Electromagnetic waves practice · Medium

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 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 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 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 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.

Option A (By applying a varying potential difference of $500 \mathrm{~V} / \mathrm{s}$) is correct because the displacement current is proportional to the rate of change of potential difference across the capacitor.

Option D ($0.02 \mathrm{~T}$) is correct because it is calculated using the relationship between the electric field and magnetic field in an electromagnetic wave, $E_0/B_0 = c$.

Option B (If both assertion and reason are true but reason is not the correct explanation of assertion) is correct because both statements are true, but the constant speed of light in free space doesn't explain the medium dependence.

Option B ($\gamma$-rays) is correct because gamma rays have the shortest wavelength and highest frequency in the electromagnetic spectrum among the given options.

Option D (Red light) is correct because red light has the longest wavelength among the given options in the electromagnetic spectrum.

Option A is correct because a gyrating (accelerating) electron emits electromagnetic waves, and circular motion implies acceleration.