ECE 3030 Electromagnetic Fields and Waves Lecture 2 - Maxwell’s Equations in Free Space

Flashcards based on ECE 3030 Electromagnetic Fields and Waves Lecture 2

Name the three coordinate systems discussed in the lecture.

Cartesian (x, y, z), Cylindrical (r, Φ, z), Spherical (r, θ, Φ)

What are the unit vector notations for the Cartesian Coordinate System?

xˆ, yˆ, zˆ or iˆ, jˆ, kˆ

What are the unit vector notations for the Cylindrical Coordinate System?

rˆ, φˆ, zˆ or rˆ, φˆ, iˆ

What are the unit vector notations for the Spherical Coordinate System?

rˆ, θˆ, φˆ or rˆ, θˆ, φˆ

What is the general representation of a vector in the Cartesian coordinate system?

A = Ax xˆ + Ay yˆ + Az zˆ or A = Ax iˆ + Ay jˆ + Az kˆ

What is the general representation of a vector in the Cylindrical coordinate system?

A = Ar rˆ + Aφ φˆ + Az zˆ or A = Ar rˆ + Aφ φˆ + Az iˆ

What is the general representation of a vector in the Spherical coordinate system?

A = Ar rˆ + Aθ θˆ + Aφ φˆ or A = Ar iˆ + Aθ iˆ + Aφ iˆ

What is a Scalar Field?

A scalar quantity at every point in space. Example: volume charge ρ(x,y,z,t) or ρ(r,t)

What is a Vector Field?

A vector associated with every point in space. Examples: Electric Field E(x,y,z,t) or E(r,t), Magnetic Field H(x,y,z,t) or H(r,t)

Name the physical quantities discussed in the lecture.

Electric Field (E), Magnetic Field (H), Permittivity of Free Space (εo), Permeability of Free Space (μo), Electronic Unit of Charge (q), Volume Charge Density (ρ), Current Density (J), Electric Flux Density (D), Magnetic Flux Density (B)

What is the notation for the gradient of a scalar function φ?

∇φ

What is the gradient of a scalar function?

Vector ⊥ to level curves or surfaces

What is the notation for the divergence of a vector A?

∇ ⋅ A or div A

What is the notation for the curl of a vector A?

∇ ∧ A or rot A or ∇ × A

What are the four Maxwell's Equations?

Gauss' Law for E, Gauss' Law for H, Faraday's Law, Ampere's Law

What is the integral form of Gauss' Law for E?

∫∫ εo E ⋅ da = ∫∫∫ ρ dV

What is the differential form of Gauss' Law for E?

∇ ⋅ εo E = ρ

What is the integral form of Gauss' Law for H?

∫∫ μo H ⋅ da = 0

What is the differential form of Gauss' Law for H?

∇ ⋅ μo H = 0

What is the integral form of Faraday's Law?

∫ E ⋅ ds = - ∂/∂t ∫∫ B ⋅ da

What is the differential form of Faraday's Law?

∇ × E = - ∂B/∂t

What is the integral form of Ampere's Law?

∫ H ⋅ ds = ∫∫ J ⋅ da + ∂/∂t ∫∫ εo E ⋅ da

What is the differential form of Ampere's Law?

∇ × H = J + ∂/∂t εo E

What is the Lorentz Force Law?

F = q(E + v × B)

What does Gauss' Law for E establish about charges and electric fields?

Charges are the sources and sinks of the electric field. Positive charges source electric field lines, and negative charges terminate them.

What does Gauss' Law for H imply about magnetic charges?

There are no magnetic charges that can emanate or terminate magnetic field lines.

What does Faraday's Law state about the relationship between magnetic and electric fields?

Time-changing magnetic fields can generate electric fields.

What does Ampere's Law state about the relationship between electric currents, electric fields, and magnetic fields?

Electrical currents and time-changing electric fields can generate magnetic fields.

Are time varying electric and magnetic fields coupled or uncoupled?

Coupled

What conclusion did Maxwell make about light?

Light is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.

In electrostatics and magnetostatics, what produces electric and magnetic fields, respectively?

Electric fields are produced only by electric charges. Magnetic fields are produced only by electric currents.