🔄 بنك الأسئلة: المجالات الكهربائية والمغناطيسية في الفراغ

📌 Idea: When a charge accelerates, it produces a changing electric field, which in turn generates a changing magnetic field, and so each field keeps regenerating the other — the two propagate together as an electromagnetic wave.

📌 Speed: All electromagnetic waves (radio, microwave, X-ray...) travel at the same speed \(c=3\times10^8\,m/s\) in vacuum, regardless of frequency.

📌 Frequency and wavelength: Spectrum order from lowest frequency: radio, then microwave, then infrared, then visible, then ultraviolet, then X-ray, then gamma. So among the three mentioned, X-rays have the highest frequency and shortest wavelength.

📌 Idea: An oscillator (typically an LC circuit) generates an oscillating electrical signal at a fixed, well-defined frequency, used as a "carrier wave" for broadcasting.

📌 Relation: \(c=f\lambda \Rightarrow \lambda=c/f\). Since \(c\) is constant, increasing \(f\) means \(\lambda\) decreases (inverse relation).

📌 Refractive index: \(n=\sqrt{K}=\sqrt{2.28}\approx1.51\)

📌 Speed: \(v=\dfrac{c}{n}=\dfrac{3\times10^8}{1.51}\approx2\times10^8\,m/s\)

📌 Idea: As the spectrum figure shows, visible light is a very narrow band within the full spectrum — most electromagnetic waves (radio, microwave, infrared, ultraviolet, X-ray, gamma) are not visible to the human eye at all.

📌 Formula: \(f=\dfrac{c}{\lambda}=\dfrac{3\times10^8}{5\times10^{-7}}=6\times10^{14}\,Hz\)

📌 Idea: The microwave oven uses microwaves, while the mobile phone and radio both use radio waves — all three devices rely on different types of electromagnetic waves.

📌 Spectrum order (lowest frequency first): radio → microwave → infrared → visible → ultraviolet → X-ray → gamma.

📌 Comparing the four options: among (gamma, ultraviolet, visible, infrared), infrared has the lowest frequency and longest wavelength — it comes immediately before visible light in the spectrum.

📌 Rule: in an electromagnetic wave, \(\vec E\) and \(\vec B\) are perpendicular to each other and to the direction of propagation (\(\vec E\times\vec B\) points along the propagation direction).

📌 Application: propagation is to the right, and \(\vec E\) oscillates in and out (perpendicular to the page), so \(\vec B\) must oscillate within the page, perpendicular to the propagation direction — i.e. north and south.

📌 Idea: the constant speed \(c\) only holds in vacuum. In material media, the speed of an electromagnetic wave depends on the medium's refractive index (\(v=c/n\)), and also varies with the wave's own frequency (dispersion).

📌 Both conditions together: frequency higher than visible ⟵ rules out radio, microwave, infrared, and visible. Wavelength longer than X-ray ⟵ rules out X-ray and gamma (which are shorter than X-ray).

📌 Result: the only wave type lying between visible and X-ray in the spectrum is ultraviolet.

📌 One-way time: \(t_1=\dfrac{x}{c}=\dfrac{3.7\times10^8}{3\times10^8}\approx1.23\,s\)

📌 Round-trip time: \(t=2\times t_1\approx2.46\,s\)

📌 Half-wave dipole rule: its optimal (resonant) length equals half the wavelength: \(L=\lambda/2\)

📌 Calculation: \(L=8/2=4\,m\)

📌 Formula: \(v=c/n=c/\sqrt{K}\), so \(\dfrac{v_1}{v_2}=\dfrac{\sqrt{K_2}}{\sqrt{K_1}}=\sqrt{\dfrac{K_2}{K_1}}\)

📌 Calculation: \(\dfrac{v_1}{v_2}=\sqrt{\dfrac{1.77}{2.28}}=\sqrt{0.776}\approx0.88\)

📌 Inverse relation: lowest frequency corresponds to longest wavelength, i.e. \(\lambda_{max}=10\,nm=1\times10^{-8}\,m\)

📌 Calculation: \(f_{min}=\dfrac{c}{\lambda_{max}}=\dfrac{3\times10^8}{1\times10^{-8}}=3\times10^{16}\,Hz\)

📌 Oscillation principle in an LC circuit: the total energy continuously shifts between the capacitor (electric energy \(\frac12\frac{Q^2}{C}\)) and the inductor (magnetic energy \(\frac12 L i^2\)).

📌 Case D: the capacitor is fully charged (+ and - charges shown), and the current \(i\) is just starting near zero — energy is fully electric.

📌 Case C: the capacitor shows no charge on its plates (fully discharged), while the current is at its maximum \(i_m\) and the inductor shows strong field lines — energy is fully magnetic.

📌 Wavelength: \(\lambda=2L=2\times3.2\times10^{-2}=6.4\times10^{-2}\,m\)

📌 Frequency: \(f=\dfrac{c}{\lambda}=\dfrac{3\times10^8}{6.4\times10^{-2}}\approx4.7\times10^9\,Hz\)

📌 Idea: microwaves are practically generated by devices such as the magnetron, which uses a resonant cavity to oscillate electrons and produce waves at a specific frequency within the microwave band.

📌 Formula: \(f=\dfrac{c}{\lambda}=\dfrac{3\times10^8}{3.2\times10^{-7}}\approx9.37\times10^{14}\,Hz\)

The correct order from lowest to highest frequency:

1. Radio waves
2. Infrared
3. Visible light
4. Ultraviolet
5. X-rays

📌 Wavelength in vacuum: \(\lambda_0=\dfrac{c}{f}=\dfrac{3\times10^8}{600\times10^{12}}=5\times10^{-7}\,m=500\,nm\)

📌 Wavelength in the material: \(\lambda=\dfrac{\lambda_0}{n}=\dfrac{500}{2.0}=250\,nm\)