Electromagnetic waves practice · Mixed difficulty

Option A (6.9) is correct because the RMS value of displacement current is calculated using the formula $I_d = VC\omega$.

Option B (Audible waves) is correct because audible waves are mechanical waves, not electromagnetic waves, and generally have lower frequencies than radio waves.

Option B (Modified Ampere's law) is correct because the given equation is the mathematical representation of Ampere-Maxwell's law, which is the modified form of Ampere's law.

Option A is correct because visible radiation (Cherenkov radiation) is emitted when a charged particle travels through a dielectric medium faster than the speed of light in that medium.

Option B is correct. Coherence is the key property of laser beams that allows them to maintain a small spot size over long distances, making them suitable for locating distant objects.

Option A ($245.01 \mathrm{~V} / \mathrm{m}$) is correct because it is the amplitude of the electric field calculated from the power of the lamp and the distance, considering uniform radiation.

Option D is correct because electromagnetic waves, as they propagate through space, inherently carry both energy and momentum.

Option A ($1.26 \mathrm{~cm}, 23.9 \mathrm{~GHz}$) is correct because it is derived from comparing the given equation with the standard wave equation and calculating wavelength and frequency.

Option B (magnetic field) is correct because Maxwell's hypothesis states that a changing electric field gives rise to a magnetic field.

The correct answer is A (5) because the eye is approximately 5 times more sensitive than the ear as a power detector, based on the calculated minimum intensity detectable by the eye compared to the ear.

Option A (53.1) is correct because the intensity of the wave is calculated using $I = \frac{1}{2} \varepsilon_0 E_0^2 c$.

Option A ($6 \times 10^4 \mathrm{~N} \mathrm{~C}^{-1}, 0.016 \mathrm{~J} \mathrm{~m}^{-3}$) is correct because it's the maximum electric field and average energy density calculated from the given magnetic field.

Option D (Laser light is highly coherent) is correct because coherence is a defining characteristic of laser light.

Option A is correct. Solar radiation consists of transverse electromagnetic waves, including visible light, ultraviolet, and infrared radiation.

Option C is correct. The direction of propagation of an electromagnetic wave is given by the Poynting vector, which is in the direction of $\mathbf{E} \times \mathbf{B}$.

Option B (An EM wave is a wave radiated by a charge at rest and propagates through electric field only) is the wrong statement because EM waves are radiated by accelerating charges and propagate through both electric and magnetic fields.

Option B (Only outside the pipe) is correct because, according to Ampere's Law, the magnetic field inside a hollow conductor carrying a direct current is zero.

Option B (4.24 W/m²) is correct because the intensity of an electromagnetic wave is proportional to the square of the electric field amplitude.

Option C (10 m) is correct because the wavelength is calculated using the formula $\lambda = c/f$, where c is the speed of light and f is the frequency.

Option A is correct because a pulsar is indeed a source of radio waves with regular intensity variations, and this is due to it being a rotating neutron star.

Option C (Shear modulii $<$ Young's modulii $<$ bulk modulii) is correct because for most materials, the bulk modulus is the highest, followed by Young's modulus, and then the shear modulus.

Option A (0.25) is correct because the speed of light is inversely proportional to the square root of the product of permeability and permittivity.

Option B (6 V/m) is correct because the peak electric field strength is the product of the peak magnetic field and the speed of light.

Option B (Gamma-rays) is correct because gamma rays have the highest frequency in the electromagnetic spectrum, are produced in nuclear reactions, and are used in medicine to destroy cancer cells.

The correct answer is C ($E \times B$) because electromagnetic waves propagate in the direction of the Poynting vector, which is parallel to $E \times B$.

Option D (The given electromagnetic wave is plane polarised) is correct because the electric field vector is confined to a plane.

Option A ($\left[ {\overrightarrow E = {E_0}\hat i,\\,\overrightarrow B = {B_0}\hat j} \right]$) is correct because the direction of propagation of an electromagnetic wave is given by the direction of $\overrightarrow E \times \overrightarrow B$.

$\sqrt{\mu_0 \varepsilon_0}$ is the correct answer because the refractive index is the square root of the product of permeability and permittivity.

Option C (2.5 s) is correct because it is calculated by dividing the total distance (twice the distance to the moon) by the speed of light.

Option C (both ac and dc) is correct because the conduction and displacement currents are equal regardless of whether the source is AC or DC.