10 questions · 1 mark each · Correct answer highlighted with explanation
10 questions · 3 marks each · Full model answers included
An oscillating (accelerating) charge produces a continuously changing electric field around itself. According to Maxwell's theory, a changing electric field itself generates a changing magnetic field, and this changing magnetic field in turn generates a changing electric field, and so on — this mutual regeneration of changing electric and magnetic fields propagates outward from the source as a self-sustaining electromagnetic wave, without requiring any material medium.
In order of increasing wavelength (equivalently, decreasing frequency and energy):
Gamma rays < X-rays < Visible light < Microwaves < Radio waves
This ordering reflects the fundamental inverse relationship between wavelength and both frequency ($v=f\lambda$) and photon energy ($E=hf$) across the electromagnetic spectrum.
Displacement current is a term Maxwell introduced into Ampere's law, proportional to the rate of change of electric flux, accounting for situations (like between charging capacitor plates) where a changing electric field exists without any actual conduction current flowing through that specific region.
Maxwell found this necessary because the original Ampere's law, without this additional term, gave inconsistent results when applied to a charging capacitor circuit — the displacement current term resolves this inconsistency, ensuring the modified Ampere-Maxwell law holds correctly in all situations, and crucially, this addition is precisely what predicts the existence of self-propagating electromagnetic waves.
Any three of: (1) Microwave ovens, for efficiently heating food by exciting water molecule rotation; (2) Radar systems, for detecting aircraft, ships, and weather patterns; (3) Satellite and mobile phone communication, since microwaves can penetrate the atmosphere effectively; (4) Certain medical diathermy treatments, using controlled microwave heating.
Sound waves are mechanical waves that require a material medium (like air, water, or a solid) to propagate — they travel via the physical vibration of medium particles transmitting the disturbance from one particle to the next; without particles present (as in vacuum), sound cannot propagate.
Electromagnetic waves, by contrast, propagate through the self-sustaining, mutual regeneration of oscillating electric and magnetic fields — a purely field-based phenomenon that does not require any material particles or medium to transmit the disturbance, which is precisely why EM waves (including visible light from the Sun) can successfully travel through the vacuum of space to reach Earth.
Photon energy is directly proportional to frequency ($E=hf$) — since gamma rays and X-rays have extremely high frequencies (and correspondingly very short wavelengths), their individual photons carry very high energy.
This high photon energy is sufficient to ionise atoms and molecules within living tissue (knocking electrons free from atoms), potentially damaging DNA and cellular structures, leading to mutations, radiation sickness, or cancer with sufficient exposure. Radio waves, having vastly lower frequency and photon energy, generally lack sufficient energy per photon to cause this kind of ionising damage, making them comparatively much safer.
Ultraviolet radiation, particularly UV-B and UV-C, carries sufficient photon energy to damage biological molecules, especially DNA, in living organisms exposed to it — excessive UV exposure significantly increases risks like skin cancer and other cellular damage.
The ozone layer in Earth's stratosphere absorbs a very large fraction of this harmful incoming UV radiation before it reaches the surface, significantly reducing the intensity of UV exposure experienced by living organisms at ground level — this crucial protective, absorptive function is precisely why ozone layer depletion (discussed in the context of certain human-made chemicals) is considered such a serious environmental and health concern.
Maxwell showed, from his theoretical equations governing electric and magnetic fields, that the speed of electromagnetic waves in vacuum is given by:
$c = \dfrac{1}{\sqrt{\mu_0\epsilon_0}}$
Remarkably, when Maxwell calculated this value using the independently measured values of $\mu_0$ and $\epsilon_0$ (determined from separate magnetic and electric experiments), the result closely matched the already experimentally measured speed of light — this striking numerical agreement was strong evidence that light itself is an electromagnetic wave.
Infrared radiation's frequency closely matches the natural vibrational and rotational frequencies of many molecular bonds found in common materials, including those in human skin — when infrared radiation is absorbed by these molecules, this absorbed energy efficiently excites molecular vibration/rotation, which manifests macroscopically as an increase in temperature (heat).
This efficient absorption and conversion to molecular vibrational energy is precisely why infrared radiation is so strongly associated with the sensation of warmth/heat when it strikes the skin — for example, feeling the warmth of sunlight or a heat lamp is largely due to absorbed infrared radiation.
10 questions · 5 marks each · Detailed step-by-step solutions
$\lambda = \dfrac{c}{f} = \dfrac{3\times10^8}{6\times10^{14}}$
$\lambda = 0.5\times10^{-6}\text{ m} = 5\times10^{-7}\text{ m} = \mathbf{500\text{ nm}}$
This wavelength (500 nm) falls within the visible light spectrum (approximately 400-700 nm), corresponding to green-ish light.
$\lambda = \dfrac{c}{f} = \dfrac{3\times10^8}{100\times10^6} = \dfrac{3\times10^8}{1\times10^8}$
$\lambda = \mathbf{3\text{ m}}$
$c = \dfrac{1}{\sqrt{\mu_0\epsilon_0}}$
$\mu_0\epsilon_0 = 4\pi\times10^{-7}\times8.85\times10^{-12}$
$4\pi \approx 12.566$; so $\mu_0\epsilon_0 \approx 12.566\times8.85\times10^{-19} \approx 111.2\times10^{-19} = 1.112\times10^{-17}$
$c = \dfrac{1}{\sqrt{1.112\times10^{-17}}} = \dfrac{1}{3.335\times10^{-9}} \approx \mathbf{3\times10^8\text{ m/s}}$, matching the known speed of light.
$f = \dfrac{c}{\lambda} = \dfrac{3\times10^8}{0.1\times10^{-9}} = \dfrac{3\times10^8}{1\times10^{-10}}$
$f = \mathbf{3\times10^{18}\text{ Hz}}$
Displacement current: $I_d = \epsilon_0A\dfrac{dE}{dt}$
Area: $A = \pi r^2 = \pi(0.05)^2 = \pi\times0.0025 \approx 0.00785\text{ m}^2$
$I_d = 8.85\times10^{-12}\times0.00785\times2\times10^{12}$
$I_d = 8.85\times0.00785\times2 \approx \mathbf{0.139\text{ A}}$
Radio wavelength: $\lambda_{radio} = 300\text{ m}$
Visible light wavelength: $\lambda_{light} = 500\text{ nm} = 500\times10^{-9}\text{ m} = 5\times10^{-7}\text{ m}$
Factor: $\dfrac{\lambda_{radio}}{\lambda_{light}} = \dfrac{300}{5\times10^{-7}} = 6\times10^8$
The radio wave's wavelength is about $6\times10^8$ times (600 million times) larger than the visible light wave's wavelength.
$\lambda = \dfrac{c}{f} = \dfrac{3\times10^8}{2.45\times10^9}$
$\lambda = \dfrac{3}{2.45}\times10^{-1}$
$\lambda \approx 1.224\times10^{-1} = \mathbf{0.122\text{ m} = 12.2\text{ cm}}$
$E = \dfrac{hc}{\lambda} = \dfrac{6.63\times10^{-34}\times3\times10^8}{600\times10^{-9}}$
Numerator: $6.63\times3 = 19.89$, so $19.89\times10^{-26}$
$E = \dfrac{19.89\times10^{-26}}{6\times10^{-7}} = 3.315\times10^{-19}\text{ J}$
$E \approx \mathbf{3.32\times10^{-19}\text{ J}}$ (approximately 2.07 eV)
Since $\lambda = c/f$, wavelength ratio is the inverse of frequency ratio:
$\dfrac{\lambda_1}{\lambda_2} = \dfrac{f_2}{f_1} = \dfrac{3\times10^{16}}{3\times10^9} = 10^7$
The first wave's wavelength is $10^7$ times larger than the second's. The first wave ($3\times10^9$ Hz) falls in the microwave range, while the second ($3\times10^{16}$ Hz) falls in the ultraviolet/X-ray boundary region.
Convert time to seconds: $8.3\text{ min} = 8.3\times60 = 498\text{ s}$
Distance = speed × time: $d = c\times t = 3\times10^8\times498$
$d = 1494\times10^8 = 1.494\times10^{11}\text{ m}$
$d \approx \mathbf{1.5\times10^{11}\text{ m} = 1.5\times10^8\text{ km}}$ — matching the well-known average Earth-Sun distance (approximately 1 astronomical unit).