ElectromagnetismHigh Yield (1 Q in JEE)

Electromagnetic Waves (EM Waves) Formulas

Maxwell equations, displacement current, wave speed in vacuum, Poynting vector, and electromagnetic spectrum.

8 Formulas•299+ Questions in Bank

Core Formulas & Mathematical Identities

c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = \frac{E_0}{B_0} = \frac{E_{\text{rms}}}{B_{\text{rms}}} \approx 3 \times 10^8 \text{ m/s}

Fundamental connection between permittivity, permeability, and optical field amplitudes.

Examiner Tip: In a medium of refractive index n: v = c / n = 1 / √(μ ε).

u_{\text{avg}} = \frac{1}{2}\varepsilon_0 E_0^2 = \frac{B_0^2}{2\mu_0}, \quad I = u_{\text{avg}} c = \frac{1}{2}\varepsilon_0 c E_0^2

Energy is divided equally between electric and magnetic fields.

Examiner Tip: Poynting vector S = (1/μ₀)(E × B) represents directional power flux.

I_d = \varepsilon_0 \frac{d\Phi_E}{dt} = C \frac{dV}{dt}

Maxwell's addition to Ampere's circuital law inside capacitor dielectric gap.

Examiner Tip: Displacement current between capacitor plates equals conduction current in lead wires.

\vec{S} = \frac{1}{\mu_0}(\vec{E} \times \vec{B}), \quad I = \langle S \rangle = \frac{E_0 B_0}{2\mu_0} = \frac{E_0^2}{2\mu_0 c} = \frac{1}{2}\varepsilon_0 c E_0^2

Instantaneous directional energy flow per unit area carried by propagating electromagnetic waves.

Examiner Tip: Wave propagates strictly in the direction of vector cross product (E × B).

p = \frac{U}{c}, \quad P_{\text{rad}} = \begin{cases} \frac{I}{c} & (\text{Complete Absorption}) \\ \frac{2I}{c} & (\text{Complete Reflection}) \end{cases}

Mechanical force per unit area exerted by electromagnetic radiation on physical surfaces.

Examiner Tip: For oblique incidence at angle θ: P_rad = (I/c) cos²θ (absorption); P_rad = (2I/c) cos²θ (reflection).

Z_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}} = \frac{E_0}{H_0} \approx 376.7 \,\Omega \approx 120\pi \,\Omega

Intrinsic wave impedance of vacuum. Frequency order: Radio < Micro < IR < Visible < UV < X-ray < Gamma.

Examiner Tip: Memory mnemonic for increasing frequency / decreasing wavelength: R-M-I-V-U-X-G (Radio, Microwave, IR, Visible, UV, X-ray, Gamma).

\oint \vec{E}\cdot d\vec{A} = \frac{Q}{\varepsilon_0}, \; \oint \vec{B}\cdot d\vec{A} = 0, \; \oint \vec{E}\cdot d\vec{l} = -\frac{d\Phi_B}{dt}, \; \oint \vec{B}\cdot d\vec{l} = \mu_0\left(I_c + \varepsilon_0\frac{d\Phi_E}{dt}\right)

Unification of electricity and magnetism describing generation of fields by charges, currents, and time-varying opposite fields.

Examiner Tip: Gauss's law for magnetism ∮ B · dA = 0 implies that magnetic monopoles do not exist in nature.

v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{\sqrt{\mu_r \varepsilon_r}} = \frac{c}{n} \implies n \approx \sqrt{\varepsilon_r} = \sqrt{K} \quad (\text{for } \mu_r \approx 1)

Maxwell's relation linking optical refractive index n to static dielectric constant K.

Examiner Tip: Both E and B amplitudes decrease by factor n in dielectric medium, while wave frequency f remains constant.

Frequently tested misconceptions in Electromagnetic Waves (EM Waves)

•Ratio of amplitudes of electric and magnetic fields equals speed of light: E₀ / B₀ = c.
•Electric and magnetic vectors are mutually perpendicular and oscillate IN PHASE.