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An infinite time-harmonic electric current sheet flows on the z=0 plane at the interface between two dissimilar materials, as shown in the figure at right. Find the resulting E and fields in the two materials (Hint: assume plane wave solutions propagating away from the current sheet and enforce the boundary conditions).

An infinite time-harmonic electric current sheet flows on the z=0 plane at the interface between two dissimilar materials, as shown in the figure at right. Find the resulting E and fields in the two materials (Hint: assume plane wave solutions propagating away from the current sheet and enforce the boundary conditions).

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**Problem 7:** An infinite time-harmonic electric current sheet flows on the \(z = 0\) plane at the interface between two dissimilar materials, as shown in the figure. Find the resulting \(\vec{E}\) and \(\vec{H}\) fields in the two materials. *Hint: Assume plane wave solutions propagating away from the current sheet and enforce the boundary conditions.* --- **Diagram Explanation:** The diagram illustrates the interface between two regions at the \(z = 0\) plane, where an infinite time-harmonic electric current sheet, denoted by \(\vec{J}_s = \hat{x}J_0\) A/m, is located. - **Region 1** (left side): - Material properties: \(\varepsilon_1, \mu_1\) - **Region 2** (right side): - Material properties: \(\varepsilon_2, \mu_2\) The \(z\)-axis is horizontal, and the interface is represented as a vertical line at \(z = 0\), highlighting the transition between the two materials with different permittivities and permeabilities. The electric current sheet flows in the \(x\) direction.
Transcribed Image Text:**Problem 7:** An infinite time-harmonic electric current sheet flows on the \(z = 0\) plane at the interface between two dissimilar materials, as shown in the figure. Find the resulting \(\vec{E}\) and \(\vec{H}\) fields in the two materials. *Hint: Assume plane wave solutions propagating away from the current sheet and enforce the boundary conditions.* --- **Diagram Explanation:** The diagram illustrates the interface between two regions at the \(z = 0\) plane, where an infinite time-harmonic electric current sheet, denoted by \(\vec{J}_s = \hat{x}J_0\) A/m, is located. - **Region 1** (left side): - Material properties: \(\varepsilon_1, \mu_1\) - **Region 2** (right side): - Material properties: \(\varepsilon_2, \mu_2\) The \(z\)-axis is horizontal, and the interface is represented as a vertical line at \(z = 0\), highlighting the transition between the two materials with different permittivities and permeabilities. The electric current sheet flows in the \(x\) direction.
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