A monochromatic plane wave of wavelength 500 μm is propagating in the direction as shown in the figure below. $\mathop {{E_i}}\limits^ \to $, $\mathop {{E_r}}\limits^ \to $ and $\mathop {{E_t}}\limits^ \to $ denotes incident,reflected and transmitted electric field vectors associate with the wave.The expression for $\mathop {{E_i}}\limits^ \to $ and $\mathop {{E_r}}\limits^ \to $ are

Question

A monochromatic plane wave of wavelength 500 μm is propagating in the direction as shown in the figure below. $\mathop {{E_i}}\limits^ \to $, $\mathop {{E_r}}\limits^ \to $ and $\mathop {{E_t}}\limits^ \to $ denotes incident,reflected and transmitted electric field vectors associate with the wave.The expression for $\mathop {{E_i}}\limits^ \to $ and $\mathop {{E_r}}\limits^ \to $ are

TuteeHUB · Accepted Answer

$\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} - {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x + y} \right)}}{{5\sqrt 2 }}}}V/m$ and $ - 0.10\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} + {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x - y} \right)}}{{5\sqrt 2 }}}}V/m$

TuteeHUB · Answer

$\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} - {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x + y} \right)}}{{5\sqrt 2 }}}}V/m$ and $0.10\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} + {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x - y} \right)}}{{5\sqrt 2 }}}}V/m$

TuteeHUB · Answer

$\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} + {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x - y} \right)}}{{5\sqrt 2 }}}}V/m$ and $\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} - {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x + y} \right)}}{{5\sqrt 2 }}}}V/m$

TuteeHUB · Answer

$\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} - {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x + y} \right)}}{{5\sqrt 2 }}}}V/m$ and $\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} + {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x - y} \right)}}{{5\sqrt 2 }}}}V/m$

1.	A monochromatic plane wave of wavelength 500 μm is propagating in the direction as shown in the figure below. \(\mathop {{E_i}}\limits^ \to \), \(\mathop {{E_r}}\limits^ \to \) and \(\mathop {{E_t}}\limits^ \to \) denotes incident,reflected and transmitted electric field vectors associate with the wave.The expression for \(\mathop {{E_i}}\limits^ \to \) and \(\mathop {{E_r}}\limits^ \to \) are
A.	\(\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} - {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x + y} \right)}}{{5\sqrt 2 }}}}V/m\) and \(0.10\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} + {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x - y} \right)}}{{5\sqrt 2 }}}}V/m\)
B.	\(\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} - {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x + y} \right)}}{{5\sqrt 2 }}}}V/m\) and \( - 0.10\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} + {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x - y} \right)}}{{5\sqrt 2 }}}}V/m\)
C.	\(\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} + {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x - y} \right)}}{{5\sqrt 2 }}}}V/m\) and \(\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} - {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x + y} \right)}}{{5\sqrt 2 }}}}V/m\)
D.	\(\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} - {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x + y} \right)}}{{5\sqrt 2 }}}}V/m\) and \(\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} + {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x - y} \right)}}{{5\sqrt 2 }}}}V/m\)
Answer» B. \(\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} - {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x + y} \right)}}{{5\sqrt 2 }}}}V/m\) and \( - 0.10\frac{{{E_0}}}{{\sqrt 2 }}\,\left( {{{\hat a}_x} + {{\hat a}_y}} \right){e^{ - j\frac{{2\pi \times {{10}^4}\left( {x - y} \right)}}{{5\sqrt 2 }}}}V/m\)

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