Electromagnetic waves practice · Mixed difficulty

Option C, $\frac{1}{{\sqrt {{\mu _0}{ \in _0}} }}$, is correct because it represents the inverse square root of the product of permittivity and permeability, which defines the speed of electromagnetic radiation.

Option B ($\sqrt {{\mu _0}{\varepsilon _0}} {E_0} = {B_0}$) is correct because the speed of light in vacuum is $c = \frac{E_0}{B_0} = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$, therefore $B_0 = E_0 \sqrt{\mu_0 \varepsilon_0}$.

Option D ($\mu = \frac{4}{3};\,{B_0} = \frac{8}{9} \times {10^{ - 6}}T$) is correct because the refractive index is the ratio of the speed of light in vacuum to the speed of light in the medium, and the amplitude of the magnetic field is the amplitude of the electric field divided by the speed of light in the medium.

Option A ($\overrightarrow E = {B_0}c\sin \left( {kx + \omega t} \right)\hat kV/m$) is correct because the electric field is perpendicular to the magnetic field and the direction of propagation, and its magnitude is related to the magnetic field by $E = cB$.

Option A is correct because the ozone layer primarily blocks ultraviolet radiations with wavelengths less than 3 × 10^-7 m.

Option B (160 nT) is correct because the energy density of an electromagnetic wave is related to the amplitude of the magnetic field by $u = \frac{B^2}{2\mu_0}$.

Option A ($245.01 \mathrm{~V} / \mathrm{m}$) is correct because it is calculated using the relationship between power, intensity, and electric field amplitude for electromagnetic waves.

Option A (the frequency of the microwave must match the resonant frequency of the water molecules) is correct because maximum energy transfer occurs when the microwave frequency matches the resonant frequency of water molecules, leading to efficient heating.

Option B ($2.50 \times {10^{ - 6}}N$) is correct because it is the average force calculated using the formula $F = (2IA)/c$ for a perfectly reflecting surface.

Option C is correct because the magnetic field outside the capacitor plates decreases with distance from the axis.

Option B is correct because the expression for magnetic field strength B at the point between the capacitor plates is given by $\frac{{{\varepsilon _0}{\mathrm{\mu }_0}r}}{2}dE/dt$.

Option A is correct because the total force is the sum of the force due to absorption and reflection.

Option C, $c=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$, is correct because it is the standard formula for the speed of electromagnetic waves in free space.

Option B ($\frac{{{E_0}}}{c}\left( { - \hat x + \hat y} \right)\,\sin \,\left( {kz - \omega t} \right)$) is correct because the magnetic field must be perpendicular to both the electric field and the direction of propagation, and their cross product must point in the direction of propagation.

Option B ($3 \times {10^3}V/m$) is correct because it equates the energy density of the magnetic field to the energy density of the electric field and solves for the electric field strength.

Option D (5) 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 C is correct because $k/\omega$ represents the inverse of the wave's phase velocity, which equals $1/c$ in vacuum, and thus is independent of wavelength.

Option B is correct because the relative velocity of two photons traveling in opposite directions is c, and the rest mass of a photon is zero, but the latter doesn't explain the former.

Option A ($\frac{nh}{\lambda}$) is correct because the momentum gained by the body is the sum of the momenta of the absorbed photons.

Option C ($\mathbf{D} = {\mathrm{\varepsilon }_0}\mathbf{E} + \mathbf{P}$) is correct because it represents the fundamental relationship between the electric displacement vector, electric field vector, and polarization vector in a dielectric material.

Option C ($6.0\,\widehat j\,V/m$) is correct because the electric field is related to the magnetic field by $E = cB$ and the direction is given by the Poynting vector.

Option C ($E \times B$) is correct because the direction of propagation of an electromagnetic wave is given by the Poynting vector, which is proportional to the cross product of the electric and magnetic field vectors.

Option C ($\sqrt {\frac{1}{{{\mu _0}{\varepsilon _0}}}}$) is correct because it represents the speed of light in a vacuum, where μ₀ is the permeability of free space and ε₀ is the permittivity of free space.

Option A is correct because solar radiation consists of transverse electromagnetic waves.

Option C (electric energy density is equal to the magnetic energy density) is correct because in an electromagnetic wave, the electric and magnetic energy densities are equal on average.

Option C ($I/c$) is correct because the pressure exerted by an electromagnetic wave on a non-reflecting surface is the intensity divided by the speed of light.

Option B ($6 \times 10^{-8} \mathrm{~T}$) is correct because the magnitude of the oscillating magnetic field is calculated using the formula $B_0 = \frac{E_0}{c}$, where c is the speed of light.

Option C ($1.6 \times {10^5}\mathrm{ watt}$) is correct because the total power is the product of the intensity and the area of the roof.

Option A $\left[ {\overrightarrow E = {E_0}\hat i,\\,\overrightarrow B = {B_0}\hat j} \right]$ is correct because the electric and magnetic fields must be perpendicular to each other and to the direction of propagation (+z-axis).

Option A (2) is correct because the velocity of the wave is the coefficient of t divided by the coefficient of x.