Electromagnetics Interview Questions

Q1. What is the difference between electric field intensity E and electric flux density D?

E is the force per unit charge in free space or any medium (V/m), while D is the electric flux density that accounts for the polarization of the medium: D = εE = ε₀εᵣE. In a parallel plate capacitor filled with a ceramic dielectric like BaTiO₃ with εᵣ ≈ 1000, the same applied voltage produces 1000× more D (and therefore stored charge) than the same capacitor in free space, while E is the same in both. The distinction matters when applying boundary conditions — the normal component of D is continuous across a dielectric interface, but E is not.

Follow-up: What boundary condition applies to the normal component of D at a dielectric interface?

Q2. What is the difference between magnetic field intensity H and magnetic flux density B?

H is the magnetic field intensity produced by free currents alone (A/m), while B = μH = μ₀μᵣH is the total magnetic flux density that includes the contribution from magnetized material. In a ferrite core transformer with μᵣ ≈ 2000, a given winding current produces a B that is 2000× larger than in an air-core transformer carrying the same current, which is why ferrite cores dramatically reduce the number of turns needed. The normal component of B is continuous across any material interface, while the tangential component of H is continuous across interfaces with no surface current.

Follow-up: What is the physical meaning of relative permeability μᵣ?

Q3. What is the divergence of the electric field and what does it represent?

The divergence of E equals ρv/ε (Gauss's law in differential form), where ρv is the volume charge density, meaning that electric field lines originate from positive charges and terminate on negative charges. In a uniformly charged sphere of charge density ρ₀, the divergence of E inside is ρ₀/ε₀, confirming that field lines spread outward from the distributed charge. Zero divergence means no sources or sinks — in a charge-free region, electric field lines cannot begin or end, they must curve continuously.

Follow-up: What does zero divergence of B physically mean?

Q4. What is Faraday's law and what phenomenon does it describe?

Faraday's law states that the curl of E equals -∂B/∂t, meaning a time-varying magnetic flux induces a circulating electric field (EMF) in any closed loop threading that flux. A 60 Hz power transformer exploits this directly — a sinusoidal B in the core at 1 Tesla peak induces a secondary EMF proportional to the rate of change dB/dt, generating the output voltage. The negative sign (Lenz's law) means the induced EMF always opposes the change causing it, which is why a transformer's secondary current creates a flux opposing the primary flux.

Follow-up: What is the integral form of Faraday's law and how does it relate to transformer operation?

Q5. What is the continuity equation in electromagnetics?

The continuity equation ∇·J = -∂ρv/∂t states that the net outflow of current density from any volume equals the rate of decrease of charge inside that volume, expressing conservation of charge. In a good conductor like copper carrying DC current, ρv = 0 inside the conductor at steady state because any excess charge dissipates extremely quickly — the relaxation time for copper is about 1.5 × 10⁻¹⁹ seconds. At high frequencies, this equation links the displacement current term in Maxwell's equations to the requirement that charge conservation must hold even when ∇·J ≠ 0.

Follow-up: How does the continuity equation relate to the displacement current term in Maxwell's equations?

Q6. What is the skin effect and at what depth does it become significant?

The skin effect is the concentration of AC current near the conductor surface due to eddy currents opposing field penetration, with the skin depth δ = √(2/(ωμσ)) where ω is frequency, μ is permeability, and σ is conductivity. In copper at 1 MHz, δ = √(2/(2π×10⁶ × 4π×10⁻⁷ × 5.8×10⁷)) ≈ 66 µm, meaning most of the current flows within a 66 µm annulus at the surface. This is why PCB traces for RF circuits above 100 MHz are often plated with gold or silver — the plating material's conductivity determines the skin depth at the operating frequency.

Follow-up: How does skin effect influence the design of inductors and RF coils?

Q7. What is the Poynting vector and what does it represent?

The Poynting vector S = E × H (W/m²) represents the instantaneous power flow density in an electromagnetic wave, pointing in the direction of energy propagation. In a coaxial cable carrying 100 W to a 50 Ω antenna, the Poynting vector in the dielectric between inner and outer conductors points axially from source to load — the power actually flows through the field in the dielectric, not through the copper conductors. Integrating S over a closed surface gives the total power flowing out of that surface, which is the basis for calculating radiated power from antennas.

Follow-up: Why does the Poynting vector point through the dielectric of a coaxial cable rather than through the conductors?

Q8. What is a uniform plane wave and what are its properties?

A uniform plane wave is an electromagnetic wave where E and H are uniform over every plane perpendicular to the direction of propagation, both fields are transverse to the direction of travel, and E and H are mutually perpendicular with |E|/|H| = η (the intrinsic impedance). In free space, a plane wave at 2.4 GHz (Wi-Fi) has an intrinsic impedance of η₀ = 377 Ω, meaning the ratio of electric to magnetic field amplitudes is always 377 V/A. Plane waves are the far-field approximation used in antenna link budget calculations, where the distance from the source is large enough that the wavefronts are approximately flat.

Follow-up: What is the intrinsic impedance of free space and how is it derived?

Q9. What is the difference between a conductor and a dielectric from an electromagnetic standpoint?

A conductor has σ >> ωε, meaning conduction current dominates over displacement current, so essentially all applied electric field drives free charge flow; a dielectric has σ << ωε, so displacement current dominates and the material stores field energy with little loss. Copper with σ = 5.8×10⁷ S/m is a good conductor even at microwave frequencies, while PTFE (Teflon) with σ ≈ 10⁻²³ S/m and εᵣ = 2.1 is an excellent microwave substrate dielectric. The loss tangent tan δ = σ/(ωε) quantifies how lossy a dielectric is; substrate materials used in high-speed PCBs like Rogers RO4003C are chosen for their low tan δ (≈ 0.0027 at 10 GHz).

Follow-up: What is the loss tangent and how does it affect microwave circuit design?

Q10. What is wave polarization and what are its types?

Wave polarization describes the orientation and rotation of the electric field vector as a function of time — a wave is linearly polarized if E stays in one plane, circularly polarized if |E| is constant and E rotates at the wave frequency, and elliptically polarized in the general case. A half-wave dipole antenna radiates linearly polarized waves in the plane containing the antenna, which is why TV antennas must be oriented to match the transmitter's polarization for maximum signal. Circular polarization is used in satellite communication (GPS uses right-hand circular polarization) to eliminate the polarization mismatch problem that occurs when the satellite's orientation changes.

Follow-up: Why is circular polarization used in satellite communications instead of linear polarization?

Q11. What is the boundary condition for the tangential component of E at a conductor surface?

The tangential component of E is zero at a perfect conductor surface because any tangential E would drive infinite current in a zero-resistance conductor, which is physically impossible, and boundary conditions enforce Etan = 0. In a microwave waveguide made of copper, the boundary condition Etan = 0 on the walls forces the electric field to be normal to the walls, which determines which modes can propagate and at what cutoff frequencies. This condition is the fundamental reason why waveguide dimensions determine the frequency band of operation.

Follow-up: What boundary condition applies to the normal component of B at a conductor surface?

Q12. What is displacement current and why did Maxwell add it to Ampere's law?

Displacement current Jd = ∂D/∂t is the equivalent current produced by a time-varying electric field in a dielectric or vacuum, and Maxwell added it to Ampere's law to make the equation mathematically consistent with the continuity of charge. Without displacement current, Ampere's law predicts different magnetic fields on two surfaces bounded by the same loop when a capacitor is charging — which is physically impossible. Adding displacement current not only resolves this contradiction but also predicts the existence of electromagnetic waves propagating through free space, since a changing E generates H which generates E and so on.

Follow-up: How does the addition of displacement current lead to the prediction of electromagnetic waves?

Q13. What is the relaxation time of a conductor and what does it tell you?

The relaxation time τ = ε/σ is the time constant for free charge to redistribute to the surface of a conductor after being placed inside it; for good conductors this time is so short that interior charge density is always essentially zero. For copper, τ = ε₀/σ = 8.85×10⁻¹²/(5.8×10⁷) ≈ 1.5×10⁻¹⁹ seconds, meaning any interior charge dissipates almost instantaneously. This extremely short relaxation time is why static charges always reside on the surface of conductors and why copper is effectively charge-free inside for all practical operating frequencies.

Follow-up: What is the relaxation time of seawater compared to copper, and what does this imply about RF propagation underwater?

Q14. What is the right-hand rule in electromagnetics and where is it applied?

The right-hand rule states that if the thumb of the right hand points in the direction of current flow, the fingers curl in the direction of the magnetic field encircling the conductor, which follows from Ampere's law ∮H·dl = I_enclosed. In a solenoid wound with 500 turns on a ferrite core, the right-hand rule applied to any turn immediately tells you the direction of B inside the core, which determines the polarity of transformer windings and the direction of force on a current-carrying conductor in a motor. The cross-product E×H in the Poynting vector also follows the right-hand rule, consistently defining the power flow direction.

Follow-up: How do you apply the right-hand rule to find the force on a current-carrying conductor in a magnetic field?

Q15. What is the condition for total internal reflection and what is its application?

Total internal reflection occurs when a wave traveling from a denser medium to a less dense medium hits the interface at an angle greater than the critical angle θc = arcsin(n₂/n₁), where n is the refractive index, causing all incident power to be reflected back into the first medium with no transmitted wave. In a glass optical fiber with core refractive index 1.5 and cladding index 1.46, the critical angle is arcsin(1.46/1.5) ≈ 76.7°, and any ray hitting the cladding at more than 76.7° is totally reflected, guiding the light along the fiber. Total internal reflection is the principle behind not only optical fiber but also the frustrated total internal reflection used in fingerprint scanners and waveguide couplers.

Follow-up: What is the evanescent field in total internal reflection and does it carry power?