EE380: Electromagnetic Theory Department of Electrical Engineering Quiz 1 Semester: Summer 2019 Date: 17.07.2019 Time: 11:00 a.m. Max. Marks: 100 Duration: 12 hrs Q.1 Tabularize the physical quantities, their symbols and their units, we have learnt so far. Also list down any relationships between them, if exists. (10) Q.2 Argue, by considering different cases and supporting diagrams that: CLO3 CLO3 • the point, where E = 0, lies between two unequal positive charges (q1 = 1µC at (0,0) and q2 = 2µC at (1,2)) and it is collinear with them. (10) • the forces of four equal negative charges placed at the vertices of a square, are equal, along the diagonal of the square and away from its center. (10) Q.3 Given that J = cos( π2 x)e(−y−z) x̂ + ln(|y|)e(−x−z) ŷ + 10|z|ẑ A/m2 ; find the current coming out of the cube |x| ≤ 2, |y| ≤ 2, |z| ≤ 2. Sketch the given volume. (10) CLO1 −z Q.4 Given the electric flux density D = sin( 23 φ) e r r̂ + cos( 23 φ)e(−z) φ̂ + 10zẑ C/m2 ; how much charge is enclosed in the volume 2 ≤ r ≤ 3, π/6 ≤ φ ≤ π/3, −1 ≤ z ≤ 2. Sketch the given volume. (10) Q.5 Find the divergence and curl of the field given in Q.4. (10+10) e−jkr e−jkr e−jkr r̂ + 5(sin θ) 2 θ̂ + 7 2 φ̂ (10) r r r Q.7 (a) Find the Electric Field E at (0,1,2) due to uniform charge distribution ρl on x = 5, y = 3, point charge q = 1µC at (4,5,6) and infinite line charge 2µC/m at x = 5, z = 3. (10) Q.8 Two charges q1 = 2µC and q2 = 1µC are placed at (0,0,0) and (2,5,0), respectively. A third charge q3 = 1µC is placed such that it experiences no force. Find the location of q3 and individual forces exerted on q3 by q1 and q2 . (10) Q.6 Find the line integral of R E.dl of field E = 3(cos θ) CLO1 CLO1 CLO1 CLO4 CLO4