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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