Practice Questions

An electromagnetic wave propagates in a vacuum. The amplitude of the magnetic field component is $B_0 = 2 \times 10^{-8} \text{ T}$. Calculate the amplitude of the electric field component of the wave. Use $c = 3 \times 10^8 \text{ m/s}$.

Justify why welders must wear special goggles that block UV radiation, but do not need similar protection from visible light, even though the welding arc produces both.

Compare the speed of gamma rays with a wavelength of $10^{-12} \text{ m}$ and radio waves with a wavelength of $100 \text{ m}$ when they travel through a vacuum.

Name the scientist who argued for the existence of displacement current.

Evaluate the technological importance of microwaves by providing two distinct applications. For each application, justify why the specific properties of microwaves make them suitable for that purpose.

List the following electromagnetic waves in order of increasing wavelength: Gamma rays, Microwaves, Ultraviolet rays, and Radio waves.

Justify why an oscillating electric dipole is considered a fundamental source of electromagnetic waves, whereas a stationary dipole is not.

List any two properties of electromagnetic waves.

Name the type of electromagnetic radiation used for killing germs in water purifiers.

Analyze the relative orientation of the electric field vector, the magnetic field vector, and the direction of propagation for a plane electromagnetic wave.

Propose a reason why the ozone layer is crucial for life on Earth by evaluating the properties of the specific part of the electromagnetic spectrum it absorbs. What would be the likely consequences of its depletion?

Describe the nature of electromagnetic waves, specifically addressing the orientation of the fields and the requirement of a medium.

A local FM radio station broadcasts at a frequency range from $92 \text{ MHz}$ to $104 \text{ MHz}$. Calculate the corresponding wavelength band for this station. Use $c = 3 \times 10^8 \text{ m/s}$.

Evaluate the claim that all electromagnetic waves travel at the speed of light. Is this statement universally true? Justify your answer by considering propagation in both a vacuum and a material medium with permittivity $\varepsilon$ and permeability $\mu$.

An electromagnetic wave travels through a non-magnetic material with a relative permittivity $\varepsilon_r = 4$. Calculate the speed of the wave in this medium.

The magnetic field of a plane electromagnetic wave is given by the equation $B_y = (4 \times 10^{-6}) \sin(2 \times 10^7 z + 6 \times 10^{15} t) \text{ T}$. Calculate the wave number and the wavelength of the wave.

Examine why a stationary charge and a charge moving with uniform velocity cannot be sources of electromagnetic waves, based on Maxwell's equations.

The speed of light in vacuum is a universal constant, $c = 1/\sqrt{\mu_0 \varepsilon_0}$. Propose how one could, in principle, determine the value of the permittivity of free space, $\varepsilon_0$, if the values of the permeability of free space, $\mu_0$, and the speed of light, $c$, are known with high precision. Formulate the necessary equation.

Recall the relationship between the amplitudes of the electric field ($E_0$) and the magnetic field ($B_0$) for an electromagnetic wave in a vacuum.

Identify which part of the electromagnetic spectrum is used in microwave ovens and explain the principle of its operation.

Recall the formula for the speed of an electromagnetic wave in a material medium and explain the terms involved.

Summarize the key contributions of James Clerk Maxwell to the theory of electromagnetism.

An LC circuit oscillates at a frequency of $10^6 \text{ Hz}$. Analyze the nature of the radiation produced and identify which part of the electromagnetic spectrum it belongs to.

A parallel plate capacitor with circular plates of radius $10 \text{ cm}$ is being charged. If the charging current is constant at $0.25 \text{ A}$, calculate the displacement current between the plates and analyze its relationship with the conduction current.

Define displacement current and write its mathematical expression.

Describe the source of electromagnetic waves.

What physical quantity is the same for X-rays of wavelength $10^{-10} \text{ m}$ and radio waves of wavelength $500 \text{ m}$ when they travel in a vacuum?

The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is $B_0 = 2 \times 10^{-7} \text{ T}$. Recall the formula and calculate the amplitude of the electric field part of the wave.

Analyze the use of three different types of electromagnetic waves in technology. For each, identify the wave, describe a specific application, and explain why its properties (like wavelength or energy) make it suitable for that application.

Apply the principle of electromagnetic wave production to explain how a radio antenna broadcasts signals.

A student claims that since gamma rays and radio waves are both electromagnetic waves, they should have similar effects on biological tissues. Critique this statement. Justify your reasoning based on the energy of the photons associated with each type of wave.

An electromagnetic wave is propagating in the negative y-direction. At a certain point and time, the electric field vector is $\mathbf{E} = 300 \hat{\mathbf{k}} \text{ V/m}$. Formulate the corresponding magnetic field vector $\mathbf{B}$ at that point and time. Justify the direction of the magnetic field.

Justify the statement: 'The symmetry between Faraday's law of induction and the Ampere-Maxwell law is the theoretical foundation for the existence of electromagnetic waves.'

Design a simple communication system using electromagnetic waves. Your design should specify the type of EM wave you would use, justify your choice based on the intended range (e.g., short-range vs. long-range), and propose a basic method for encoding information onto the wave.

Create a comparative analysis of X-rays and Ultraviolet (UV) rays. Your analysis should evaluate their: (a) typical sources, (b) relative positions in the EM spectrum, (c) penetrating power, and (d) one beneficial and one harmful effect on living organisms.

A parallel plate capacitor consists of two circular plates of radius $8.0 \text{ cm}$ separated by a distance of $1.0 \text{ mm}$. The capacitor is connected to an external source, and the charging current is a constant $0.10 \text{ A}$. (a) Calculate the rate of change of the potential difference between the plates. (b) Solve for the displacement current.

Compare and contrast conduction current and displacement current. Examine why Maxwell's concept of displacement current was essential for modifying Ampere's circuital law.

The electric field of a plane electromagnetic wave propagating in vacuum is given by $E_y = 90 \sin(0.5 \times 10^3 x - 1.5 \times 10^{11} t)$, where E is in V/m, x is in meters, and t is in seconds. Analyze this equation to determine the following: (a) The wavelength and frequency of the wave. (b) The direction of propagation. (c) The expression for the corresponding magnetic field component.

A plane electromagnetic wave is travelling along the positive z-direction in free space. At a certain point and time, the electric field is $\mathbf{E} = 9.6 \hat{\mathbf{j}} \text{ V/m}$. Calculate the corresponding magnetic field $\mathbf{B}$ at that point.

Summarize Maxwell's four fundamental equations of electromagnetism in their integral form for a vacuum.

A plane electromagnetic wave in a vacuum has a magnetic field described by the equation $\mathbf{B} = B_0 \sin(kz - \omega t) \hat{\mathbf{j}}$, where $B_0 = 2 \times 10^{-7} \text{ T}$ and the wavelength $\lambda = 1.5 \text{ m}$. Formulate the corresponding equation for the electric field vector $\mathbf{E}$. Determine the frequency of the wave and the direction of propagation.

Critique the classical Ampere's circuital law, $\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 i$, in the context of a charging capacitor. Justify why Maxwell's modification was essential for the logical consistency of electromagnetism and how it led to the prediction of electromagnetic waves.

Propose an experimental setup to demonstrate that a time-varying electric field can produce a magnetic field, thereby verifying the concept of displacement current.

Create a hypothetical scenario where an astronaut is in a region of space with no conduction current, but detects a magnetic field that oscillates with a frequency of $150 \text{ MHz}$. Formulate the equations for the oscillating electric and magnetic fields, assuming the wave propagates along the z-axis and the electric field oscillates along the x-axis with an amplitude of $E_0 = 10 \text{ N/C}$. Calculate the wavelength and the amplitude of the magnetic field.

Explain the inconsistency in Ampere's circuital law that led Maxwell to introduce the concept of displacement current.