1.
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?
2.
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 \( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \)).
3.
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:
4.
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:
5.
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 \( c = 3 \times 10^8 \, \text{m/s} \)).
6.
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.
7.
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:
8.
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.)
9.
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 \( \mathbf{k} \)?
10.
The input impedance of short circuited loss-less line of length less than a quarter wavelength 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.
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]
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.
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]
15.
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 :
16.
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 \( \text{kV/m} \).
17.
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:
18.
Maxwell's equations describe the behavior of electromagnetic fields. Which equation specifically represents the absence of magnetic monopoles?
19.
The boundary conditions for the magnetic field at the interface between two media with permeabilities
\( \mu_1 \) and \( \mu_2 \) state that:
20.
In a region where both electric and magnetic fields are time-invariant, which Maxwell equation ensures that
\( \nabla \times \mathbf{E} = 0 \)
