For the following questions answer them individually
A monochromatic plane wave of wavelength 500 µm is propagating in the direction as shown in the figure below. $$\overrightarrow{E_{i} } ,\overrightarrow{E_{r}} , \overrightarrow{E_{t}}$$ denotes incident, reflected and transmitted electric field vectors associated with the wave. The expression for $$\overrightarrow{E_{t}}$$ and $$\overrightarrow{E_{r}}$$ are
A long solenoid of radius R, having N turns per unit length carries a time dependent current $$I(t)=I_{0} \sin (\omega t)$$. The magnitude of induced electric field at a distance $$\frac{R}{2}$$ radially from the axis of the solenoid is
A parallel plate air-filled capacitor has plate area of $$10^{-4} m^{2}$$ and plate separation of $$10^{-3}$$. It is connected to a 2 V, 1.8 GHz source. The magnitude of the displacement current is $$\epsilon_{o}= \frac{1}{36 \pi \times 10^{-9} \frac{F}{m}}$$
Two rectangular waveguide have dimensions of $$1 cm \times 0.5 cm$$ and $$1 cm \times 0.25 cm$$ respectively. Their respective cut-off frequencies will be
The electric field vector of a wave is given as $$\overrightarrow{E}=E_{o} e^{j(\omega t + 3x - 4y)}\frac{8\overrightarrow{a_{x}}+6\overrightarrow{a_{y}}+5\overrightarrow{a_{z}}}{\sqrt{125}} V/m$$. Its frequency is 10 GHz. The phase velocity in Y-direction will be