Given I=Im sinωt . We see that j=(Im)/(S) sinωt=-jd=-(∂D)/(∂t) or, D=(Im)/(ωS) cosωt, so, Em=(Im

step 1 In this problem I can write the value of i is equal to i m sine omega t we can see that j is equ

Given I=Im sinωt . We see that j=(Im)/(S)...

Given $I=I_{m} \sin \omega t .$ We see that $$ j=\frac{I_{m}}{S} \sin \omega t=-j_{d}=-\frac{\partial D}{\partial t} $$ or, $D=\frac{I_{m}}{\omega S} \cos \omega t$, so, $E_{m}=\frac{I_{m}}{\varepsilon_{0} \omega S}$ is the amplitude of the electric field and is $7 \mathrm{~V} / \mathrm{cm}$

Given $I=I_{m} \sin \omega t .$ We see that
$$
j=\frac{I_{m}}{S} \sin \omega t=-j_{d}=-\frac{\partial D}{\partial t}
$$
or, $D=\frac{I_{m}}{\omega S} \cos \omega t$, so, $E_{m}=\frac{I_{m}}{\varepsilon_{0} \omega S}$ is the amplitude of the electric field and is $7 \mathrm{~V} / \mathrm{cm}$

Key Concepts

Current Density

Current density is a measure of electric current per unit area and provides a local description of how charge flows through a material. In problems involving time-varying currents, expressing the current density as a sinusoidal function allows for analysis of the temporal variation of both the conduction and displacement currents and their interrelation.

Electric Field Amplitude Calculation

In systems exposed to a sinusoidal current, determining the amplitude of the resulting electric field involves first relating the conduction current density to the displacement current via Maxwell's displacement current concept, integrating appropriately, and then connecting the displacement field to the electric field through the material's permittivity. This approach underpins the derivation of expressions for the amplitude of the electric field in dynamic electromagnetic scenarios.

Maxwell's Displacement Current

This concept was introduced by Maxwell to amend Ampère's law by including a term for the time variation of the electric displacement field (D). The displacement current, defined as the time derivative of D, plays a crucial role in ensuring the continuity of current in situations where there is no physical charge movement, such as in capacitors with a changing electric field.

Electric Displacement Field

The electric displacement field, represented as D, describes the influence of an electric field in a medium, accounting for both free and bound charges. In vacuum, it is directly related to the electric field by the relation D = ??E. When subject to a time-varying source, D typically varies sinusoidally, and its relationship with the electric field is central to many electromagnetic phenomena.

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