Electromagnetic Waves Chapter-Wise Test 6

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What enables electromagnetic waves to propagate through vacuum without a medium?

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

Presence of charged particles
High frequency of oscillation
Constant wavelength
Self-sustaining electric and magnetic fields
4

What does Maxwell's introduction of displacement current explain in the context of a charging capacitor?

The document explains that displacement current accounts for the magnetic field between the plates of a charging capacitor, where there is no conduction current, ensuring consistency with Ampere's law.

Magnetic field between the plates
Electric field outside the plates
Zero magnetic field everywhere
Conduction current inside the plates
1

An electromagnetic wave has a wave number \( k = 4 \, \text{rad/m} \). What is its wavelength in vacuum?

The wave number \( k = \frac{2 \pi}{\lambda} \). Given \( k = 4 \, \text{rad/m} \), we have \( \lambda = \frac{2 \pi}{k} = \frac{2 \pi}{4} \approx 1.57 \, \text{m} \).

0.785 m
1.57 m
3.14 m
6.28 m
2

Why are UV lamps used in LASIK eye surgery?

The document mentions that due to their shorter wavelengths, UV rays can be focused into narrow beams, making them suitable for high-precision applications like LASIK eye surgery.

They heat the cornea
They emit visible light
They can be focused into narrow beams
They penetrate deeper into tissues
3

An electromagnetic wave has an angular frequency \( \omega = 8 \times 10^{11} \, \text{rad/s} \). What is its frequency in Hz?

Frequency \( v = \frac{\omega}{2\pi} \). Given \( \omega = 8 \times 10^{11} \, \text{rad/s} \), \( v = \frac{8 \times 10^{11}}{2 \pi} \approx 1.27 \times 10^{11} \, \text{Hz} \).

\( 1 \times 10^{11} \, \text{Hz} \)
\( 1.27 \times 10^{11} \, \text{Hz} \)
\( 1.5 \times 10^{11} \, \text{Hz} \)
\( 2 \times 10^{11} \, \text{Hz} \)
2

What property of electromagnetic waves explains their ability to travel at the same speed in vacuum regardless of their frequency?

The speed of electromagnetic waves in vacuum depends only on the permittivity (\( \varepsilon_0 \)) and permeability (\( \mu_0 \)) of free space, given by \( c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \), which is constant.

Dependence on permittivity and permeability
Variation in wavelength
Dependence on frequency
Interaction with charged particles
1

What does Gauss's Law for electricity state in Maxwell's equations?

Gauss's Law for electricity states that the electric flux through a closed surface is proportional to the charge enclosed, given by \( \oint \mathbf{E} \cdot \mathrm{d} \mathbf{A} = \frac{Q}{\varepsilon_0} \).

\( \oint \mathbf{E} \cdot \mathrm{d} \mathbf{A} = \frac{Q}{\varepsilon_0} \)
\( \oint \mathbf{B} \cdot \mathrm{d} \mathbf{A} = 0 \)
\( \oint \mathbf{E} \cdot \mathrm{d} \mathbf{l} = -\frac{d \Phi_B}{dt} \)
\( \oint \mathbf{B} \cdot \mathrm{d} \mathbf{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d \Phi_E}{dt} \)
1

In electromagnetic theory, what explains the ability of waves to exhibit coherence?

Coherence arises from the wave-like nature of electromagnetic waves, where consistent phase relationships between oscillations allow phenomena like interference to occur.

Static fields
Medium properties
Particle nature
Wave-like nature
4

Why are electromagnetic waves classified into different types in the spectrum?

Electromagnetic waves are classified based on their frequency (or wavelength), which determines their energy, interaction with matter, and applications.

Their speed of propagation
Their direction of travel
Their medium of propagation
Their frequency or wavelength
4

An electromagnetic wave has a wavelength of \( 3 \, \text{m} \) in vacuum. What is its wave number \( k \)?

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

\( 2.09 \, \text{rad/m} \)
\( 1.05 \, \text{rad/m} \)
\( 4.18 \, \text{rad/m} \)
\( 6.28 \, \text{rad/m} \)
1

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