1. 
The input impedance of short circuited loss-less line of length less than a quarter wavelength is

2. 
A spherical conductor with a radius of 10 cm is charged to 2 μC.

Calculate the electric field just outside the sphere’s surface in \( \text{kV/m} \).

3. 
A parallel-plate capacitor

with plate separation \( d \) is filled with two dielectrics of relative permittivities \( \epsilon_1 \) and \( \epsilon_2 \) occupying equal thickness. The equivalent capacitance is:

4. 
A plane electromagnetic wave propagates in a lossless dielectric medium

with \( \epsilon_r = 4 \) and \( \mu_r = 1 \). Calculate the phase velocity in \( \text{m/s} \). (Use \( c = 3 \times 10^8 \, \text{m/s} \)).

5. 
A uniform plane wave in free space has an electric field amplitude of 120 V/m.

Calculate the power density in \( \text{W/m}^2 \). (Use \( \eta_0 = 377 \, \Omega \), the intrinsic impedance of free space.)

 
6. 
A plane electromagnetic wave with an incident electric field 𝐸 = 50  V/m strikes the boundary between air and a perfect conductor. What is the tangential component of 𝐸 at the boundary?

7. 
A transmission line has a characteristic impedance of

 \( Z_0 = 75 \, \Omega \) and is terminated with a load impedance of \( Z_L = 150 \, \Omega \). Calculate the magnitude of the reflection coefficient.

8. 
In a region where both electric and magnetic fields are time-invariant, which Maxwell equation ensures that

\( \nabla \times \mathbf{E} = 0 \)

9. 
A cylindrical conductor of radius 1 mm carries a uniformly distributed current of 5 A. Calculate the magnetic field at the surface of the conductor in mT.

(Use \( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \)).

10. 
The electromagnetic power flow per unit area for a plane wave in free space is given by the Poynting vector

\( \mathbf{S} \). If \( E = 50 \, \text{V/m} \), the magnitude of \( \mathbf{S} \) is:

11. 
A rectangular waveguide

has dimensions \( a = 4 \, \text{cm} \) and \( b = 2 \, \text{cm} \). If the operating frequency is 6 GHz, calculate the cutoff frequency for the \( \text{TE}_{10} \) mode in GHz.

12. 
In a region of free space, an electromagnetic wave is propagating.

Which statement is always true about the relationship between the electric field \( \mathbf{E} \), magnetic field \( \mathbf{B} \), and the direction of wave propagation \( \mathbf{k} \)?

13. 
A material has permittivity

\( \epsilon = 2\epsilon_0 \) and permeability \( \mu = 3\mu_0 \). The velocity of electromagnetic waves in this material is:

14. 
A circular loop of radius 𝑅 carries a current 𝐼 . The magnetic field at a point along the axis of the loop at a distance 𝑥 from its center is:

15. 
Maxwell’s equations describe the behavior of electromagnetic fields. Which equation specifically represents the absence of magnetic monopoles?

16. 
A rectangular waveguide supports a dominant

\( \text{TE}_{10} \) mode at an operating frequency of 10 GHz. If the width of the waveguide is 2.5 cm, the cut-off wavelength is approximately:

17. 
The skin dept δ in a conductor with conductivity

 \( \sigma = 5.8 \times 10^7 \, \text{S/m} \), permeability \( \mu = \mu_0 \), and frequency \( f = 1 \, \text{MHz} \) is :

18. 
The electric field of a uniform plane electromagnetic wave is given E. The polarization of the wave is _______.

\( \mathbf{E} = \bigl(a_x + j 4 a_y\bigr) e^{j(2\pi \times 10^7 t – 0.2z)} \)
[GATE – 2015]

19. 
A medium is divided into regions I and II abour X = 0 plane, as shown in the figure below, an electromagnetic wave with electric field E given, is incident normally on the interface from region-I. The electric field E2 in region – II at the interface is ______.

\( \mathbf{E_1} = 4\hat{a}_x + 3\hat{a}_y + 5\hat{a}_z \)

[GATE – 2006]

20. 
The boundary conditions for the magnetic field at the interface between two media with permeabilities

\( \mu_1 \) and \( \mu_2 \) state that:

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