Check each statement:
A: E⊥B⊥propagation = TRUE ✓ | B: travel in vacuum = TRUE ✓
C: "Same speed in ALL media" = FALSE ✗ → v = c/n < c in any medium
D: Carry energy and momentum = TRUE ✓
Answer: Speed same in all media (INCORRECT statement)
Maxwell\'s equations predict EM waves: $\nabla \cdot \vec{E} = \rho/\varepsilon_0$ (Gauss), $\nabla \cdot \vec{B} = 0$ (no magnetic monopoles), $\nabla \times \vec{E} = -\partial\vec{B}/\partial t$ (Faraday), $\nabla \times \vec{B} = \mu_0\vec{J} + \mu_0\varepsilon_0 \partial\vec{E}/\partial t$ (Ampere-Maxwell). Maxwell added the displacement current $(\varepsilon_0 \partial\vec{E}/\partial t)$ to Ampere\'s law, making it symmetric and predicting EM waves propagating at $c = 1/\sqrt{\mu_0\varepsilon_0} \approx 3\times 10^8$ m/s. Hertz experimentally confirmed EM waves in 1887.
An EM wave propagating in the +x direction: $\vec{E} = E_0 \sin(kx - \omega t)\hat{j}$, $\vec{B} = B_0 \sin(kx - \omega t)\hat{k}$ where $E_0/B_0 = c$, $k = 2\pi/\lambda$ (wave vector), $\omega = 2\pi f$ (angular frequency), $c = \omega/k = f\lambda$. The Poynting vector $\vec{S} = \frac{1}{\mu_0}(\vec{E}\times\vec{B})$ gives instantaneous energy flux. Average intensity $I = \frac{c\varepsilon_0 E_0^2}{2} = \frac{E_0 B_0}{2\mu_0}$. Radiation pressure on a perfect absorber = $I/c$; on a perfect reflector = $2I/c$.
Gamma rays ($\lambda < 0.01$ nm): nuclear reactions, cancer treatment (radiotherapy). X-rays (0.01–10 nm): medical imaging, crystallography. UV (10–400 nm): sterilisation, vitamin D synthesis, fluorescence. Visible (400–700 nm): sight, photosynthesis, photography. IR (700 nm–1 mm): thermal imaging, TV remotes, heating. Microwaves (1 mm–10 cm): cooking (microwave oven, 2.45 GHz), radar, mobile communication. Radio waves (>10 cm): AM/FM radio, TV broadcasting, MRI (RF pulses).
In a material medium with relative permittivity $\varepsilon_r$ and relative permeability $\mu_r$: speed $v = c/n$ where $n = \sqrt{\mu_r \varepsilon_r}$. For non-magnetic media ($\mu_r = 1$): $n = \sqrt{\varepsilon_r}$. Snell\'s law at interface: $n_1\sin\theta_1 = n_2\sin\theta_2$. Total internal reflection when $\theta > \theta_c$ where $\sin\theta_c = n_2/n_1$ (for $n_1 > n_2$). Dispersion: $n$ depends on $\lambda$ → prism separates white light into spectrum (violet bends most, red least because $n_{violet} > n_{red}$).
Maxwell's contribution was the displacement current, $I_d = \varepsilon_0 \frac{d\Phi_E}{dt}$, which he added to Ampere's law to make it consistent. Without it, the law gives contradictory results for a charging capacitor depending on which surface you choose. With it, a changing electric field produces a magnetic field just as a changing magnetic field produces an electric one — and that symmetry is what makes a self-sustaining electromagnetic wave possible.
E and B oscillate in phase, perpendicular to each other and to the direction of travel, making the wave transverse — which is why light can be polarised. Their amplitudes are locked by $E_0 = cB_0$, and the wave speed in vacuum is $c = 1/\sqrt{\mu_0\varepsilon_0}$, a value Maxwell computed from purely electrical measurements and found to match the measured speed of light. That coincidence was the evidence that light is an electromagnetic wave.
From longest wavelength to shortest: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Frequency and energy rise in the same direction, so gamma rays are the most energetic. All travel at c in vacuum — only the wavelength and frequency differ. Questions here usually test the order, the production method, or one characteristic use, such as microwaves in radar and infrared in thermal imaging.
Thinking energy is carried only by the electric field. Energy is shared equally between the electric and magnetic fields, each contributing half the total energy density.
Assuming EM waves need a medium. They propagate through vacuum, which is precisely what distinguishes them from sound and other mechanical waves.