Electromagnetic Field And Waves

Daffodil International University Department of Electrical and Electronic Engineering Faculty of Engineering Mid-term Examination, Fall – 2026 Course Code: 0714-225 Course Title: Electromagnetic Fields and Waves Section: A, B, C, D Level-Term: L2-T3 Teacher's Initial: MFI Full Marks: 25 Exam Date: November 03, 2026 Time: 1.5 Hours [Notes: Answer all the following questions CO's represent one of the learning outcomes of the course. Figures on the right hand side indicate marks allocated for the questions.] Q1. If E = ρcosϕa_ρ + sinϕa_ϕ, evaluate ∮E. dl around the path shown in Fig. 1 using Stokes's theorem. CO-1 C4 [5] [Figure: Closed path L bounded by radial lines at 30° and 60° and circular arcs at r = 2 and r = 5, with vertices labeled a, b, c, d] Fig. 1 Q2. Determine D at (4, 0, 3) if there is a point charge -5π mC at (4, 0, 0) and a line charge 3π mC/m along the y-axis. CO-1 C4 [5] Q3. A charge distribution with spherical symmetry has density ρ_v = (ρ_0 r)/R for 0 ≤ r ≤ R and zero otherwise. Determine E everywhere. CO-1 C4 [5] Q4. For an electric dipole centered at r' with dipole moment p, show that the potential at r is given by V(r) = p.(r - r') / (4πε_0 |r - r'|^3) . CO-1 C3 [5] Q5. The point charges -1 nC, 4 nC and 3 nC are located at (0,0,0), (0,0,1) and (1,0,0) respectively. Find the energy in the system. CO-1 C4 [5]