7. Time-Varying Fields and Maxwell’s EquationsIntroduction and ContextElectrostatics and magnetostatics provide powerful descriptions of electric and magnetic fields when charges and currents do not vary appreciably with time. Many important engineering systems, however, operate under dynamic conditions. Power transformers, antennas, transmission lines, electric machines, radar systems, wireless links, sensors, and optical devices all involve fields that change with time. Under such conditions, electric and magnetic fields are not independent phenomena: a changing magnetic field produces an electric field, while a changing electric field produces a magnetic field. The unified description of these interactions is provided by Maxwell’s equations. They combine Gauss’s law for electric fields, Gauss’s law for magnetism, Faraday’s law of electromagnetic induction, and the Ampère–Maxwell law. Together with constitutive relations and material properties, these equations form the foundation of classical electromagnetic theory. This chapter develops the equations in integral and differential form, explains the physical meaning of displacement current, introduces electromagnetic potentials and gauge conditions, and establishes the continuity relation for charge conservation. It also examines quasistatic approximations, which are essential when a full wave analysis is unnecessary or computationally expensive. Learning ObjectivesAfter studying this chapter, the reader should be able to: 1. Explain electromagnetic induction and derive Faraday’s law in integral and differential forms. 2. Identify the inconsistency in the original Ampère law for time-varying charge distributions. 3. Derive the displacement-current term and formulate the Ampère–Maxwell law. 4. State and interpret Maxwell’s equations in differential and integral forms. 5. Use electromagnetic potentials and distinguish gauge-dependent quantities from physical fields. 6. Apply the Lorenz and Coulomb gauge conditions appropriately. 7. Derive the continuity equation and relate it to charge conservation. 8. Select suitable electroquasistatic or magnetoquasistatic approximations. 9. Analyze practical electromagnetic systems using the field equations. 10. Recognize modeling limitations, boundary-condition requirements, and professional considerations in dynamic-field analysis. From Induction to Field CouplingFaraday’s law of electromagnetic inductionFaraday’s law states that the electromotive force around a closed path equals the negative time rate of change of magnetic flux through any surface bounded by that path: \[ \oint_C \mathbf{E}\cdot d\mathbf{l}=-\frac{d}{dt}\int_S \mathbf{B}\cdot d\mathbf{S}. \] The magnetic flux is \[ \Phi_B=\int_S\mathbf{B}\cdot d\mathbf{S}. \] The negative sign is Lenz’s law. The induced electric field acts in a direction that opposes the change in magnetic flux producing it. This opposition does not mean that induction prevents change; rather, it determines the polarity and direction of the induced electric field. For a stationary contour and surface, application of Stokes’ theorem gives \[ \oint_C\mathbf{E}\cdot d\mathbf{l}=\int_S(\nabla\times\mathbf{E})\cdot d\mathbf{S}. \] Therefore, \[ \boxed{\nabla\times\mathbf{E}=-\frac{\partial\mathbf{B}}{\partial t}}. \] This differential form states that a time-varying magnetic flux density creates a circulating electric field. Unlike an electrostatic field, this induced electric field is generally nonconservative, so its line integral around a closed path need not be zero. Consequently, it cannot in general be represented solely as the negative gradient of a scalar potential. If the contour itself moves through a magnetic field, the total electromotive force includes motional induction. For a conductor moving with velocity \(\mathbf{v}\), the force per unit charge is \(\mathbf{E}+\mathbf{v}\times\mathbf{B}\), and the emf is \[ \mathcal{E}=\oint_C(\mathbf{E}+\mathbf{v}\times\mathbf{B})\cdot d\mathbf{l}. \] The field equation \(\nabla\times\mathbf{E}=-\partial\mathbf{B}/\partial t\) describes transformer emf for a fixed spatial contour; the motional term is needed when the circuit moves. Gauss’s law and magnetic fluxGauss’s law for electricity relates electric flux to enclosed charge: \[ \oint_S\mathbf{D}\cdot d\mathbf{S}=Q_{\text{enc}}, \] or, in differential form, \[ \boxed{\nabla\cdot\mathbf{D}=\rho_v}. \] Here \(\rho_v\) is volume charge density and \(\mathbf{D}\) is electric flux density. In a linear, isotropic medium, \(\mathbf{D}=\varepsilon\mathbf{E}\). There are no experimentally observed isolated magnetic charges in classical electromagnetism. Magnetic flux lines therefore form closed paths, expressed by \[ \oint_S\mathbf{B}\cdot d\mathbf{S}=0, \] and \[ \boxed{\nabla\cdot\mathbf{B}=0}. \] The divergence-free nature of \(\mathbf{B}\) permits the introduction of a magnetic vector potential. The Displacement Current and the Completion of Ampère’s LawFor steady currents, Ampère’s circuital law is \[ \oint_C\mathbf{H}\cdot d\mathbf{l}=I_{\text{enc}}, \] or \[ \nabla\times\mathbf{H}=\mathbf{J}. \] This form is inadequate for time-varying systems. Consider a charging capacitor. Conduction current flows through the connecting wires, but no conduction current crosses the dielectric gap. If an Amperian loop surrounds the wire, a surface spanning the loop can intersect the conduction current. Another surface can pass between the capacitor plates and intersect no conduction current. The original law would predict different magnetic circulation values for the same loop, which is impossible. Maxwell resolved this inconsistency by introducing displacement current density: \[ \mathbf{J}_d=\frac{\partial\mathbf{D}}{\partial t}. \] The total current density in the generalized law is therefore \[ \mathbf{J}_{\text{total}}=\mathbf{J}+\frac{\partial\mathbf{D}}{\partial t}. \] The Ampère–Maxwell law becomes \[ \boxed{\nabla\times\mathbf{H}=\mathbf{J}+\frac{\partial\mathbf{D}}{\partial t}} \] and its integral form is \[ \boxed{\oint_C\mathbf{H}\cdot d\mathbf{l}=\int_S\mathbf{J}\cdot d\mathbf{S}+\frac{d}{dt}\int_S\mathbf{D}\cdot d\mathbf{S}}. \] Displacement current is not necessarily the motion of physical charges through a material. It is the time variation of electric flux and produces magnetic fields in precisely the way required by the generalized law. In a capacitor, it allows the magnetic field around the circuit to remain continuous while the capacitor charges. Taking the divergence of the differential Ampère–Maxwell law gives \[ 0=\nabla\cdot\mathbf{J}+\frac{\partial}{\partial t}(\nabla\cdot\mathbf{D}). \] Using Gauss’s law, \[ \boxed{\nabla\cdot\mathbf{J}+\frac{\partial\rho_v}{\partial t}=0}. \] This is the continuity equation. Its derivation demonstrates that the displacement-current term is required by charge conservation, not merely a mathematical correction. Maxwell’s Equations as a Unified FrameworkFor macroscopic electromagnetic fields, Maxwell’s equations are \[ \nabla\cdot\mathbf{D}=\rho_v, \] \[ \nabla\cdot\mathbf{B}=0, \] \[ \nabla\times\mathbf{E}=-\frac{\partial\mathbf{B}}{\partial t}, \] \[ \nabla\times\mathbf{H}=\mathbf{J}+\frac{\partial\mathbf{D}}{\partial t}. \] Their integral forms are \[ \oint_S\mathbf{D}\cdot d\mathbf{S}=Q_{ enc}, \] \[ \oint_S\mathbf{B}\cdot d\mathbf{S}=0, \] \[ \oint_C\mathbf{E}\cdot d\mathbf{l}=-\frac{d}{dt}\int_S\mathbf{B}\cdot d\mathbf{S}, \] \[ \oint_C\mathbf{H}\cdot d\mathbf{l}=\int_S\mathbf{J}\cdot d\mathbf{S}+\frac{d}{dt}\int_S\mathbf{D}\cdot d\mathbf{S}. \] The differential forms describe local field behavior at a point, whereas the integral forms describe flux or circulation over finite regions. The divergence theorem connects flux equations with divergence equations, and Stokes’ theorem connects circulation equations with curl equations. The field equations must be supplemented by constitutive relations. For a simple linear isotropic medium, \[ \mathbf{D}=\varepsilon\mathbf{E},\qquad \mathbf{B}=\mu\mathbf{H},\qquad \mathbf{J}=\sigma\mathbf{E}. \] In anisotropic, nonlinear, dispersive, or hysteretic materials, these relations may be tensorial, field-dependent, frequency-dependent, or history-dependent. The distinction between free and bound charge, and between conduction and polarization effects, becomes important in material modeling. Potentials and Gauge ConditionsBecause \(\nabla\cdot\mathbf{B}=0\), the magnetic flux density can be expressed as the curl of a vector potential: \[ \mathbf{B}=\nabla\times\mathbf{A}. \] Substitution into Faraday’s law gives \[ \nabla\times\left(\mathbf{E}+\frac{\partial\mathbf{A}}{\partial t}\right)=0. \] A curl-free field can be represented as the gradient of a scalar potential. Thus, \[ \boxed{\mathbf{E}=-\nabla V-\frac{\partial\mathbf{A}}{\partial t}}. \] The scalar potential \(V\) and vector potential \(\mathbf{A}\) are not unique. If a scalar function \(\chi(\mathbf{r},t)\) is selected, the transformations \[ \mathbf{A}'=\mathbf{A}+\nabla\chi, \] \[ V'=V-\frac{\partial\chi}{\partial t} \] leave \(\mathbf{E}\) and \(\mathbf{B}\) unchanged. This freedom is called gauge freedom. A gauge condition chooses one convenient representation from the family of mathematically equivalent potentials. The Lorenz gauge is \[ \boxed{\nabla\cdot\mathbf{A}+\mu\varepsilon\frac{\partial V}{\partial t}=0}. \] For a homogeneous, source-free medium with constant \(\mu\) and \(\varepsilon\), the potentials satisfy wave equations of the form \[ \nabla^2V-\mu\varepsilon\frac{\partial^2V}{\partial t^2}=-\frac{\rho_v}{\varepsilon}, \] \[ \nabla^2\mathbf{A}-\mu\varepsilon\frac{\partial^2\mathbf{A}}{\partial t^2}=-\mu\mathbf{J}. \] The wave speed is \[ v=\frac{1}{\sqrt{\mu\varepsilon}}. \] In free space this becomes the speed of light, \(c=1/\sqrt{\mu_0\varepsilon_0}\). The Lorenz gauge is especially useful for wave propagation and relativistically consistent formulations. The Coulomb gauge is defined by \[ \nabla\cdot\mathbf{A}=0. \] It is often useful in electrostatic-like or low-frequency calculations, although the resulting scalar and vector potential equations are more strongly coupled in a time-varying problem. Gauge choice does not alter measurable fields; it affects mathematical convenience, numerical conditioning, and interpretation. Quasistatic ApproximationsA full electromagnetic analysis includes propagation, radiation, induction, conduction, and displacement effects. In many engineering problems, one group of effects dominates and a quasistatic approximation is justified. In the electroquasistatic approximation, magnetic induction is neglected: \[ \nabla\times\mathbf{E}\approx 0. \] The electric field can then be approximated by \[ \mathbf{E}\approx-\nabla V. \] This approximation is appropriate when the physical dimensions are much smaller than the electromagnetic wavelength and magnetic induction is insignificant. Capacitive sensors and slowly varying electric-field systems are common examples. In the magnetoquasistatic approximation, displacement current is neglected relative to conduction current: \[ \frac{\partial\mathbf{D}}{\partial t}\ll\mathbf{J}. \] Ampère’s law becomes \[ \nabla\times\mathbf{H}\approx\mathbf{J}. \] This model is useful for power-frequency magnetic devices, transformers, motors, inductors, and low-frequency eddy-current systems, provided the displacement current is genuinely small in the region of interest. For a homogeneous conductor with \(\mathbf{J}=\sigma\mathbf{E}\), the ratio of displacement-current magnitude to conduction-current magnitude is approximately \[ \frac{|\partial\mathbf{D}/\partial t|}{|\mathbf{J}|}\approx\frac{\omega\varepsilon}{\sigma}. \] Thus conduction dominates when \(\omega\varepsilon\ll\sigma\), whereas displacement effects become important when \(\omega\varepsilon\) is comparable to or larger than \(\sigma\). This criterion is material- and frequency-dependent; it should not be applied without identifying the relevant medium. A second criterion concerns geometric scale. If a system dimension \(L\) is much smaller than the wavelength \(\lambda\), phase variation across the device may be small. Nevertheless, small size alone does not automatically justify neglecting induction or displacement current. The field mechanism and material properties must also be examined. Boundary Conditions for Time-Varying FieldsMaxwell’s equations lead to field boundary conditions that are central to device and wave analysis. At an interface with unit normal directed from medium 1 to medium 2, \[ \hat{\mathbf{n}}\cdot(\mathbf{D}_2-\mathbf{D}_1)=\rho_s, \] where \(\rho_s\) is free surface charge density, and \[ \hat{\mathbf{n}}\cdot(\mathbf{B}_2-\mathbf{B}_1)=0. \] For tangential fields, \[ \hat{\mathbf{n}}\times(\mathbf{E}_2-\mathbf{E}_1)=\mathbf{0} \] for an ideal interface considered without singular magnetic flux, while \[ \hat{\mathbf{n}}\times(\mathbf{H}_2-\mathbf{H}_1)=\mathbf{J}_s, \] where \(\mathbf{J}_s\) is free surface current density. These relations follow by applying Maxwell’s equations to an infinitesimal pillbox or rectangular loop. In practical computation, incorrect boundary conditions are a frequent source of physically meaningless results. Interfaces involving conductors, dielectric layers, magnetic cores, periodic structures, and radiation boundaries require distinct formulations. Applied Scenario: Displacement Current in a Charging CapacitorBackgroundConsider two circular conducting plates of area \(A\), separated by a dielectric of permittivity \(\varepsilon\). The capacitor is connected to a time-varying source and carries conduction current \(I(t)\) in the wires. Situation and analysisBetween the plates, the electric field is approximately uniform and related to the voltage by \(E\approx V/d\), where \(d\) is the separation. The electric flux density is \(\mathbf{D}=\varepsilon\mathbf{E}\). The displacement current through the dielectric is \[ I_d=\frac{d}{dt}\int_S\mathbf{D}\cdot d\mathbf{S}. \] For a uniform field, \[ I_d=\varepsilon A\frac{dE}{dt}=C\frac{dV}{dt}, \] which is exactly the circuit current associated with the capacitor relation \(I=C\,dV/dt\). Maxwell-based solutionAn Amperian loop surrounding the connecting wire may use a surface cutting through the conductor, yielding \[ \oint_C\mathbf{H}\cdot d\mathbf{l}=I. \] The same loop may use a surface passing between the plates, where conduction current is zero. The displacement current through that surface is \(I_d=I\), so \[ \oint_C\mathbf{H}\cdot d\mathbf{l}=I_d. \] The magnetic circulation is therefore independent of the selected spanning surface. Outcome and learning pointsThe capacitor gap does not require conduction current for a magnetic field to be associated with the changing electric field. The displacement-current term preserves consistency, enforces charge conservation, and allows the electromagnetic field description to remain continuous through the circuit. In high-frequency capacitors, dielectric loss, fringing fields, and radiation may require a more complete model than the ideal parallel-plate approximation. Practical and Professional ApplicationsMaxwell’s equations guide the design and verification of: - transformers, reactors, motors, generators, and inductors;
- transmission lines, waveguides, antennas, and microwave circuits;
- capacitive and inductive sensors;
- electromagnetic compatibility and interference-control systems;
- wireless power-transfer and radio-frequency identification systems;
- biomedical imaging, heating, and stimulation equipment;
- eddy-current inspection and non-destructive testing;
- electromagnetic shielding, grounding, and lightning-protection systems.
In engineering practice, field equations are often solved using finite-element, finite-difference, method-of-moments, or transmission-line tools. A reliable simulation requires an appropriate material model, excitation, mesh or discretization, boundary condition, and validation strategy. Software output is not a substitute for physical reasoning: conservation checks, limiting-case comparisons, convergence studies, and experimental correlation remain essential. Electromagnetic compatibility is also a professional responsibility. A design that satisfies its intended function may still interfere with communication, medical, navigation, or control equipment. Engineers must therefore consider radiated and conducted emissions, immunity, shielding, grounding, and applicable safety and regulatory requirements. Exposure assessments should use validated models and relevant standards rather than unsupported assumptions. Common Errors and Modeling LimitationsSeveral mistakes recur in time-varying field analysis. First, the original Ampère law is sometimes used without displacement current in a region where electric flux changes significantly. Second, the negative sign in Faraday’s law is ignored, producing an incorrect induced-field direction. Third, electrostatic formulas are applied to a situation in which \(\nabla\times\mathbf{E}\neq0\). Fourth, conduction and displacement currents are compared without accounting for frequency and material permittivity. Other errors include confusing \(\mathbf{B}\) with \(\mathbf{H}\), omitting surface charge or surface current at material interfaces, applying a quasistatic approximation outside its range of validity, and treating potentials as unique physical observables. Numerical models can additionally suffer from insufficient mesh resolution, artificial reflections at truncated boundaries, poorly represented material dispersion, or failure to resolve skin depth. The skin depth in a good conductor is approximately \[ \delta=\sqrt{\frac{2}{\omega\mu\sigma}}. \] If a conductor is modeled with elements much larger than the skin depth, predicted losses and current distributions may be inaccurate. Such limitations should be documented whenever field calculations inform safety, compliance, reliability, or major design decisions. Current DevelopmentsModern electromagnetic analysis increasingly combines Maxwell solvers with optimization, uncertainty quantification, reduced-order modeling, and multiphysics simulation. High-frequency systems require dispersive and sometimes anisotropic material descriptions, while electric machines and power converters require coupling between electromagnetic, thermal, mechanical, and circuit domains. Data-driven surrogate models and machine-learning-assisted optimization can reduce computational cost, but they must remain constrained by Maxwell’s equations, passivity, causality, and conservation laws. Automated design is valuable only when training data cover the relevant operating range and when independent validation is performed. Digital twins of electromagnetic devices similarly depend on calibrated models and trustworthy sensor data. Best Practices for AnalysisA disciplined workflow begins by identifying sources, geometry, materials, frequency range, and characteristic dimensions. The analyst should then determine whether a full-wave, electroquasistatic, magnetoquasistatic, or circuit-field coupled model is appropriate. Maxwell’s equations should be written with consistent sign conventions and units before simplifying. The model should include the relevant constitutive laws and boundary conditions. Results should be checked using charge continuity, energy balance, symmetry, limiting cases, and mesh or time-step convergence. Where possible, analytical approximations and measurements should be used for independent validation. Finally, assumptions, omitted effects, uncertainty, and applicable standards should be recorded so that the result can be interpreted responsibly by other engineers. Chapter SummaryTime-varying electric and magnetic fields are coupled through Faraday’s law and the Ampère–Maxwell law. Faraday’s law states that changing magnetic flux produces a circulating electric field, while Maxwell’s correction states that conduction current and changing electric flux produce magnetic circulation. Along with the two Gauss laws, these relations form Maxwell’s four equations in differential and integral forms. The continuity equation follows directly from the divergence of the Ampère–Maxwell law and expresses local charge conservation. Electromagnetic potentials provide an alternative formulation: \(\mathbf{B}=\nabla\times\mathbf{A}\) and \(\mathbf{E}=-\nabla V-\partial\mathbf{A}/\partial t\). Gauge conditions, including the Lorenz and Coulomb gauges, select convenient potential representations without changing physical fields. Quasistatic approximations simplify analysis when propagation or one of the two current mechanisms is demonstrably negligible. Appropriate boundary conditions, constitutive relations, validation, and professional judgment are essential in applying these equations to engineering systems. Key TermsMaxwell’s equations: Four coupled equations describing electric and magnetic fields and their sources. Faraday’s law: Law stating that changing magnetic flux produces electromotive force. Displacement current: The current density \(\partial\mathbf{D}/\partial t\) associated with changing electric flux. Ampère–Maxwell law: Relation stating that magnetic circulation is produced by conduction and displacement currents. Electric flux density: Field \(\mathbf{D}\) related to electric field and material polarization. Magnetic flux density: Field \(\mathbf{B}\) representing magnetic flux per unit area. Magnetic field intensity: Field \(\mathbf{H}\) related to magnetic sources and material response. Continuity equation: Differential statement \(\nabla\cdot\mathbf{J}+\partial\rho_v/\partial t=0\) of charge conservation. Electromagnetic induction: Production of an electric field by changing magnetic flux. Electromotive force: Work done per unit charge around a circuit. Scalar potential: Potential \(V\) used with a vector potential to represent the electric field. Vector potential: Potential \(\mathbf{A}\) whose curl gives magnetic flux density. Gauge freedom: Nonuniqueness of potentials that generate the same physical fields. Lorenz gauge: Condition \(\nabla\cdot\mathbf{A}+\mu\varepsilon\partial V/\partial t=0\). Coulomb gauge: Condition \(\nabla\cdot\mathbf{A}=0\). Electroquasistatic approximation: Approximation neglecting magnetic induction in the electric-field equation. Magnetoquasistatic approximation: Approximation neglecting displacement current relative to conduction current. Constitutive relation: Material equation connecting fields such as \(\mathbf{D}\) and \(\mathbf{E}\). Skin depth: Characteristic penetration distance of alternating fields into a conductor. Boundary condition: Relation specifying field behavior at an interface or computational boundary. Review QuestionsShort Answer Questions1. State Faraday’s law in differential form and explain the meaning of its negative sign. 2. Define displacement current density and explain why it is needed in a charging capacitor. 3. Write Maxwell’s four differential equations for macroscopic fields. 4. What is gauge freedom in electromagnetic potentials? 5. State the continuity equation and identify the physical conservation law it represents. Long Answer Questions1. Derive the differential form of Faraday’s law from its integral form using Stokes’ theorem. 2. Explain the inconsistency in the original Ampère law for a charging capacitor and derive the Ampère–Maxwell law. 3. Derive the continuity equation from the Ampère–Maxwell law and Gauss’s law. 4. Explain electromagnetic potentials and compare the Lorenz and Coulomb gauge conditions. 5. Discuss the assumptions, uses, and limitations of electroquasistatic and magnetoquasistatic approximations. Analytical / Application Questions1. A dielectric capacitor is driven by a sinusoidal voltage. Determine the displacement-current density and explain how its relative importance changes with frequency. 2. An engineer proposes a magnetoquasistatic model for a high-frequency, low-conductivity dielectric structure. Identify the quantities that must be compared before accepting or rejecting the approximation. 3. A finite-element model predicts discontinuous normal magnetic flux at an interface with no magnetic monopoles. Diagnose the modeling error and state the correct boundary condition. 22. Multiple Choice Questions with AnswersQuestion 1Which differential equation expresses Faraday’s law for a stationary contour? A. ∇·D = ρv B. ∇×E = −∂B/∂t C. ∇·B = 0 D. ∇×H = J Correct Answer: B. ∇×E = −∂B/∂t Question 2Why was the displacement-current term introduced into Ampère’s law? A. To account for magnetic monopoles B. To eliminate electric flux from dielectric materials C. To preserve consistency with charge conservation during capacitor charging D. To replace conduction current in all conductors Correct Answer: C. To preserve consistency with charge conservation during capacitor charging Question 3For a homogeneous medium, which relation defines displacement current density? A. Jd = σE B. Jd = μH C. Jd = ∂D/∂t D. Jd = ∇×B Correct Answer: C. Jd = ∂D/∂t Question 4What does ∇·B = 0 imply? A. Electric fields are conservative B. Magnetic flux lines have no isolated sources or sinks C. Conduction current is zero D. Magnetic fields cannot vary with time Correct Answer: B. Magnetic flux lines have no isolated sources or sinks Question 5Which equation represents charge conservation? A. ∇·J + ∂ρv/∂t = 0 B. ∇×E = 0 C. ∇·D = 0 D. ∇×H = ∂B/∂t Correct Answer: A. ∇·J + ∂ρv/∂t = 0 Question 6Which potential representation automatically satisfies ∇·B = 0? A. B = −∇V B. B = ∇·A C. B = ∇×A D. B = ∂A/∂t Correct Answer: C. B = ∇×A Question 7Which gauge condition is the Lorenz gauge? A. ∇·A = 0 B. ∇×A = 0 C. ∇·A + με ∂V/∂t = 0 D. ∇V + ∂A/∂t = 0 Correct Answer: C. ∇·A + με ∂V/∂t = 0 Question 8A magnetoquasistatic approximation is most justified when A. ωε is much greater than σ B. displacement current is negligible compared with conduction current C. the system dimension is always larger than its wavelength D. the electric field is identically zero Correct Answer: B. displacement current is negligible compared with conduction current Question 9At an interface with no magnetic monopoles, which boundary condition is correct? A. n̂·(B2 − B1) = 0 B. n̂·(D2 − D1) = 0 in every case C. n̂×(H2 − H1) = 0 in the presence of any surface current D. n̂×(E2 − E1) = Js Correct Answer: A. n̂·(B2 − B1) = 0 Question 10For a conducting medium, the approximate ratio of displacement-current magnitude to conduction-current magnitude is A. σ/(ωε) B. ωε/σ C. με/σ D. σ/(με) Correct Answer: B. ωε/σ
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