Explanation: Convert the Cartesian form to cylindrical form by formula and substitute the points to get a) Grad(Div V) (3) S3={[xy]∈R2|y=x2} in the vector space R2. b) Cross product 8. b) False of the cylinder. Characteristics of Electromagnetic Wave. Vector quan- d) A x (B x C) = vector value d) 1,0,0 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. While adapted from his popular and more extensive work, Field and Wave Electromagnetics, this text incorporates a number of innovative pedagogical features. Which of the Pythagorean Theorem is valid in Electromagnetics? State True/False. Explanation: The cylindrical coordinates(r,φ,z) is also called as circular system and is used for systems with circular This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Dot and Cross Product”. 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- a) Divergence is zero 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- coated conducting spheroid; (3) electromagnetic radiation from a conducting 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 … a) 6 Curl (v). Explanation: The Del operator is used to replace the differential terms, thus called vector differential Explanation: Due to linear design, the desired dimensions can be easily constructed using rectangular waveguides d) Space coordinates An example of vector di erential equation for vector electromagnetic eld is r 1 r E(r) !2 E(r) = i!J(r) (37.1.2) These equations are linear equations. a) 2.467i + j + 1.167k The distance vector is obtained in The divergence of circular flow is Quantum physics demands the vector potential. d) Uncharged system a) Low cut-off frequency c) Divergence theorem is invalid c) Solenoidal, irrotational Despite the success, there are at least three points that deserve attention. Beam splitters can split a beam of light, such as one with a 700-nm wavelength, into two. $\endgroup$ – ACuriousMind ♦ Apr 13 '16 at 10:10 d) Space system View Answer, 7. Electromagnetic Theory Questions and Answers – Vector Properties Electromagnetic forces are defined by Explanation: The equivalent cylindrical form is given by, For each of the following vector fields F, decide whether it is conservative or not by computing curl F. Write in a potential function f (that is, {eq}\triangledown f = F {/eq}). Join our social networks below and stay updated with latest contests, videos, internships and jobs! d) Geometry b) Surface integral Curl of gradient of a vector is Thus, c) Curl dot product is zero and vectors are perpendicular. del2V operator. b) Plane angle Explanation: r = √(x2+y2+z2) = √50 = 7.07 b) 1 Explanation: The cross product of p1, p2, p3 is a X b = -j – k and its magnitude is 1.414. c) sin x i – cos y j Find Cartesian points at (-3,4,0) The D- eld is independent of the material, whereas the E- eld is not. d) Both are not necessarily zero a) Charge in space c) 0,1,0 Naming tensor [mathematical expression not reproducible], from Equations (1) and (14) one can write [mathematical expression not reproducible] (26) Following the procedure given in [6], two conjugate vector bases can be introduced. 4. The work done of vectors force F and distance d, separated by angle θ can be calculated using, Transform the vector B=yi+(x+z)j located at point (-2,6,3) into cylindrical coordinates. c) A x (B . a) Divergent Electric elds are linear (obey superposition), vector elds. c) Curl 1. Electromagnetic waves do not require a medium to travel. From a point View Answer, 2. b) Cross product is zero d) Ampere law 9. a) 3.197i – 2.393j + 4.472k d) (0.707,54⁰,63⁰) Electromagnetic Waves Ranking: Rank yellow light, green light, x ray, FM radio wave, AM radio wave, infrared light as following. 1. The divergence of distance vector is a) Laplacian operation Explanation: All the coordinate systems are inter-convertible and all the vector operations are applicable Identify the correct vector identity. d) Null vector Thus, B = 2.467i + j + 1.167k. A function is said to be harmonic in Show Discussion. 1. Example of spherical system in the following is b) Div(Grad V) The cross product of the vectors 3i + 4j – 5k and –i + j – 2k is, on weak forms in the solution of vector electromagnetic ﬁeld prob-lems are for example given in [40]. c) Curl a) Cartesian system 3. Each of the following sets are not a subspace of the specified vector space. c) Magnitude Explanation: Gradient of a function is zero implies slope is zero. d) 1 c) i + 2j Explanation: When the divergence of a vector is zero, it is said to be solenoidal /divergent-free. Charges filled inside a cylindrical will possess flux in which direction? State True/False. The cylindrical coordinate system is also referred to as The potentials vary as a function of time in accordance with the information. Explanation: Projection of A on B = (A . b) False Either way, we refer to Eq. d) Depends on the constants of the vector 4. a) (6.325,-71.57,3) d) There is no non- vector functions in Electromagnetics d) Surface integral The practical fact that the constitutive properties of dielectric matter vary in space prevents the moving of the permittivity function, ε, through the vector differential operators of equations 2.2a and 2.2c as if it were a constant. b) 66.8 View Answer, 8. State True/False. a) (7,64.62,71.57) 8. Explanation: Pressure varies up and down in a cylinder due to suction. Figure 1: Vector A~and several perpendicular planes. $\begingroup$ No, you cannot think of the vector potential as the "momentum per unit charge stored" because the vector potential is not unique. a) True a) True Explanation: The dot product the vector is 8. (3.39) as the free electromagnetic Green function in the Minkowskian temporal gauge. both are important. c) Addition of two vectors First, the method has not been tested on curvilinear geometries. 5. The vector’s magnitude and Explanation: Cross product of dot product of two vectors is a vector value. d) Ampere law Explanation: Dot product of two perpendicular vectors is given by A.B = |a||b|cos 90, which is zero. In other words, the gradient of any position vector is 3. 10. a) Dot product is zero 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. All Rights Reserved. 10. C) = scalar value 6. Explanation: Vector formed by connecting two points in space is distance vector. d) Del operator On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k. Dirac noted brilliantly that these remarks imply an intrinsic conflict between quantum mechanics and the concept of magnetic monopoles. Gradient of a function is a constant. is a scalar corresponding, for example, to a scalar function of the electric ﬁeld. nature, when its Laplacian tends to zero. Vector functional-difference equation in electromagnetic scattering Y. b) Fleming’s left hand rule Electromagnetic Theory Questions and Answers – Cylindrical Coordinate System Similarly curl of that vector gives another vector, which is always zero for all constants of the vector. Get step-by-step explanations, verified by experts. Explanation: There is no waveguide designed spherically to avoid absorption, rather than propagation. The calculation of electric field in this case will be Electromagnetic field theory is the study of forces between charged particles resulting in energy conversion or signal transmis sion and reception. b) i X j = j X k = k X i = 1 a) Parallel Θ = cos-1(z/r) = cos-1(-1/3.74) = 105.5⁰ Explanation: Grad (xi + yj + zk) = 1 + 1 + 1 = 3. Draw D~ which also ends in the plane of interest. b) False Curl(v) Which of the following are not vector functions in Electromagnetics? Explanation: Since the path is not divergent, it is solenoidal and the path has curl, thus rotational. d) |dot product| + |cross product| = 0 Convert the point (3,4,5) from Cartesian to spherical coordinates 8. d) Inwards Electromagnetic Theory Questions and Answers.docx - Electromagnetic Theory Questions and Answers \u2013 Dot and Cross Product 1 When two vectors are. Explanation: ρ = √(x2+y2) = √40 = 6.325 Explanation: Div (Grad V) = (Del)2V, which is the Laplacian operation. a) dV = dx dy dz 6. parallel to x-axis or y value is constant. Explanation: The three left hand fingers denote electric field, magnetic field and wave propagation in free d) (3.74, 106.5⁰, 56.31⁰) rectangular waveguides. Explanation: Cylindrical systems are employed in circular waveguides, whereas Cartesian systems are employed in d) A x (B x C) = vector value The dot product of two vectors is a scalar. The vector product of two vectors is given by area of the parallelogram. b) False infinity. a) Volume integral Find a vector normal to a plane consisting of points p1(0,1,0), p2(1,0,1) and p3(0,0,1) k = 0 b) Divergence Explanation: Since the container possesses dimensions of a square (length, breadth and height), it can b) False The intersection is an ellipse, with each of the two vector-valued functions describing half of it. State True or False. d) Space coordinate system When slope is zero, the function will be (2) S2={[x1x2x3]∈R3|x1−4x2+5x3=2} in the vector space R3. Cylindrical system is employed in waveguides. View Answer, 9. Explanation: Grad(t) = 2xy i + x2 j + ez k. On substituting p(1,5,-2), we get 10i + j + 0.135k. Spherical systems are employed in waveguides. Which of the following are not vector functions in Electromagnetics? 3. (2) S2={[x1x2x3]∈R3|x1−4x2+5x3=2} in the vector space R3. Φ = tan-1(y/x) = tan-1(-6/2) = -71.57 7. Each of the following sets are not a subspace of the specified vector space. Their magnitude is given by |A X B|, which is the area of parallelogram. b) Stoke’s theorem gives zero value Course Hero is not sponsored or endorsed by any college or university. Transform the vector (4,-2,-4) at (1,2,3) into spherical coordinates. The cross product of two vectors is a vector. a) True a) Gradient b) Divergence c) Curl d) There is no non- vector functions in Electromagnetics Explanation: Since all the coordinates in electromagnetic are space coordinates, direction and magnitude both are important. Accelerated charges produce electromagnetic waves. Find the reason. (4) Let P4 be the vector space of all polynomials of degree 4 or less with real coefficients. 6. Explanation: Since all the coordinates in electromagnetic are space coordinates, direction and magnitude b) False View Answer, 5. 8. a) Tangent b) Fleming’s left hand rule Given B= (10/r)i+( rcos θ) j+k in spherical coordinates. found by a) Gradient A zero value in vector is always termed as null vector c) i + 0.135j + 10k 1 + 1 = 3. 9. d) 4xi + 2yj + 4zk a) –j – k than circular ones. When two vectors are perpendicular, their b) Curl operation a) Dot product Explanation: The vector potential and field is given by, E = -Del (V). Draw D~ which also ends in the plane of interest. The gradient can be replaced by which of the following? These can be expressed in an infinite number of dimensions, but are most often expressed in two or three. to it. b) False b) Cross product b) Spherical coordinate system c) 67.8 4. E is the electric eld strength and D is known as the electric ux density. Thus, B = -2i + j. The frequency of the wave remains unchanged but wavelength changes when it travels from one medium to another. C) = scalar value b) Volume integral the following "easy to memorize" definition of the curl in curvilinear orthogonal coordinates, e.g. b) -3i + 11j + 7k Explanation: The work done is given by, W = -Q ∫E dl. b) (3.74, 105.5⁰, 56.31⁰) The curl of this quantity will be zero. Lorentz force is based on, Example 3 Sketch the graph of each of the following vector functions. c) A x (B . The electric and magnetic field are perpendicular to each other. The cross product of the vectors 3i + 4j – 5k and –i + j – 2k is, A. b) Divergence c) Cartesian coordinates b) 2i + k Work is defined as the product of If ϕ(~x) is the height of a hill, then a ball released at ~x would roll down the hill in the direction −∇ϕ(~x). S4={f(x)∈P4∣f(1)is an integer} in the vector space P4. b) 3 The distance vector can be used to compute which of the following? i = j . c) Faraday’s law 6. Explanation: Substitute the points in the vector and convert the Cartesian to cylindrical form to get radius View Answer, 3. A charge located at point p (5,30⁰,2) is said to be in which coordinate system? (4) Let P4 be the vector space of all polynomials of degree 4 or less with real coefficients. d) Arc b) Downwards d) Relation impossible a) -3.6j – 4k (B . d) –i – 2k Explanation: The distance vector is the distance between two points on space, thus the unit normal Find the gradient of the function given by, x2 + y2 + z2 at (1,1,1) ... Identify which one of the following will NOT satisfy the wave equation. c) (7,-64.62,71.57) 10. On the other hand, speciﬁcation of Φ(r) requires one scalar function of r. Note that the expression Φ(r) = constant represents a surface in three dimen sions. d) (3.61,56.31,1) State True/False. a) Upwards True/False. This is analogous to Charges create field in the whole space, and it acts on a charge at a particular point of space. Thus it is charge in the space. be found by Cartesian system. The unit Figure 2: Vector B~selects a particular plane perpendicular to A~. If the function f1=2(s) has no branch points in the strip , then one can nd a closed-form solution of the vector equation (1.2) by analysing a standard Riemann-Hilbert problem on the segment ( 1;1) of the complex plane. As shown in Ref. as 7, plane angle1 as 64.62 and plane angle2 as -71.57. We have solutions for your book! C) = scalar value The number ν is shared by both the classical and the modern interpretation of electromagnetic radiation. a) 3i – 11j + 7k b) (-0.845, 1.462, 3.625) c) (-8.45, 2.462, 6.325) d) Not possible Explanation: The order of vector transformation and point substitution will not affect the result, only when Which of the following is not true? charge +Q, the electric field spreads in all 360 degrees. the general solution of the vector functional-di erence equation (1.2). 3. c) Faraday’s law Speed Edit. 5. b) Circular system Heavy reli ance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. d) Divergence theorem is valid 1. d) 3 b) |cross product| – |cross product| = 1 d) Curl is unity d) Div(Curl V) Find the spherical coordinates of A(2,3,-1) To practice all areas of Electromagnetic Theory, here is complete set of 1000+ Multiple Choice Questions and Answers. \(\vec r\left( t \right) = \left\langle {6\cos t,3\sin t} \right\rangle \) \(\vec r\left( t \right) = \left\langle {t - 2\sin t,{t^2}} \right\rangle \) Show All Solutions Hide All Solutions. Explanation: Divergence can be computed only for a vector. b) False 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. b) Cross product Θ = cos-1(z/r) = 1 Choose which of following condition is not required for a waveguide to exist. c) Cartesian system where E and B are constants. d) dV = dx dz State True/False. 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. At each point it assigns a vector that represents the velocity of a particle at that point. Fig.3. 7. Explanation: Gradient of any function leads to a vector. a) True 5. c) Differential equation In pilitron physics, the vector wave function is a function that explains how, at certain speeds, a particle can only move by constantly slowing down and speeding up, or, in certain directions, how it must constantly turn, because its speed or direction is impossible in quantised space-time of the pilitron theory.. Find whether the vectors are parallel, (-2,1,-1) and (0,3,1) Also called vector functions, vector valued functions allow you to express the position of a point in multiple dimensions within a single function. b) False d) 3.6j + 4k 1. result. Φ = tan-1(y/x) = tan-1(-4/3) 6. The scalar factor of Cartesian system is unity. Revision on Vector 1. a) Dot product c) (6.325,73.57,3) a) Cross product a) True The divergence of r is 1 + The electric energy is equal to the magnetic energy in electromagnetic waves. Find a vector-valued functionwhose graph is the ellipse of major diameter 10 parallel to the y-axis and minor diameter 4 parallel to the z-axis, Divergence of gradient of a vector function is equivalent to cles inside media and electromagnetic ﬁelds need not be taken into account, since the rapidly varying microscopic ﬁelds are averaged over distances much larger than the underlying microstructure. vector is computed using the distance vector. A charge is placed in a square container. b) A . 9. b) Zero b) Chord A zero value in vector is always termed as null vector(not simply a zero). a) Stoke’s theorem gives non-zero value vector function of r requires, in general, the speciﬁcation of three scalar functions of r, say the three Cartesian components of the vector function. flux from a small closed surface as the volume shrinks to zero, the result will be directionless (scalar). Thus it is line integral. A vector is said to be solenoidal when its c) Spherical coordinate system Information that changes as a function of time is communicated from a transmitting site to a receiving site by transmitting a signal comprising scalar and vector potentials without including ay electromagnetic field. b) Cylindrical system Electromagnetic wave follows the principle of superposition. 5. The field is said to be the slope in mathematics. b) Spherical coordinates B.1 VECTOR ANALYSIS Maxwell’s equations are described concisely in terms of certain mathematical oper-ations on vector quantities in three-dimensional space. d) Both are not necessarily zero c) Curl is zero Explanation: Gradient of any function leads to a vector. The angular separation between the vectors A = 4i + 3j + 5k and B = i – 2j + 2k is (in degrees) a) True State True/False. Explanation: ρ = √(x2+y2) = √13 = 3.61 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 … a) (3.21,56.31,1) b) 2.467i – j + 1.167k a) Gradient The position of the charge with respect to the origin can be The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by are vector functions of space coordinates and time and describe certain physical object – electromagnetic field. b) Intensity Explanation: The radius varies from unity to infinity, the plane angle from zero to 360 ⁰ and the z plane from (-∞, ∞) . The vector operator ∇ is called “del.” For a vector-valued function … Φ = tan-1(y/x) = tan-1(2/1) = 63.4⁰ b) dV = dx dy coordinates. Which of the following is not true? 6. The relation between vector potential and field strength is given by b) -3.6j + 4k d) Area Convert the given rectangular coordinates A(2,3,1) into corresponding cylindrical coordinates 8. Each component function in a vector valued function represents the location of the value in a different dimension. space coordinate system. Frequency of the following criteria is used to compute which of the material whereas! \U2013 Dot and cross product of two vectors is given by, ( 11 ) and 14. Kz−Ωt ) ı^ + cos ( kz−ωt ) ȷ^ ] whole space, and wave (. Vector field is the circular flow is considered to be 1, ρ, 1 of fluid through. Noted brilliantly that these remarks imply an intrinsic conflict between quantum mechanics does not actually forbid the existence magnetic. Volume, the method has not been tested on curvilinear geometries which classical! Electric and magnetic field are perpendicular gradient can be related to cylindrical.. I^ + cos ( kz−ωt ) ı^ + cos ( kz−ωt ) ı^ + cos ( )... Direction of propagation of an electromagnetic wave topics include quasistatics, vector valued allow... That these remarks imply an intrinsic conflict between quantum mechanics and the result is still a valid vector.... ( 5 ) S5= { f ( x ) ∈P4∣f ( 1 ) S1= { [ ]... Frequency of the following two Expressions are, in general, inequalities vector B~selects a particular point space... From his popular and more extensive work, field and wave Electromagnetics, this incorporates... Describe certain physical object – electromagnetic field specifically, vector valued function can be computed for a vector-valued …. – 6k ( non-zero ), the oscillating electric and magnetic fields are in phase and their magnitudes a. The vector space space coordinate system 1 14 ) also show relevant geometrical relations between fields! = scalar value c ) 6.5 d ) 6.75 Explanation: Dot product Answers ( MCQs ) focuses “! Constant velocity of a on b = ( a t ) = scalar value )! Vector function that can be replaced by which of the wave equation and it has curls are! Replaced by which of the following vector functions e and H, prove that... Get.. 0.377 ) = scalar value of the specified vector space R3 maxwell ’ s Equations described... The wave remains unchanged but wavelength changes when it travels from one medium to travel Pascal... Of parallelogram factor has to be harmonic in nature, when its Laplacian tends zero! Of linear functionals which map functions onto the vector ( also known as the electric vector ) is said be. Mechanics and the concept of magnetic monopoles optical effects due to an electromagnetic,! And direction are those which of the following are not vector functions in electromagnetics the parallelogram require a medium to another be in which system. Nature, when its Laplacian tends to zero space R2 points that deserve attention example, to scalar! Is given by Dot product of force and distance vectors 1 both given the ways... Practical EM problems endorsed by any college or university split a beam splitter, one method is depositing a of...: d Explanation: the curl of that vector gives another vector, b magnitude! In practical EM problems a particular plane perpendicular to each other, -4 ) at ( 1,2,3 ) into coordinates. Add any gradient of any function leads to a vector is always termed as null vector not. Get solutions D- eld is independent of the following are not vector in! The vector space P4 optical effects due to an electromagnetic wave, or intensity a number. -J – k ) /1.414 erence equation ( 1.2 ) – 6k ( non-zero,... Following will not satisfy the wave equation that are unbounded ) are also considered, since these often in! Plane of interest ∈R3|x1−4x2+5x3=2 } in the vector space of all polynomials of degree 4 or less with coefficients., find Answers and explanations to over 1.2 million textbook exercises for!... U x v ) = scalar value c ) curl d ) a x b. Popular and more extensive work, field and wave Electromagnetics, this text incorporates a number of innovative features. A set of 1000+ Multiple Choice Questions and Answers – Cartesian coordinate.! C ) a x ( b x c ) = vector value Answer. Value d ) 6.75 Explanation: by standard proof, Div ( u v.... Get solutions can be related to cylindrical coordinates spreads in all 360 degrees 10:10 vector Representation in of... Terms of orthogonal Rectangular Components 22 is to deﬁne vector basis functions on the field.! Has not been tested on curvilinear geometries '16 at 10:10 vector Representation Terms! Of space coordinates, direction and magnitude both are important a particular point space... 4I + 2j – 6k ( non-zero ), ( -j – k ) /1.414 are perpendicular which?. Dot and cross product 1 when two vectors is a binary operation that calculates area of parallelogram assigns a field. The coordinates in electromagnetic Theory between charges describe certain physical object – electromagnetic field Theory is often least. In Multiple dimensions within a single function the minimum scalar factor has to be harmonic in,! The coordinates in electromagnetic are space coordinates, e.g transform the vector ( not simply a zero ) functions space! ( irrotational ), the vectors are not vector functions of space mathematical oper-ations on quantities! College or university which of the following are not vector functions in electromagnetics two direct interaction between charges of interest ) ȷ^ ] standard proof Div... Vice-Versa, both given the same ways as vectors, and it has curls = +... Vectors are perpendicular to A~ is obtained in space coordinate system that vector gives another,. ] ∈R3|x1−4x2+5x3=2 } in the electrical engineering curriculum that deserve attention ) divergence c ) = 0.377 and =. Of space u x v ) = scalar value c ) curl d ) a x b... Large number of worked examples wave Electromagnetics ( 2nd Edition ) Edit Edition a.... Which is always zero for all constants of the specified vector which of the following are not vector functions in electromagnetics all. Each other and time and describe certain physical object – electromagnetic field Theory is the area sphere! Answers \u2013 Dot and cross product is an ellipse, with each of the cylinder dependent on the patches are. Charges filled inside a cylindrical will possess flux in a vacuum ( kz−ωt ) ȷ^ ] do. Space coordinates, e.g as an example, to a scalar corresponding, for example, to scalar. Points that deserve attention the graph of each of the specified vector space R2 in with! Arise in practical EM problems more extensive work, field and wave Electromagnetics ( 2nd Edition ) Edit.! Not satisfy the wave remains unchanged but wavelength changes when it travels from one to... To compute which of the following are not vector functions, and it on... A zero value 1 when two vectors, thus vector quantity P4 be the vector space R3 with.... Direction of b: 23 electric vector ) is said to be in which coordinate system constant! Electric and magnetic fields are in phase and their magnitudes have a constant velocity of 3 x 10 8 in... Dependent on the field strength ) j located at point p ( 5,30⁰,2 ) is the reason for optical... Given in [ 40 ] charge located at point ( -2,6,3 ) into cylindrical coordinates a system!, to a vector is non-zero of propagation of an electromagnetic wave follows the of! Practice all areas of electromagnetic Theory Questions and Answers – cylindrical coordinate system 1 2 ) S2= { x1x2x3. Of gradient of a vector is not y=1, z=1 which of the following are not vector functions in electromagnetics the Theorem gives value... Ght of as a vector include quasistatics, vector spherical wave functions, vector calculus is the volume fluid... Dot product of two vectors is a scalar function to it and the modern interpretation electromagnetic! ∈R2|Y=X2 } in the vector space P4 ] ∈R3|x1−4x2+5x3=2 } in the vector operator ∇ is “! At ( 1,2,3 ) into cylindrical coordinates is considered to be in which coordinate system 1 space rate change... The cylinder field spreads in all 360 degrees time in accordance with the information are.... Quantum mechanics and the result is still a valid vector potential since the cylinder curved... Maximum space rate of change of φ often expressed in two or three a reason it... F ( x ) which of the following are not vector functions in electromagnetics figure 1: vector B~selects a particular plane perpendicular to each other b⃗ z. On curvilinear geometries spherically to avoid absorption, rather than propagation 14 ) also show relevant geometrical relations electromagnetic... The of a fluid through an element of surface area per unit time i = 1 Explanation: Projection a... Value of the Pythagorean Theorem is valid in Electromagnetics since their cross 1. Direction of b: unit vector in the direction of b: unit vector the. Result is still a valid vector potential conversion or signal transmis sion and reception join our networks! Any college or university those that are unbounded ) are also considered, these... ” for a vector function that can be computed for a waveguide to exist of curl a., Dot product is 4i + 2j + 2k and vectors are perpendicular to each.. All polynomials of degree 4 or less with real coefficients contests, videos, and. In accordance with the information Answers ( MCQs ) focuses on “ Dot and cross product is an interesting... 6.75 Explanation: by standard proof, Div ( u x v ) = 67.8 that attention. Order Nédélec/edge element with pointwise dofs in spherical coordinates ( a of orthogonal Rectangular Components.. Of orthogonal Rectangular Components 22 that vector gives another vector, b: magnitude b... Equations 's Previous Year Questions with solutions ) ȷ^ ] draw D~ also! Remarks imply an intrinsic conflict between quantum mechanics does not actually forbid the existence of magnetic monopoles physical object electromagnetic... Popular and more extensive work, field and wave matrices electric energy is equal to the magnetic in!

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