ENMG300 Electromagnetics Assignment 1 2026 | University of Dubai

ENMG300 Electromagnetics Assignment 1

Course Learning Outcomes (CLO)

Question-wise Distribution

Question 1

Recall the formulas for multiplication, division, and conjugation of complex numbers.

For z1=2+j5z_1 = 2 + j5z1​=2+j5 and z2=2−j2z_2 = 2 - j2z2​=2−j2 (r<90∘)(r < 90^\circ)(r<90∘)

a) z1z2z_1 z_2z1​z2​
b) z1/z2z_1 / z_2z1​/z2​
c) z1z2∗z_1 z_2^*z1​z2∗

(4 points)

Question 2

The electric field of a travelling electromagnetic wave is:

E(x,t)=3cos⁡(π×104t±5x) V/mE(x,t) = 3 \cos (\pi \times 10^4 t \pm 5x) \ \text{V/m}E(x,t)=3cos(π×104t±5x) V/m

From this expression, recall and find:

a) the direction of wave propagation
b) wave frequency
c) wavelength λ\lambdaλ
d) phase velocity upu_pup​

(4 points)

Question 3

An electromagnetic wave travels through seawater. Its amplitude is measured as 98.02 V/m at a depth of 10 m and 81.87 V/m at a depth of 100 m.

Using these values, recall the relation for wave attenuation and determine the attenuation constant of seawater.

(4 points)

Question 4

A parallel-plate transmission line operates at 1 GHz. It consists of copper strips of width 2.4 cm, separated by a 0.3 cm thick layer of polystyrene. The parameters are:

• Copper: μc=μ0=4π×10−7 H/m\mu_c = \mu_0 = 4\pi \times 10^{-7} \, \text{H/m}μc​=μ0​=4π×10−7H/m, σc=5.8×107 S/m\sigma_c = 5.8 \times 10^7 \, \text{S/m}σc​=5.8×107S/m
  
• Polystyrene: εr=2.6\varepsilon_r = 2.6εr​=2.6

Using these values, calculate the primary transmission line constants:

a) R′R'R′ (resistance per unit length)
b) L′L'L′ (inductance per unit length)
c) C′C'C′ (capacitance per unit length)
d) G′G'G′ (conductance per unit length)

(4 marks)

Question 5

A transmission line with characteristic impedance $Z0=50\Omega$ is terminated by
ZL=(60+j30)ΩZ_L = (60 + j30)\OmegaZL​=(60+j30)Ω. The operating wavelength is λ=50 cm\lambda = 50 \, \text{cm}λ=50cm.

Using these values, calculate:

a) the reflection coefficient
b) voltage standing wave ratio (VSWR)
c) the location of voltage maxima
d) the location of voltage minima

(4 marks)