut method: $$\oint \overrightarrow{E}\cdot \hat{n} dA = \frac{Q_{inside}}{\epsilon_0}$$

• Capacitance of a parallel-plate capacitor

• To find the capacitance, use the formula $$C=\frac{\epsilon A}{d}$$ where (\epsilon) is the permittivity of the material between the plates, (A) is the area of the plates, and (d) is the distance between the plates.

• Shortcut method: (C\propto \frac{A}{d})

Electromagnetics

• Ampère’s law

  • To use Ampère’s law, calculate the line integral of the magnetic field around a closed loop, and set it equal to the total current (I_{enclosed}) flowing through the loop multiplied by the permeability of free space (\mu_0).
  • Shortcut method: $$\oint \overrightarrow{B}\cdot \overrightarrow{dl} = \mu_0\Sigma I_{enclosed}$$

• Faraday’s law of induction

  • To use Faraday’s law, calculate the line integral of the electric field around a closed loop, and set it equal to the negative rate of change of the magnetic flux (\Phi_B).
  • Shortcut method $$\oint \overrightarrow{E}\cdot \hat{n} dA = -\frac{d\Phi_{B}}{dt}$$

• Lenz’s law

  • Remember that the direction of an induced current opposes the change in magnetic flux.

• Shortcut method: Induced current creates an opposing magnetic field

• Motor/Generator basics:

  • Motor converts electrical to mechanical energy.

• Generator converts mechanical to electrical energy.