NEET Properties of EM Waves MCQs & PYQs

A stationary charge produces only a static electric field, while a charge moving at constant velocity produces a steady magnetic field along with it.
Only an accelerating (or oscillating) charge produces continuously changing electric and magnetic fields that sustain each other.
Therefore, an accelerating charge produces a propagating electromagnetic wave.

The momentum of the incident radiation is $p = \frac{E}{C}$.
Since the surface is perfectly reflecting, the radiation reflects back with momentum $-p$.
The momentum transferred to the surface is the change in momentum: $\Delta p = p - (-p) = 2p = \frac{2E}{C}$.

The speed of an electromagnetic wave in vacuum is related to the field amplitudes by $c = \frac{E_0}{B_0}$ . Rearranging this, we get the ratio of magnetic to electric field amplitude as $\frac{B_0}{E_0} = \frac{1}{c}$ . Therefore, it is the reciprocal of the speed of light in vacuum.

The expression $(\mu_0\epsilon_0)^{-\frac{1}{2}} = \frac{1}{\sqrt{\mu_0\epsilon_0}}$ represents the speed of light in vacuum (c). The dimensional formula for velocity or speed is $[L T^{-1}]$ .

The direction of propagation of an electromagnetic wave is parallel to the Poynting vector, given by the cross product $\bar{E} \times \bar{B}$ . For option a, $\hat{i} \times \hat{j} = \hat{k}$ , which corresponds to the +z axis.

Comparing with standard form $E = E_0\cos(\omega t + kx)$ , amplitude $E_0 = 10 V/m$ (Statement 3 is correct). Angular frequency $\omega = 10^7 rad/s$ , so wave number $k = \frac{\omega}{c} = \frac{10^7}{3 \times 10^8} = 0.033 rad/m$ . Wavelength $\lambda = \frac{2\pi}{k} = \frac{2\pi}{0.033} \approx 188.4 m$ (Statement 1 is correct). The positive sign indicates propagation in the -x direction. Thus, 1 and 3 are correct.

In an electromagnetic wave, the oscillating electric and magnetic field vectors are mutually perpendicular to each other, not parallel. They are also perpendicular to the direction of propagation. Thus, option d is false.

Comparing with $E_y = E_0\cos(\omega t - kx)$ , we find $\omega = 2\pi \times 10^6 rad/s$ and $k = \pi \times 10^{-2} rad/m$ . Frequency $f = \frac{\omega}{2\pi} = 10^6 Hz$ . Wavelength $\lambda = \frac{2\pi}{k} = \frac{2\pi}{\pi \times 10^{-2}} = 200 m$ . The negative sign between the temporal and spatial terms indicates it moves in the +x direction.

According to Maxwell's theory of electromagnetism, the speed of electromagnetic waves in free space is determined by its electric and magnetic properties and is given by the formula $c = \frac{1}{\sqrt{\mu_0\epsilon_0}}$ .

The direction of propagation of an electromagnetic wave, and thus its velocity vector, is given by the direction of the Poynting vector $\bar{S} = \frac{1}{\mu_0} (\bar{E} \times \bar{B})$ . Hence, it is parallel to $\bar{E} \times \bar{B}$ .