1
GATE ECE 2015 Set 1
Numerical
+2
-0
The electric field intensity of a plane wave traveling in free space is given by the following expression

$$E\left( {x,t} \right) = {\widehat a_{_y}}24\pi \,\,\cos \left( {\omega t - {k_0}x} \right)\,\,\,\left( {V/m} \right)$$. In this field, consider a square area $$10 cm$$ $$\times$$ $$10 cm$$ on a plane $$x + y = 1$$. The total time-averaged power $$(in mW)$$ passing through the square area is ________.

2
GATE ECE 2015 Set 1
Numerical
+2
-0
Consider a uniform plane wave with amplitude $$\left( {{E_0}} \right)$$ of $$10\,\,\,V/m$$ and $$1.1 GHz$$ frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity $$\left( {{\varepsilon _r}} \right)$$ and permeability $$\left( {{\mu _r}} \right)$$ as shown in the figure.

The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance of $$10$$ cm inside the dielectric region is ________.

3
GATE ECE 2014 Set 3
+2
-0.6
A region shown below contains a perfect conducting half-space and air. The surface current $${\overrightarrow K _{_s}}$$ on the surface of the perfect conductor is $${\overrightarrow K _{_s}} = \widehat x\,2$$ amperes per meter. The tangential $$\overrightarrow H$$ field in the air just above the perfect conductor is
A
$$\left( {\widehat x + \widehat z} \right)2$$ amperes per meter
B
$$\widehat x2$$ amperes per meter
C
$$- \widehat z2$$ amperes per meter
D
$$\widehat z2$$ amperes per meter
4
GATE ECE 2014 Set 3
Numerical
+2
-0
Assume that a plane wave in air with an electric field
$$\overrightarrow E = 10\cos \left( {\omega t - 3x - \sqrt {3z} } \right){\widehat a_{_y}}\,\,\,V/m$$ is incident
on a non-magnetic dielectric slab of relative permittivity $$3$$ which covers the region $$z > 0$$ . The angle of transmission in the dielectric slab is _______ degrees.