Electromagnetic Waves Chapter-Wise Test 3

The wave number \( k = \frac{2 \pi}{\lambda} \). Given \( k = 3 \, \text{rad/m} \), we have \( \lambda = \frac{2 \pi}{k} = \frac{2 \pi}{3} \approx 2.09 \, \text{m} \).

Using \( B_0 = \frac{E_0}{c} \), we have \( B_0 = \frac{30}{3 \times 10^8} = 1 \times 10^{-7} \, \text{T} \).

The document mentions that UV lamps are used to kill germs in water purifiers due to their harmful effects on living organisms.

The document warns that X-rays can damage or destroy living tissues, so care must be taken to avoid unnecessary or overexposure.

The document mentions that microwaves range from \( 0.1 \, \text{m} \) to \( 1 \, \text{mm} \).

The document states that the speed of electromagnetic waves in a medium is \( v = \frac{1}{\sqrt{\mu \varepsilon}} \).

The Ampere-Maxwell law shows that just as a changing magnetic field induces an electric field (Faraday’s law), a changing electric field induces a magnetic field, highlighting the symmetry in electromagnetic interactions.

The speed of electromagnetic waves in vacuum is determined solely by universal constants (\( \mu_0 \) and \( \varepsilon_0 \)), as \( c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \), and is a fundamental constant in relativity.

The document mentions that cellular phones use radio waves in the UHF band, which typically falls within the general radio wave range of \( 500 \, \text{kHz} \) to \( 1000 \, \text{MHz} \), but UHF specifically is higher, often around \( 300 \, \text{MHz} \) to \( 3 \, \text{GHz} \). Here, we approximate within radio range.

In an electromagnetic wave, \( \mathbf{E} \), \( \mathbf{B} \), and the direction of propagation are mutually perpendicular. If \( \mathbf{E} \) is along \( x \)-axis and propagation is along \( z \)-axis, then \( \mathbf{B} \) must be along the \( y \)-axis (since \( \mathbf{E} \times \mathbf{B} \) gives the direction of propagation).

The document mentions that X-rays have wavelengths from about \( 10^{-8} \, \text{m} \) (10 nm) to \( 10^{-13} \, \text{m} \) (\( 10^{-4} \, \text{nm} \)).

X-rays have high energy and penetrating power, which can damage living tissues and cause cellular mutations, necessitating careful handling to avoid overexposure.

The document states that electromagnetic waves are self-sustaining oscillations of electric and magnetic fields, requiring no material medium for propagation.

Displacement current \( i_d = \varepsilon_0 \frac{d \Phi_E}{dt} \). Substituting the values, \( i_d = (8.85 \times 10^{-12}) \times (4 \times 10^{11}) = 3.54 \, \text{A} \).

The document notes that Maxwell's work unified electricity, magnetism, and light, leading to the understanding that light is an electromagnetic wave and paving the way for technologies like radio communication.