Electromagnetic Waves – NEET UG PhysicsPractice Questions & PYQs

The amplitudes of electric and magnetic fields are related by the equation $E_0 = B_0 c$, while their directional orientation is governed by the vector cross product of the magnetic field and the wave propagation direction. Multiplying the given magnetic field amplitude by the speed of light yields an electric field amplitude of 9 V/m. Applying the directional rule $\hat{E} = \hat{B} \times \hat{C}$ gives $\hat{j} \times (-\hat{i}) = \hat{k}$, producing the complete wave expression with an identical phase argument.

The relationship between the electric field magnitude $E$ and magnetic field magnitude $B$ in a plane electromagnetic wave is given by $E = cB$. Rearranging this fundamental wave relation yields the ratio of the magnetic field to the electric field as $\frac{B}{E} = \frac{1}{c}$. Thus, the ratio simplifies directly to the inverse of the speed of light in free space.

The direction of propagation of an electromagnetic wave is always given by the cross product of the electric field vector and the magnetic field vector, pointing along $\vec{E} \times \vec{B}$. Given that the wave travels along the x-axis, the correct pair of field vectors must yield a cross product parallel to that axis. Evaluating the cross product for the vector combination $(-\hat{j}+\hat{k})$ and $(-\hat{j}-\hat{k})$ results in a vector directed entirely along the positive x-axis, thereby satisfying the required orthogonal orientation.

The displacement current inside a capacitor is defined by the rate of change of electric flux, which translates to the operational relation $I_d = C \frac{dV}{dt}$. Substituting the given alternating voltage expression $V = V_0 \sin \omega t$ into this equation gives $I_d = C \frac{d}{dt}(V_0 \sin \omega t)$. Differentiating the sine function with respect to time introduces the angular frequency, resulting in the final expression $I_d = V_0 \omega C \cos \omega t$.

Einstein's photoelectric equation combined with the de-Broglie wavelength formula connects the photon wavelength to the momentum of the emitted photoelectron via $\frac{hc}{\lambda} = \frac{P^2}{2m}$. Since the work function is negligible, the entire energy of the incident photon converts into the kinetic energy of the photoelectron, allowing momentum to be expressed as $P = \sqrt{\frac{2mhc}{\lambda}}$. Substituting this momentum into the de-Broglie relation $\lambda_d = \frac{h}{P}$ and squaring both sides allows the terms to be rearranged into the relation $\lambda = \left(\frac{2mc}{h}\right) \lambda_{d}^{2}$.

The total intensity of an electromagnetic wave is shared equally between its oscillating electric and magnetic field components. Energy is transported in equal measure by both fields, meaning the average energy density stored in the electric field equals that stored in the magnetic field. Consequently, their respective contributions to the wave's overall intensity are identical, resulting in a ratio of 1 : 1.

The speed of an electromagnetic wave in a medium depends on its optical constants through the relation $v = \frac{c}{\sqrt{\mu_r \epsilon_r}}$. Using the vacuum speed of light along with the given relative permeability of 1.0 and relative permittivity of 1.44, the calculation simplifies to dividing the speed of light by the square root of 1.44. This yields a medium velocity of 2.5 x 10^8 m/s.

The conduction current in the connecting wires is governed by the relation $i_c = C \frac{dV}{dt}$, which links the capacitance and the rate of change of potential. Multiplying the capacitance of 20 µF by the potential change rate of 3 V/s yields a conduction current of 60 µA. Since Maxwell's continuity condition dictates that the displacement current inside the capacitor equals the conduction current in the wires, the displacement current is also 60 µA.

The direction of propagation of an electromagnetic wave is determined by the vector cross product $\vec{E} \times \vec{B}$, which points along the velocity vector $\vec{V}$. Given that the electric field acts along the positive y-axis and the wave propagates along the positive x-axis, applying the right-hand rule for cross products dictates that the magnetic field must point along the positive z-axis. This ensures the mutually perpendicular orientation required for electromagnetic wave propagation.

The peak magnetic field is related to the root-mean-square electric field through the combination of the wave equation $E_0 = c B_0$ and the rms definition $E_{\text{rms}} = \frac{E_0}{\sqrt{2}}$. Rearranging these relations gives the formula for the peak magnetic field as $B_0 = \frac{E_{\text{rms}} \sqrt{2}}{c}$. Substituting the given rms electric field of 6 V/m and the speed of light yields a peak magnetic field of 2.83 x 10^-8 T.

The peak value of displacement current in a series circuit is determined by dividing the peak alternating voltage by the total impedance, given by the formula $Z = \sqrt{R^2 + X_c^2}$. Substituting the given resistance and reactance values into this expression yields an impedance of $100\sqrt{2}$ ohms. The peak source voltage is obtained by multiplying the root-mean-square voltage of 220 V by $\sqrt{2}$, resulting in a peak potential of $220\sqrt{2}$ volts. Dividing this peak voltage by the total impedance gives a maximum current of 2.2 A, rendering the instantaneous charge state of the capacitor irrelevant to this peak magnitude.

Electromagnetic waves are generated exclusively by accelerating electric charges, because a changing velocity produces time-varying electric and magnetic fields that mutually induce each other and propagate outward. Stationary charges produce only static electric fields, whereas charges moving at a constant velocity generate constant magnetic fields without creating propagating waves. Therefore, only an acceleration or deceleration phase creates the dynamic field fluctuations necessary to radiate electromagnetic energy.

The momentum of electromagnetic radiation is directly proportional to its energy and inversely proportional to the speed of light, expressed as $p = \frac{E}{c}$. When this radiation strikes a perfectly reflecting surface normally, it reverses its direction of motion while retaining its initial magnitude. The momentum transferred to the surface equals the total change in momentum of the radiation, which is the difference between its initial and final momentum vectors. Subtracting the final reversed momentum from the initial incoming momentum results in a total transfer of $\frac{2E}{c}$.

Electromagnetic waves are categorized into different spectral regions based on their photon energy, with the X-ray band spanning energies from approximately 100 eV to 100 keV. An energy level of 15 keV places the radiation squarely within this characteristic X-ray domain. This region lies beyond ultraviolet light and below gamma rays, making X-rays the correct classification for these high-energy photons.

The average force exerted by radiation on a perfectly reflecting surface is calculated using the relation $F_{\text{av}} = \frac{2IA}{c}$, where $I$ is the energy flux, $A$ is the area, and $c$ is the speed of light. Substituting the given values requires converting the area from square centimeters to square meters by multiplying by $10^{-4}$. Evaluating the expression gives $F_{\text{av}} = \frac{2 \times 25 \times 10^4 \times 15 \times 10^{-4}}{3 \times 10^8}$. Simplifying this numerical fraction yields an average force of $2.5 \times 10^{-6}$ N.

The frequency of an electromagnetic wave is determined entirely by its source and remains constant when transitioning between different media. Conversely, the wave speed decreases in a dielectric medium according to the relation $v = \frac{c}{\sqrt{\varepsilon_r}}$, where $\varepsilon_r$ is the relative permittivity. Since wave speed is given by the product of frequency and wavelength, a reduction in speed while frequency stays fixed results in a proportionally shorter wavelength, meaning the wavelength is halved.

Maximum energy transfer in wave absorption systems relies on the principle of resonance, where an external driving frequency matches the natural oscillation frequency of the target medium. Water molecules in food possess specific rotational resonant frequencies that dictate how they absorb electromagnetic radiation. When the frequency of the microwaves matches this natural frequency, energy is transferred most efficiently into the kinetic energy of the molecules, resulting in rapid heating.

The wave vector of an electromagnetic wave is determined by the ratio of its angular frequency to the speed of light, expressed as $k = \frac{\omega}{c}$. Comparing the given field expression with the standard wave equation $E = E_0 \cos(kz - \omega t)$ reveals the angular frequency. Using this angular frequency of $6 \times 10^8$ and the speed of light of $3 \times 10^8$, the calculation becomes $k = \frac{6 \times 10^8}{3 \times 10^8}$, which simplifies to $2$ m$^{-1}$.

The amplitudes of the electric and magnetic fields in an electromagnetic wave traveling through a vacuum are connected by the relationship $E_0 = B_0 c$. Rearranging this fundamental expression to find the ratio of the magnetic field amplitude to the electric field amplitude gives $\frac{B_0}{E_0} = \frac{1}{c}$. Since $c$ represents the speed of light in a vacuum, this ratio is precisely the reciprocal of that speed.

Electromagnetic waves are transverse in nature, meaning the electric field vector, the magnetic field vector, and the direction of wave propagation are mutually perpendicular. The direction of propagation is dictated by the vector cross product $\vec{E} \times \vec{B}$. For a wave traveling along the positive z-axis, choosing an electric field along the x-axis and a magnetic field along the y-axis correctly produces the propagation direction since the cross product of these unit vectors yields the z-axis unit vector.