Electromagnetism

Essential formulas and concepts in electromagnetism

Coulomb’s Law

\(F = k\,\frac{q_1 q_2}{r^2}\)

Variables:

Description/Usage:

Gives the electrostatic force between two charges. The force is attractive if charges are opposite, repulsive if like-signed. It is an inverse-square law similar in form to gravity.

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Electric Field of Point Charge

\(E = k\,\frac{q}{r^2}\)

Variables:

  • \(q = source charge, r = distance from the charge, E = electric field magnitude at that distance (radially outward for q>0, inward for q<0).\)

Description/Usage:

The electric field is force per unit charge. For a point charge, it diminishes with distance squared.

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Electric Potential (Point Charge)

\(V = k\,\frac{q}{r}\)

Variables:

  • \(q = point charge, r = distance from the charge, V = electric potential (voltage) at that point relative to infinity.\)

Description/Usage:

The electric potential is the potential energy per unit charge. For a point charge, it falls off as \(1/r\). Differences in \(V\) between two points give the work per charge to move between those points.

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Capacitance (Parallel Plate)

\(C = \dfrac{\varepsilon_0 A}{d}\)

Variables:

Description/Usage:

Capacitance is the ability to store charge per unit voltage (\(C=Q/V\)). For parallel plates, larger area or smaller gap yields bigger \(C\). This formula is a basic design equation for capacitors.

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Ohm’s Law

\(V = I R\)

Variables:

  • \(V = voltage (potential difference across a resistor or circuit element), I = current through it, R = resistance.\)

Description/Usage:

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Electrical Power

\(P = V I = I^2 R = \frac{V^2}{R}\)

Variables:

  • \(P = power (rate of electrical energy consumption or production), V = voltage across a component, I = current through it, R = resistance (if using that form).\)

Description/Usage:

Different forms of the power formula useful depending on known quantities. For instance, a 60 W light bulb on household 120 V draws \(I = P/V = 0.5\) A. The formulas also explain joule heating: \(I^2R\) is heat dissipated in a resistor.

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Lorentz Force (on a charge)

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

Variables:

Description/Usage:

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Speed of Light from EM Constants

\(c = \dfrac{1}{\sqrt{\mu_0\,\varepsilon_0}}\)

Variables:

Description/Usage:

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