Section 1 - Electromagnetic Theory

Question 1

The divergence of a vector field represents:

A. The rotation of the field at a point

B. The net outward flux per unit volume at a point

C. The line integral around a closed path

D. The magnitude of the field at a point

Question 2

The curl of a vector field represents:

A. The net outward flux per unit volume

B. The circulation per unit area, indicating rotation

C. The gradient of a scalar field

D. The magnitude of the field

Question 3

Gauss's law for electric fields (differential form) states:

A. curl E = 0

B. div D = rho (volume charge density)

C. div B = 0

D. curl H = J

Question 4

Gauss's law for magnetic fields states that:

A. div B = rho

B. div B = 0 (no magnetic monopoles)

C. curl B = mu_0 J

D. curl B = 0

Question 5

Faraday's law of electromagnetic induction in differential form is:

A. curl E = -dB/dt

B. curl H = J + dD/dt

C. div D = rho

D. div B = 0

Question 6

Ampere's law modified by Maxwell to include the displacement current is:

A. curl E = -dB/dt

B. curl H = J + dD/dt

C. div E = rho / epsilon

D. div H = 0

Question 7

The displacement current density was introduced by Maxwell to:

A. Explain conduction in metals

B. Maintain the continuity of current in time-varying fields (e.g., across a capacitor)

C. Explain magnetostatic phenomena

D. Account for losses in dielectrics

Question 8

The electric field inside a perfect conductor in electrostatic equilibrium is:

A. Equal to the applied field

B. Zero

C. Infinite

D. Equal to the surface charge density

Question 9

Boundary condition on the tangential component of the electric field at the interface between two dielectrics is:

A. It is discontinuous by an amount equal to the surface charge

B. It is continuous across the boundary

C. It is zero on both sides

D. It is proportional to the normal component of B

Question 10

The intrinsic (wave) impedance of free space is approximately:

A. 50 ohms

B. 75 ohms

C. 120 pi ohms (approximately 377 ohms)

D. 600 ohms

Question 11

The velocity of a plane electromagnetic wave in free space is:

A. 1 / sqrt(mu_0 epsilon_0)

B. sqrt(mu_0 / epsilon_0)

C. sqrt(mu_0 epsilon_0)

D. 1 / (mu_0 epsilon_0)

Question 12

In a plane electromagnetic wave travelling in free space, the electric and magnetic fields are:

A. Parallel to each other and to the direction of propagation

B. Mutually perpendicular and both perpendicular to the direction of propagation

C. Both parallel to the direction of propagation

D. 180 degrees out of phase

Question 13

The skin depth in a good conductor:

A. Increases with frequency

B. Decreases with frequency

C. Is independent of frequency

D. Depends only on the applied voltage

Question 14

The Poynting vector represents:

A. Energy stored per unit volume in an electromagnetic field

B. Power flow per unit area of an electromagnetic wave

C. Force per unit charge in a magnetic field

D. The direction of the magnetic field only

Question 15

The characteristic impedance of a lossless transmission line is given by:

A. sqrt(L/C)

B. sqrt(C/L)

C. L * C

D. 1 / (L * C)

Question 16

The reflection coefficient at the load of a transmission line is zero when:

A. The load is short-circuited

B. The load is open-circuited

C. The load impedance equals the characteristic impedance

D. The line is lossless

Question 17

A perfectly matched transmission line has a VSWR of:

A. 0

B. 1

C. Infinity

D. -1

Question 18

The Smith chart is used primarily for:

A. Designing filters

B. Solving transmission line and impedance-matching problems graphically

C. Analyzing time-domain waveforms

D. Calculating Fourier series

Question 19

In a rectangular waveguide, the dominant mode is:

A. TE11

B. TE10

C. TM11

D. TEM

Question 20

A rectangular waveguide cannot support the propagation of:

A. TE modes

B. TM modes

C. TEM mode

D. Higher order TE modes

Question 21

The cutoff frequency of a waveguide is the frequency below which:

A. The wave is attenuated and does not propagate

B. The wave propagates without loss

C. The wave is reflected back to the source only

D. The waveguide behaves as a perfect conductor

Question 22

The radiation resistance of a Hertzian dipole (short dipole) of length dl is approximately:

A. 73 ohms independent of length

B. 80 pi^2 (dl / lambda)^2 ohms

C. 377 ohms

D. 50 ohms

Question 23

The radiation resistance of a half-wave dipole antenna is approximately:

A. 37 ohms

B. 50 ohms

C. 73 ohms

D. 300 ohms

Question 24

The directivity of an antenna is defined as:

A. The ratio of maximum radiation intensity to the average radiation intensity

B. The ratio of input power to radiated power

C. The ratio of radiated power to input power

D. The ratio of near-field intensity to far-field intensity

Question 25

For an antenna, the effective aperture Ae is related to its gain G and wavelength lambda by:

A. Ae = G / (4 pi) * lambda^2

B. Ae = G * lambda

C. Ae = G / lambda

D. Ae = G * lambda^2

Questions

Section 1 - Electromagnetic Theory - Set 1