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Maxwell's equation derived from AmpereтАЩs law is
Div(I) = H
Div(H) = J
Curl(H) = J
Curl(B) = D
Curl(H) = J
Maxwell's equation derived from Ampere's Law relates the magnetic field intensity (H) to the conduction current density (J). In its static form, the curl of the magnetic field intensity is equal to the current density, denoted as тИЗ├ЧH=J.
Maxwell's equation derived from Ampere's Law relates the magnetic field intensity (H) to the conduction current density (J). In its static form, the curl of the magnetic field intensity is equal to the current density, denoted as тИЗ├ЧH=J.
тИЗ├ЧH=J тАФ Differential form of Ampere's Law for static fields
тИоCтАЛHтЛЕdl=IencтАЛ тАФ Integral form of Ampere's Law
Ampere's circuital law states that the line integral of the magnetic field intensity around a closed path is equal to the current enclosed by that path. Applying Stokes' theorem to this line integral transforms it into the point form (differential form), resulting in тИЗ├ЧH=J. This equation describes how moving electric charges (currents) serve as a source for the magnetic field.
The curl operator (тИЗ├Ч) indicates the circulation density of the magnetic field.
Ampere's law establishes the link between electricity and magnetism.
In time-varying fields, this equation is modified to тИЗ├ЧH=J+тИВtтИВDтАЛ by adding the displacement current term.
Provides a local relationship between fields and sources.
Essential for solving electromagnetic boundary value problems.
Does not account for time-varying displacement current in the static form.
Requires knowledge of vector calculus for implementation.
Calculation of magnetic fields around current-carrying conductors.
Design of inductors and transformers.
Option C is the static form. The full Maxwell-Ampere law includes the displacement current density тИВtтИВDтАЛ.
Option A is incorrect as divergence of current is typically related to charge continuity.
Option B is incorrect; тИЗтЛЕB=0 is Gauss's Law for magnetism.
C is correct тАФ The differential (point) form of Ampere's law is given by тИЗ├ЧH=J.
Always verify if the question refers to static fields or time-varying fields, as the latter requires the inclusion of the displacement current тИВtтИВDтАЛ.