Electromagnetism

Charges, fields, light · 11 formulas

Electromagnetism★★★★★

Coulomb's Law

F=ke∣q1q2∣r2F = k_e \frac{|q_1 q_2|}{r^2}

Electric force between two charges falls off as the square of the distance between them.

Electromagnetism★★★★★

Electric Field of a Point Charge

E⃗=14πε0qr2r^\vec{E} = \frac{1}{4\pi\varepsilon_0} \frac{q}{r^2} \hat{r}

Each charge creates a field that tells other charges how much force they would feel.

Electromagnetism★★★★★

Gauss's Law

∮E⃗⋅dA⃗=Qencε0\oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}

The total electric flux through a closed surface equals the enclosed charge divided by ε₀.

Electromagnetism★★★★★

Electric Potential (Point Charge)

V=14πε0qrV = \frac{1}{4\pi\varepsilon_0} \frac{q}{r}

Potential is the energy per unit charge — it falls off as 1/r, not 1/r².

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Parallel Plate Capacitor

C=ε0AdC = \varepsilon_0 \frac{A}{d}

Bigger plates and smaller gaps store more charge per volt.

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Ohm's Law

V=IRV = IR

Voltage is the push, resistance is the friction, current is how much flows.

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Biot–Savart Law

dB⃗=μ04πI dl⃗×r^r2d\vec{B} = \frac{\mu_0}{4\pi} \frac{I \, d\vec{l} \times \hat{r}}{r^2}

Each bit of current creates a magnetic field perpendicular to both the current and distance.

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Ampère's Law (with Maxwell's correction)

∮B⃗⋅dl⃗=μ0(Ienc+ε0dΦEdt)\oint \vec{B} \cdot d\vec{l} = \mu_0 \left( I_{\text{enc}} + \varepsilon_0 \frac{d\Phi_E}{dt} \right)

Magnetic field loops around currents; total circulation equals enclosed current times μ₀.

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Faraday's Law of Induction

E=−dΦBdt\mathcal{E} = -\frac{d\Phi_B}{dt}

A changing magnetic flux through a loop induces a voltage that opposes the change.

Electromagnetism★★★★★

Lorentz Force Law

F⃗=q(E⃗+v⃗×B⃗)\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})

Electric fields push charges; magnetic fields deflect moving charges sideways.

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Gauss's Law for Magnetism

∮B⃗⋅dA⃗=0\oint \vec{B} \cdot d\vec{A} = 0

Magnetic field lines always close on themselves — no isolated north or south poles.