info4eee.blogspot.com | AN EEE BLOGGURU NANAK EDUCATION TRUST GROUP OF INSTITUTIONELECTROMAGNETIC FIELD THEORY (TEC-401)PRE-UNIVERSITY EXAMINATIONSession: 2012-13 / EVEN SEMESTERB.TECH (ECE) 2ndYearWrite down your Roll No on the Question paper. M.M. 100Attempt All Questions. Time: 2.30 Hr1. Attempt any four questionsa. If A = 10 ax – 4 ay + 6 az and B = 2 ax + ay, find (i) thecomponent of A along ay, (ii) the magnitude of 3A – B,(iii) a unit vector along A + 2B.b. Three field quantities are given byP = 2 ax – azQ = 2 ax – ay + 2 azR = 2 ax – 3 ay + azDeterminei. ( P + Q ) X ( P – Q )ii. P . Q X Riii. A unit vector perpendicular to both Q and Rc. Given that F = x2ax – xz ay – y2az , calculate thecirculation of F around the closed pathd. Determine the gradient of the following scalar fields:i. U = x2y + xyzRoll No. +
info4eee.blogspot.com | AN EEE BLOGii. V = ρ z sinφ + z2cos2φ + ρ2iii. F = cosθ sinφ ln(r) + r2φe. If r is the position vector of a point, then evaluatei. Grad ( r )ii. Grad ( 1 / r )f. Transform the following vector to sphericalcoordinates. The vector is A = 5 ax)2. Attempt any four questionsa. The finite sheet 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 on the z = 0 planehas a charge density ρs = xy ( x2+ y2+ 25 )3/2nC/m2.Findi. The total charge on the sheetii. The electric field at (0, 0, 5)iii. The force experienced by a -1 mC charge located at(0, 0, 5)b. Given the potential sinθ cosφi. Find the electric flux density D at (2, π/2, 0).ii. Calculate the work done in moving a 10) )c. Derive dielectric – dielectric boundary conditions.d. Explain convection current and conduction current.Derive ohm’s law in point form.e. Two extensive homogeneous isotropic dielectrics meeton a plane z = 0. For z > 0, εr1 = 4 and for z < 0, εr2 = 3. Auniform electric field E1 = 5 ax – 2 ay + 3 az kV/m existsfor z ≥ 0. Findi. E2 for z ≤ 0ii. The energy densities (in J/m3) in both dielectricsf. Find the electric flux density at point P (6, 4, -5) causedby a uniform line charge ρL = 20 μC/m on z-axis.3. Attempt any four questionsa. Explain Biot-savart law and ampere’s circuit law.b. The conducting triangular loop In fig. carries a currentof 10 A. Find H at (0, 0, 5) due to side 3 of thetriangular loop.c. Planes z = 0 and z = 4 carry current K = -10 ax A/m andK = 10 ax A/m respectively. Determine H ati. (1, 1, 1)ii. (0, -3, 10)d. A charged particle of mass 2 kg and charge 3 C starts atpoint (1, -2, 0) with velocity 4 ax + 3 az m/s in anelectric field 12 ax + 10 ay V/m. At time t = 1 s,determinei. The acceleration of the particleii. Its velocityiii. Its kinetic energye. What are inductors? Define inductance.f. Define:i. Magnetic dipole and magnetic dipole moment.ii. Magnetization (M)4. Attempt any two questionsa. Define the following:i. Skin depthii. Intrinsic depthiii. Phase velocityiv. Pointing vectorb. (i) Explain Faraday law and Maxwell’s equations.(ii) Explain wave propagation in lossy dielectrics.
info4eee.blogspot.com | AN EEE BLOGc. How the wave propagation takes place in dispersivemedium? Light is incident from air to glass atBrewsters angle. Determine the incident andtransmitted angles.5. Attempt any two questionsa. Derive transmission line differential equation. Derivethe condition of lossless transmission from it.b. Derive input impedance of transmission line. Definestanding wave ratio?c. Define:i. Reflection coefficientii. Propagation constantAnswers:1. (a)i. The component of A along ay is Ay = -4.ii. 3 A – B = 28 ax – 13 ay + 18 az.iii. A unit vector along A + 2 B = 0.9113 ax – 0.1302 ay +0.3906 az.1. (b)i. (P + Q) X (P - Q) = 2 ax +12 ay + 4 azii. P. (Q X R) = 14.iii. +- (0.745 ax + 0.298 ay – 0.596 az)1. (c)1. (d)i. y (2x + z) ax + x (x + z) ay + xy az.ii. (z Sinφ + 2ρ) aρ + (2 cosφ – z2/ρ Sin2φ) aφ + (ρ Sinφ + 2zCos2φ) az.iii. (Cosθ Sinφ/r + 2ρφ) aρ – Sinθ Sinφ/r ln(r) aθ + (CotθCosφ ln(r)/r + r Cosecθ) aφ.1. (e)i.ii.1. (f) A = -1.057 ar – 2.27 aθ – 4.33 aφ2. (a)i. Q = 33.15 nCii. E = (-1.5 ax – 1.5 ay + 11.25 az) V/miii. F = (1.5 ax + 1.5 ay - 11.25 az)mN2. (b)i. D = 2.5 ε0 ar C/m2= 22.1 ar pC/m2ii. W = 28.125 μ J2. (e)i. E2 = 5 ax – 2 ay + 4 az kV/mii. WE1 = 672 μ J/m3WE2 = 597 μ J/m32. (f) D = (0.37 ax + 0.25 ay) μC/m23. (b) H = (-30.63 ax + 30.63 ay) mA/m3. (c)i. H = 10 ay A/mii. H = 0 A/m3. (d)i. a = 18 ax + 15 ayii. u = (22 ax + 15 ay + 3 az) m/s (At t = 1)iii. K.E. = 718 J