Find the gradient of the function given by, x2 + y2 + z2 at (1,1,1) Either way, we refer to Eq. Electromagnetic Theory Questions and Answers – Cylindrical Coordinate System d) |dot product| + |cross product| = 0 2 Vector Analysis Chap 1 GATE CLOUD Electromagnetics By RK Kanodia & Ashish Murolia For View Only Shop Online at www.nodia.co.in.com EXERCISE 1.1 MCQ 1.1.1 The field lines of vector Ba=r q is MCQ 1.1.2 Given the two vectors Ma a a=-+52 4 xy z and Naaa=- - +87 2 xy z. Explanation: Two vectors are parallel when their cross product is zero. d) 10i + 0.135j + k Φ = tan-1(y/x) = tan-1(4/3) = 53⁰. Explanation: Projection of A on B = (A . a) Laplacian operation Example. (2) S2={[x1x2x3]∈R3|x1−4x2+5x3=2} in the vector space R3. b) 2i + 2j + 2k The cross product of two vectors is a vector. d) -3i + 11j – 7k a) Dot product is zero The graph of a function of two variables, say, z=f(x,y), lies in Euclidean space, which in the Cartesian coordinate system consists of all ordered triples of real numbers (a,b,c). d) The statement is false b) False coordinates. Explanation: r = √(x2+y2+z2) = √14 = 3.74 Explanation: On double integrating the differential volume, the area can be computed for a sphere. The image shows the magnitude of the electromagnetic wave, where red and blue are high and low values, respectively. The curl of gradient of a vector is non-zero. Explanation: Gradient of any function leads to a vector. Vector quan- Explanation: The vector product of two vectors is A X B = AB sin θ. n, where n is the unit normal vector to c) Both are zero Find a vector normal to a plane consisting of points p1(0,1,0), p2(1,0,1) and p3(0,0,1) b) -3.197i + 2.393j – 4.472k a) |dot product| + |dot product| = 1 Thus the minimum scalar factor has to be 1, ρ , 1. These can be expressed in an infinite number of dimensions, but are most often expressed in two or three. b) 10i + j + 0.135k 3. a) True 7. Thus it is line integral. the plane given by A and B. vector field. Θ = cos-1(z/r) = 1 d) Inwards 3. b) Curl free 2. found by The area of sphere can be computed from the sphere volume. (B . the slope in mathematics. The vector operator ∇ is called “del.” For a vector-valued function … c) Curl 7. vector is given by, (-j – k)/1.414. Explanation: Cross product of two vectors is, A X B = (a2*b3 – b2*a3)i – (a1*b3 – b1*a3)j + (a1*b2 – State True/False. Explanation: Since all the coordinates in electromagnetic are space coordinates, direction and magnitude Explanation: r = √(x2+y2+z2) = √50 = 7.07 a) Grad(Div V) b) Divergence a) (6.325,-71.57,3) View Answer, 2. Electromagnetic wave follows the principle of superposition. Explanation: Dot product of two perpendicular vectors is given by A.B = |a||b|cos 90, which is zero. Electromagnetic forces are defined by cos-1(0.377) = 67.8. Put x=1, y=1, z=1, the gradient will be 2i + 2j + 2k. State True/False. Explanation: The distance vector is the distance between two points on space, thus the unit normal a) -2i + j (5) S5={f(x)∈P4∣f… First, the method has not been tested on curvilinear geometries. For each set, give a reason why it is not a subspace. a) Divergence is zero 6. , as I alluded to in chapter III.4. b) False State True or False. d) Geometry c) 2 State View Answer. S4={f(x)∈P4∣f(1)is an integer} in the vector space P4. d) Null vector Electromagnetic Theory Questions and Answers – Gradient c) Not parallel b) Spherical coordinates C) = scalar value a) cos x i – sin y j At (5, π/2, -2), r = √(52+-22) = √29 Explanation: Force is a vector quantity, whereas distance is scalar. 3. Explanation: Cross product of dot product of two vectors is a vector value. Explanation: Div (Grad V) = (Del)2V, which is the Laplacian operation. d) (6.325,-73.57,3) C) = scalar value (1) S1={[x1x2x3]∈R3|x1≥0} in the vector space R3. Moreover, Equations (8), (11) and (14) also show relevant geometrical relations between electromagnetic fields. This gives cos x i – sin y j Questions and unofficial answers 1993 M.pdf, Capitol University - Corrales Ext., Cagayan de Oro City • ENGINEERIN 2032560, Cagayan de Oro College - Carmen, Cagayan de Oro City • EDUCATION 101, Cagayan de Oro College - Carmen, Cagayan de Oro City • ECON MISC, Capitol University - Corrales Ext., Cagayan de Oro City • CME 09876, Cagayan de Oro College - Carmen, Cagayan de Oro City • FINANCE 073, Cagayan de Oro College - Carmen, Cagayan de Oro City • CAS 007. Problem 33P from Chapter 2: For two differentiable vector functions E and H, prove that ... Get solutions . The notion of electromagnetic field excludes direct interaction between charges. 4. which is always zero for all constants of the vector. The following topics are covered in the this book: (1) theory of the eigen- value problem, spheroidal harmonics, and spheroidal vector wave functions; (2) electromagnetic scattering by a conducting spheroid and a dielectric- 3. parallel to x-axis or y value is constant. 8. Therefore, the following two expressions are, in general, inequalities. I can add any gradient of a scalar function to it and the result is still a valid vector potential. d) 4xi + 2yj + 4zk Fig.3. Pilitron physics measured speed in Planck lengths per Planck time. An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. b) Curl Maxwell Equations's Previous Year Questions with solutions of Electromagnetics from GATE ECE subject wise and chapter wise with solutions. d) dV = dx dz Find the reason. c) Curl(Div V) c) Solenoidal, irrotational b) Divergence is unity Explanation: r = √(x2+y2+z2) = 3.74 This is analogous to B = (10sin θ/r + rcos2θ)i + j + (10cos θ/r –r sin θ cos θ)k a) Cartesian coordinate system Angle of separation is cos θ = 8/ (7.07 X 3) = 0.377 and θ = a) Low cut-off frequency Given A = 10j + 3k and B = 4j + 5k. a) (0.845, 1.462, 3.625) \$\begingroup\$ No, you cannot think of the vector potential as the "momentum per unit charge stored" because the vector potential is not unique. These forces vary in magnitude and direction with time and throughout space so that the theory is a heavy user of vector, differential, and integral calculus. d) (8.45, 2.462, 6.325) a) True c) 2.467i – j – 1.167k a) Distance Which of the following is not true? 8. operator in electromagnetics. View Answer, 4. Find Cartesian points at (-3,4,0) Cylindrical system is employed in waveguides. c) Unit normal vector a) True The vector’s magnitude and Electric elds are linear (obey superposition), vector elds. 9. Which of the following are not vector functions in Electromagnetics? b) Collinearly parallel State True/False. b) False 5. They have one commonality, i.e., they can be abstractly written as Lf= g (37.1.3) where L is the di erential operator which is linear, and f … 1. Accelerated charges produce electromagnetic waves. The authors then discuss the approximation of vector functions, and summarize the various classes of vector basis functions that have been used by the professional community. Naming tensor [mathematical expression not reproducible], from Equations (1) and (14) one can write [mathematical expression not reproducible] (26) Following the procedure given in , two conjugate vector bases can be introduced. b) |cross product| – |cross product| = 1 Rectangular waveguides dominate the circular waveguides. a) 1, ρ ,1 d) 1,0,0 1 + 1 = 3. While adapted from his popular and more extensive work, Field and Wave Electromagnetics, this text incorporates a number of innovative pedagogical features. The light vector (also known as the electric vector) is the reason for the optical effects due to an electromagnetic wave. 10. A B This is the plane of interest. The calculation of electric field in Thus it is charge in the space. Explanation: Stoke’ theorem is given by, ∫ A.dl = ∫ (Curl A). those functions in electromagnetic theory. Despite the success, there are at least three points that deserve attention. Adding B~indicates which particular plane we need. d) Depends on the constants of the vector The D- eld is independent of the material, whereas the E- eld is not. Characteristics of Electromagnetic Wave. a) True b) False Explanation: Since gradient is the maximum space rate of change of flux, it can be replaced by differential The vector normal to these points is a X b = -j – k. Vector Expressions in Rectangular Coordinates General Vector, B: Magnitude of B: Unit Vector in the Direction of B: 23. c) (6.325,73.57,3) A field has zero divergence and it has curls. a) (3.74, 105.5⁰, 56.13⁰) c) Curl A. d) Space coordinate system Explanation: By standard proof, Div (u X v) = v . d) 1 b) Fleming’s left hand rule d) Arc b) –i – j A charge is placed in a square container. Thus, B = 2.467i + j + 1.167k. d) Space system d) There is no non- vector functions in Electromagnetics Electromagnetic Waves Ranking: Rank yellow light, green light, x ray, FM radio wave, AM radio wave, infrared light as following. Electromagnetic Theory Questions and Answers – Vector Properties Course Hero is not sponsored or endorsed by any college or university. 9. b) Chord The gradient is a vector that points in the direction of the fastest change of ϕ, and its magnitude is equal to the rate of change in that direction. charge +Q, the electric field spreads in all 360 degrees. State True or False. b) Curl operation Explanation: Gradient of any scalar function may be defined as a vector. flux from a small closed surface as the volume shrinks to zero, the result will be directionless (scalar). It is fascinating to me that Maxwell's equations can so succinctly and elegantly express so many phenomena, from electric and magnetic interactions to light (electromagnetic … True/False. Explanation: Grad(t) = 2xy i + x2 j + ez k. On substituting p(1,5,-2), we get 10i + j + 0.135k. Explanation: Gradient of a function is zero implies slope is zero. Find whether the vectors are parallel, (-2,1,-1) and (0,3,1) to it. 4. Explanation: Grad (xi + yj + zk) = 1 + 1 + 1 = 3. Thus the answer is 40/6.4= 6.25. They are defined more precisely by a set of linear functionals which map functions onto the vector space . Electromagnetic waves do not require a medium to travel. Show Discussion. Explanation: When the divergence of a vector is zero, it is said to be solenoidal /divergent-free. d) Space coordinate system 1. Explanation: The equivalent cylindrical form is given by, S4={f(x)∈P4∣f(1)is an integer} in the vector space P4. I can add any gradient of a scalar function to it and the result is still a valid vector potential. a) i + j + k Explanation: All the coordinate systems are inter-convertible and all the vector operations are applicable a) Cross product The divergence of circular flow is d) Vector differential operator Find whether the vectors are parallel, (-2,1,-1) and (0,3,1) b) Collinearly parallel z = 3. For each set, give a reason why it is not a subspace. b) False a) Upwards The volume of a parallelepiped in Cartesian is on weak forms in the solution of vector electromagnetic ﬁeld prob-lems are for example given in . 8. c) -3i – 11j – 7k Spherical systems are employed in waveguides. c) (-i – j)/1.414 Figure 2: Vector B~selects a particular plane perpendicular to A~. c) i + 2j b) Downwards a) (7,64.62,71.57) An electromagnetics-based co-simulation of the linear net- ... where and are the vector basis functions used to expand ... Modiﬁed Nodal Analysis , which results in the following nonlinear system of equations: (9) where the unknown vector , in which is a vector Curl(u) – u . B)/|B|. This non-linear function (the fraction factor before W(t) 0) experiences a break even before reaching speed of light, Fig.3. Each of the following sets are not a subspace of the specified vector space. c) 3.197i + 2.393j + 4.472k 1. 5. They are related by: D = 0 r E where, 0 is the permittivity of free space, and r is the relative permittivity. b) Fleming’s left hand rule Explanation: Since the container possesses dimensions of a square (length, breadth and height), it can Thus all functions are vector only. Revision on Vector 1. 1. c) 67.8 d) A x (B x C) = vector value c) Not parallel Vector calculus: Differentiation and integration of vectors; Line, surface, and volume integrals; “del” operator; Gradient, divergence, and curl operations A deficiency in vector analysis in the study of electromagnetics is similar to a deficiency in algebra and calculus in the study of physics. Solutions of Electromagnetics from GATE ECE subject wise and Chapter wise with solutions of Electromagnetics from GATE ECE wise! Is said to be harmonic in nature, when curl is zero, method! Factor has to be zero draw D~ which also ends in the vector B=yi+ ( x+z ) located! Linear functionals which map functions onto the vector functional-di erence equation ( 1.2 ) the existence magnetic. ( x ) ∈P4∣f… figure 1: vector B~selects a particular plane perpendicular to A~ flow. Example given in [ 40 ] map functions onto the vector space of all polynomials of degree 4 or with. 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