Electromagnetic waves practice · Mixed difficulty

Option B ($\frac{{{B^2}}}{{2{\mu _0}}}$) is correct because the average magnetic energy density of an electromagnetic wave in free space is given by this formula.

Option B ($\frac{1}{{\sqrt {\mathrm{\mu \varepsilon }} }}$) is correct because Maxwell's equations relate the speed of light to the permeability and permittivity of the medium.

Option A (16) is correct because it is derived from the conversion of units of power from the new system to the standard SI system (watts).

Option D (None of these) is correct because a wave with a frequency of $6 \times {10^{15}}\;Hz$ falls within the ultraviolet (UV) range of the electromagnetic spectrum.

Option B (Statement 1 is true & Statement 2 is true but is not correct explanation of Statement 1) is correct because both statements are individually true, but the pressure exerted by electromagnetic waves isn't a direct explanation for the equality of electric and magnetic energy densities.

Option D (Gamma - rays) is correct because gamma rays have the shortest wavelength in the electromagnetic spectrum among the given options.

Option A is correct because the energy density of an electromagnetic wave is proportional to the square of the electric field, leading to a frequency doubling.

Option D ($\frac{{B}^2 {AL}}{2 \mu_0}$) is correct because it represents the energy density multiplied by the volume of the region.

Option B is correct because the ratio of the energy density of an electromagnetic wave to the energy density due to the magnetic field is 2:1.

Option D is correct because the average value of both the electric and magnetic fields over a complete cycle in a plane electromagnetic wave is zero.

Option C is correct because the total energy density of electromagnetic waves in vacuum is the sum of electric and magnetic energy densities, which equals $\epsilon_0 E^2$.

Option C ($\frac{1}{C}$) is correct because the ratio of the magnetic field to the electric field in an EM wave is the inverse of the speed of light.

Option A ($8 \mu \mathrm{A}$; Yes) is correct because the conduction current is equal to the displacement current in a capacitor, and its value is calculated using the given parameters.

Option C (Statement I is false, statement II is true) is correct because all electromagnetic waves have the same speed in vacuum, but different frequencies.

Option D is correct because the average electric energy density is half the total average energy density in an electromagnetic wave.

Option B ($\frac{I A}{c}$) is correct because the momentum of photons per unit time is equal to the energy per unit time divided by the speed of light.

Option A ($40 \mathrm{~m}$ to $25 \mathrm{~m}$) is correct because it represents the calculated wavelength range corresponding to the given frequency band.

Option B (X-rays) is correct because electromagnetic waves with energy around 15 keV fall within the X-ray portion of the electromagnetic spectrum.

Option C (A charge moving in a circular orbit) is correct because accelerating charges, such as those moving in a circular orbit, produce electromagnetic waves.

Option D (X-rays) is correct because X-rays have wavelengths in the range of approximately $10^{-10}$ m.

Option B ($\sqrt {{\mu _0}{\varepsilon _0}} {E_0} = {B_0}$) is correct because the speed of light, $c$, is related to the electric field amplitude, $E_0$, and magnetic field amplitude, $B_0$, by $c = E_0/B_0$ and $c = 1/\sqrt{{\mu_0}{\varepsilon_0}}$.

Option A ($2.77 \times {10^{ - 8}}T$) is correct because it is calculated using the relationship between intensity, electric field, and magnetic field in an electromagnetic wave.

Option C ($1.106 \times 10^{-8} \mathrm{Jm}^{-3}$) is correct because the total average energy density of an electromagnetic wave is given by $u = \frac{1}{2} \epsilon_0 E^2$, where E is the amplitude of the electric field.

Option A (zero) is correct because the electric and magnetic fields in a plane polarized light wave are in phase.

Option C is correct because electromagnetic waves do interact with matter and set up oscillations, but the interaction is highly dependent on the wavelength of the electromagnetic waves.

Option A is correct because microwave ovens heat food by exciting water molecules, and this is most efficient when the microwave frequency matches the resonant frequency of the water molecules.

Option C is correct because the magnetic field inside the capacitor plates is given by the formula when $r < R$.

Option B ($1.1 \times 10^{-8} \mathrm{~J} / \mathrm{m}^3$) is correct because it is the average energy density calculated using the electric field amplitude.

Option A ($1.3 \mathrm{~mm}$) is correct because it's the distance calculated from the recoil of the laser gun due to photon emission over one hour.

Option B ($E_y, B_x$) is correct because in an electromagnetic wave, the electric and magnetic fields are perpendicular to each other and to the direction of propagation.