The value of magnetic field between plates of capacitor, at...

The value of magnetic field between plates of capacitor, at distance of $1 \mathrm{~m}$ from centre where electric field varies by $10^{10} \mathrm{~V} / \mathrm{m} / \mathrm{s}$ will be
(A) $5.56 \mathrm{~T}$
(B) $5.56 \mu \mathrm{T}$
(C) $5.56 \mathrm{mT}$
(D) $55.6 \mathrm{nT}$

Key Concepts

Maxwell’s Displacement Current

This is the concept introduced by Maxwell to account for the changing electric field in regions where there is no conduction current. It is added as an extra term in Ampère’s law (resulting in the Maxwell-Ampère law), allowing it to correctly predict the generation of magnetic fields even in the absence of charge motion. The displacement current term, proportional to the time rate of change of the electric field, provides the bridge between static electric and magnetic fields and their dynamic counterparts in electromagnetic theory.

Time-Varying Electric Fields

Time-varying electric fields describe electric fields that change with time. These variations are fundamental to the generation of magnetic fields in situations where there may be no conventional current. The rate of change of the electric field is crucial in many electromagnetic phenomena, and it appears directly in Maxwell's equations, linking rapidly changing electric fields to the production of magnetic fields in space, as seen in the analysis of dynamic systems like capacitors in transient states.

Maxwell-Ampère Law

This law is one of Maxwell’s equations that relates magnetic fields to the currents and changes in electric fields that produce them. In its extended form, the law incorporates not only conduction currents but also the displacement current, making it applicable in situations with time-varying electric fields. This unification is key to explaining electromagnetic wave propagation and the intrinsic link between electric and magnetic fields in dynamic regimes.

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