Which of the following represents the divergence of the electric field in Maxwell's equations? A) ∇·E = ρ/ε₀ B) ∇·B = 0 C) ∇×E = -∂B/∂t D) ∇·J = 0

A) ∇·E = ρ/ε₀

Fill in the blank: The scalar potential V is undetermined up to a ______.

Constant

True or False: The magnetic field can be expressed as the gradient of a scalar function.

False. The magnetic field is a vector field and is expressed as a curl of another vector.

What is the Lorentz Gauge condition used for in the context of potentials?

It decouples the equations involving scalar and vector potentials.

Riddle: I am the rate of energy flow per unit area in an electromagnetic field, often represented as S. What am I?

Poynting vector

Which law states that a changing magnetic flux induces an electromotive force?

Faraday's Law

Fill in the blank: The total energy density in an electromagnetic field is given by ______.

U = (1/2)εE² + (1/2)(B²/μ)

True or False: The divergence of the magnetic field is always non-zero.

False. The divergence of the magnetic field is always zero (∇·B = 0).

What is the physical significance of the Poynting vector?

It represents the directional energy flux (the rate of energy transfer per unit area) of an electromagnetic field.

Which equation relates the electric field E and the magnetic field B in a propagating wave?

E = cB

Fill in the blank: The mutual inductance between two circuits is denoted as ______.

M

True or False: Self-inductance L is defined as the ratio of induced emf to the rate of change of current in the same circuit.

True

What does the term 'displacement current' refer to in Maxwell's equations?

It refers to the term added to Ampere's Law to account for changing electric fields.

Riddle: I can be defined as the proportion of the electric field to the magnetic field in a plane wave. What am I?

Intrinsic impedance

The energy density of the electric field is given by ______.

U_E = (1/2)εE²

True or False: In Coulomb gauge, the divergence of the vector potential A is zero.

True

What is the relationship between the speed of light c, permittivity ε, and permeability μ in a vacuum?

C = 1/√(εμ)

Fill in the blank: The condition for total internal reflection occurs when the angle of incidence exceeds the ______.

Critical angle

Which law can be modified to include displacement current to resolve the anomaly with time-varying electric fields?

Ampere's Law

Riddle: I am a measure of how much an electric field can penetrate into a conductor, my depth is known as skin depth. What am I?

Skin depth

What is the expression for the induced emf in a circuit due to changing magnetic flux?

Ε = -dΦ/dt

Fill in the blank: The total energy density in an electromagnetic field is given by the sum of electric and magnetic energy densities, expressed as ______.

U = u_E + u_B

True or False: The electric field and magnetic field in an electromagnetic wave are always in phase.

False. The electric field and magnetic field are perpendicular to each other and to the direction of propagation.

What is the critical angle defined in terms of refractive indices for total internal reflection?

Sin(θ_c) = n₂/n₁

Riddle: I am the phenomenon where light bends when entering a new medium. What am I?

Refraction

Which equation expresses the relationship in a linear isotropic medium between the electric field E and the displacement field D?

D = εE

Fill in the blank: The electromagnetic wave equation is derived from Maxwell's equations and involves the second derivative with respect to time and space, resulting in ______.

Wave propagation

True or False: Electromagnetic waves can propagate in a vacuum without any medium.

True

What does the term 'attenuation constant' refer to in the context of wave propagation in conductors?

It measures how quickly the amplitude of the wave decreases as it travels through the conductor.

Riddle: I am the angle at which light reflects off a surface such that the reflected and refracted rays are perpendicular. What am I?

Brewster's angle

Which principle states that the tangential components of the electric and magnetic fields must be continuous at an interface?

Boundary conditions

Fill in the blank: The energy stored in the magnetic field is given by ______.

U_B = (1/2)(B²/μ)

Which of the following is a condition for the Lorentz Gauge to be satisfied? A) The divergence of the vector potential must be zero. B) The divergence of the scalar potential must be zero. C) There exists a scalar function whose gradient can be added to the vector potential. D) The electric field must be conservative.

C) There exists a scalar function whose gradient can be added to the vector potential.

What is the expression for the energy density of the electromagnetic field in a linear electric medium? ______.

U_E = (1/2)εE²

True or False: The displacement current density is equal to the conduction current density in a capacitor during charging.

False

Displacement current differs from conduction.

• In capacitors, fields change.

• Conduction current involves charge flow.

• Both currents serve distinct roles.

Riddle: I am a phenomenon that occurs when light passes from a denser to a rarer medium, causing no transmission beyond a critical angle. What am I?

Total Internal Reflection

According to Maxwell's equations, the divergence of the magnetic field is always ______.

Zero

What is the Poynting vector given by the equation P = E × H? Define the terms involved.

The Poynting vector describes energy flow.

• P is energy flux

• E is electric field

• H is magnetic field

Fill-in-the-blanks: The principle that describes how a changing magnetic field induces an electric field is known as ______.

Faraday's law of electromagnetic induction

Which of the following statements regarding mutual inductance is true? A) It is always greater than self-inductance. B) It is a function of the geometrical arrangement of the coils. C) It can only be negative. D) It is independent of the distance between the coils.

B) It is a function of the geometrical arrangement of the coils.