27 + Interview Questions in Vector Analysis And Applications in Electromagnetic Theory Page 1 InterviewSolution

1.	A field has zero divergence and it has curls. The field is said to be(a) Divergent, rotational(b) Solenoidal, rotational(c) Solenoidal, irrotational(d) Divergent, irrotationalI got this question during an online interview.My doubt stems from Vector Properties in chapter Vector Analysis and Applications of Electromagnetic Theory
Answer» RIGHT OPTION is (b) Solenoidal, rotational Explanation: Since the path is not DIVERGENT, it is solenoidal and the path has curl, thus rotational.

Discussion

2.	The magnetic field intensity is said to be(a) Divergent(b) Curl free(c) Solenoidal(d) RotationalI have been asked this question in an interview for job.Enquiry is from Vector Properties in section Vector Analysis and Applications of Electromagnetic Theory
Answer» The correct CHOICE is (C) Solenoidal To ELABORATE: By Maxwell’s equation, the magnetic field intensity is solenoidal DUE to the absence of magnetic monopoles.

Discussion

3.	A vector is said to be solenoidal when its(a) Divergence is zero(b) Divergence is unity(c) Curl is zero(d) Curl is unityI have been asked this question in an interview for job.I'm obligated to ask this question of Vector Properties in section Vector Analysis and Applications of Electromagnetic Theory
Answer» The CORRECT option is (a) DIVERGENCE is ZERO To EXPLAIN I would say: When the divergence of a vector is zero, it is said to be solenoidal /divergent-free.

Discussion

4.	Identify the correct vector identity.(a) i . i = j . j = k . k = 0(b) i X j = j X k = k X i = 1(c) Div (u X v) = v . Curl(u) – u . Curl(v)(d) i . j = j . k = k . i = 1I got this question during an online exam.My question is from Vector Properties in division Vector Analysis and Applications of Electromagnetic Theory
Answer» Right CHOICE is (c) Div (u X v) = v . Curl(u) – u . Curl(v) The EXPLANATION is: By STANDARD proof, Div (u X v) = v . Curl(u) – u . Curl (v).

Discussion

5.	The curl of gradient of a vector is non-zero. State True or False.(a) True(b) FalseThis question was addressed to me during an online exam.My doubt is from Vector Properties in section Vector Analysis and Applications of Electromagnetic Theory
Answer» The CORRECT option is (B) False Easiest explanation: The differential FLOW of flux in a VECTOR is a vector. The curl of this quantity will be zero.

Discussion

6.	The divergence of curl of a vector is zero. State True or False.(a) True(b) FalseThe question was asked in final exam.I want to ask this question from Vector Properties topic in portion Vector Analysis and Applications of Electromagnetic Theory
Answer» RIGHT answer is (a) True To explain: The CURL of a vector is the circular FLOW of flux. The divergence of circular flow is CONSIDERED to be zero.

Discussion

7.	The Laplacian operator is actually(a) Grad(Div V)(b) Div(Grad V)(c) Curl(Div V)(d) Div(Curl V)I have been asked this question in an online interview.My enquiry is from Vector Properties in portion Vector Analysis and Applications of Electromagnetic Theory
Answer» The CORRECT option is (b) Div(Grad V) EASIEST explanation: The Laplacian operator is the DIVERGENCE of GRADIENT of a VECTOR, which is also called del^2V operator.

Discussion

8.	The del operator is called as(a) Gradient(b) Curl(c) Divergence(d) Vector differential operatorThis question was posed to me in an internship interview.This key question is from Vector Properties topic in portion Vector Analysis and Applications of Electromagnetic Theory
Answer» Correct OPTION is (d) Vector differential operator Easy EXPLANATION: The DEL operator is used to REPLACE the differential terms, thus called vector differential operator in ELECTROMAGNETICS.

Discussion

9.	The relation between vector potential and field strength is given by(a) Gradient(b) Divergence(c) Curl(d) Del operatorThis question was addressed to me in a job interview.My doubt stems from Vector Properties topic in division Vector Analysis and Applications of Electromagnetic Theory
Answer» Right answer is (a) Gradient Easy EXPLANATION: The VECTOR potential and FIELD is given by, E = -Del (V).

Discussion

10.	Find the projection of A on B. Given A = 10j + 3k and B = 4j + 5k.(a) 6(b) 6.25(c) 6.5(d) 6.75I have been asked this question in a job interview.This is a very interesting question from Position and Distance Vectors in portion Vector Analysis and Applications of Electromagnetic Theory
Answer» The CORRECT option is (B) 6.25 For EXPLANATION: PROJECTION of A on B = (A . B)/\|B\|. Thus the answer is 40/6.4= 6.25.

Discussion

11.	Distance and position vectors rely on field strength. State True/False.(a) True(b) FalseI have been asked this question in exam.My question is based upon Position and Distance Vectors topic in portion Vector Analysis and Applications of Electromagnetic Theory
Answer» The correct ANSWER is (a) True The best I can explain: Position or distance of a VECTOR is dependent on the FIELD strength.

Discussion

12.	The distance vector can be used to compute which of the following?(a) Dot product(b) Cross product(c) Unit normal vector(d) AreaI have been asked this question in unit test.My enquiry is from Position and Distance Vectors in chapter Vector Analysis and Applications of Electromagnetic Theory
Answer» Right option is (c) Unit normal vector The explanation: The DISTANCE vector is the distance between TWO points on SPACE, thus the unit normal vector is computed using the distance vector.

Discussion

13.	The work-electric field relation is given by(a) Volume integral(b) Surface integral(c) Line integral(d) Relation impossibleThe question was asked in quiz.I need to ask this question from Position and Distance Vectors topic in portion Vector Analysis and Applications of Electromagnetic Theory
Answer» The correct choice is (C) Line integral To EXPLAIN I would say: The WORK DONE is given by, W = -Q ∫E dl. Thus it is line integral.

Discussion

14.	The polar form of Cartesian coordinates is(a) Circular coordinates(b) Spherical coordinates(c) Cartesian coordinates(d) Space coordinatesI have been asked this question in an international level competition.The above asked question is from Position and Distance Vectors in division Vector Analysis and Applications of Electromagnetic Theory
Answer» Right ANSWER is (a) CIRCULAR coordinates Explanation: The radius in the polar coordinates is the PYTHAGOREAN triplet-(R,x,y).Thus it is the circular coordinates.

Discussion

15.	Find a vector normal to a plane consisting of points p1(0,1,0), p2(1,0,1) and p3(0,0,1)(a) –j – k(b) –i – j(c) –i – k(d) –i – j – kThe question was posed to me by my college director while I was bunking the class.This is a very interesting question from Position and Distance Vectors topic in chapter Vector Analysis and Applications of Electromagnetic Theory
Answer» CORRECT answer is (a) –j – k The explanation is: Distance vector from p1 and P2 is a = i – j + k. Distance vector from p1 and p3 is B = –j + k. The vector NORMAL to these points is a X b = -j – k.

Discussion

16.	The unit vector to the points p1(0,1,0), p2(1,0,1), p3(0,0,1) is(a) (-j – k)/1.414(b) (-i – k)/1.414(c) (-i – j)/1.414(d) (-i – j – k)/1.414The question was posed to me in an online interview.The above asked question is from Position and Distance Vectors topic in chapter Vector Analysis and Applications of Electromagnetic Theory
Answer» Right choice is (a) (-j – K)/1.414 To explain: The CROSS product of p1, P2, P3 is a X b = -j – k and its magnitude is 1.414. The unit normal VECTOR is given by, (-j – k)/1.414.

Discussion

17.	The distance vector is obtained in(a) Cartesian coordinate system(b) Spherical coordinate system(c) Circular coordinate system(d) Space coordinate systemI got this question at a job interview.The question is from Position and Distance Vectors topic in section Vector Analysis and Applications of Electromagnetic Theory
Answer» Correct ANSWER is (d) SPACE coordinate system The best explanation: VECTOR formed by CONNECTING two points in space is distance vector. Thus, it is OBTAINED in space coordinate system.

Discussion

18.	The divergence of distance vector is(a) 0(b) 3(c) 2(d) 1I got this question in final exam.The doubt is from Position and Distance Vectors topic in section Vector Analysis and Applications of Electromagnetic Theory
Answer» CORRECT answer is (b) 3 Easy explanation: The distance VECTOR of any coordinates is GENERALLY, r = xi + YJ + zk. The divergence of r is 1 + 1 + 1 = 3.

Discussion

19.	Lorentz force is based on,(a) Dot product(b) Cross product(c) Both dot and cross product(d) Independent of bothI got this question by my college director while I was bunking the class.My doubt stems from Dot and Cross Product topic in division Vector Analysis and Applications of Electromagnetic Theory
Answer» Correct choice is (b) Cross PRODUCT To explain I would SAY: Lorentz FORCE is given by, F = q (v X B).Thus cross product is the answer.

Discussion

20.	Electromagnetic forces are defined by(a) Fleming’s right hand rule(b) Fleming’s left hand rule(c) Faraday’s law(d) Ampere lawI had been asked this question in an online quiz.I'm obligated to ask this question of Dot and Cross Product topic in chapter Vector Analysis and Applications of Electromagnetic Theory
Answer» Right OPTION is (b) Fleming’s left hand rule The best I can explain: The three left hand fingers denote electric FIELD, magnetic field and WAVE propagation in free space, ANALOGOUS to force, magnetic field and current RESPECTIVELY in any conductor.

Discussion

21.	Which of the Pythagorean Theorem is valid in Electromagnetics?(a) \|dot product\| + \|dot product\| = 1(b) \|cross product\| – \|cross product\| = 1(c) \|dot product\|^2 + \|cross product\|^2 = 1(d) \|dot product\| + \|cross product\| = 0I had been asked this question during an interview for a job.The question is from Dot and Cross Product in chapter Vector Analysis and Applications of Electromagnetic Theory
Answer» Correct choice is (c) \|dot product\|^2 + \|cross product\|^2 = 1 To explain I would say: Option \|dot product\|^2 + \|cross product\|^2 = 1 GIVES \|cos\|^2 + \|sin\|^2 = 1, which is the right ANSWER.

Discussion

22.	The dot product of two vectors is a scalar. The cross product of two vectors is a vector. State True/False.(a) True(b) FalseThe question was asked in homework.I'm obligated to ask this question of Dot and Cross Product in division Vector Analysis and Applications of Electromagnetic Theory
Answer» Correct OPTION is (a) True To explain: Dot product is an algebraic operation that takes two EQUAL length sequences and returns a scalar. CROSS product is a BINARY operation that calculates area of two vectors, thus vector quantity.

Discussion

23.	When two vectors are perpendicular, their(a) Dot product is zero(b) Cross product is zero(c) Both are zero(d) Both are not necessarily zeroThe question was asked during an interview for a job.I want to ask this question from Dot and Cross Product in division Vector Analysis and Applications of Electromagnetic Theory
Answer» The CORRECT answer is (a) DOT product is zero For explanation: Dot product of two perpendicular vectors is GIVEN by A.B = \|a\|\|b\|cos 90, which is zero. THUS, dot product is zero and vectors are perpendicular.

Discussion

24.	Find whether the vectors are parallel, (-2,1,-1) and (0,3,1)(a) Parallel(b) Collinearly parallel(c) Not parallel(d) Data insufficientThis question was posed to me during an internship interview.Question is from Dot and Cross Product in section Vector Analysis and Applications of Electromagnetic Theory
Answer» The correct answer is (C) Not parallel For explanation I would say: Two vectors are parallel when their CROSS PRODUCT is ZERO. Since their cross product is 4i + 2j – 6K (non-zero), the vectors are not parallel.

Discussion

25.	Which of the following are not vector functions in Electromagnetics?(a) Gradient(b) Divergence(c) Curl(d) There is no non- vector functions in ElectromagneticsThis question was posed to me in an internship interview.My doubt is from Dot and Cross Product in section Vector Analysis and Applications of Electromagnetic Theory
Answer» The correct ANSWER is (d) There is no non- vector functions in Electromagnetics Easy EXPLANATION: Since all the COORDINATES in electromagnetic are SPACE coordinates, direction and magnitude both are IMPORTANT. Thus all functions are vector only.

Discussion

26.	The work done of vectors force F and distance d, separated by angle θ can be calculated using,(a) Cross product(b) Dot product(c) Addition of two vectors(d) Cannot be calculatedThe question was asked in my homework.My question is taken from Dot and Cross Product in portion Vector Analysis and Applications of Electromagnetic Theory
Answer» The correct CHOICE is (b) DOT product Easiest explanation: Force is a vector quantity, whereas distance is scalar. WORK is DEFINED as the product of force and distance, which is given by dot product.

Discussion

27.	The cross product of the vectors 3i + 4j – 5k and –i + j – 2k is,(a) 3i – 11j + 7k(b) -3i + 11j + 7k(c) -3i – 11j – 7k(d) -3i + 11j – 7kThis question was posed to me by my college professor while I was bunking the class.This question is from Dot and Cross Product in portion Vector Analysis and Applications of Electromagnetic Theory
Answer» Correct option is (b) -3i + 11j + 7k Easiest explanation: Cross product of two vectors is, A X B = (A2b3 – b2a3)i – (a1b3 – B1a3)J + (a1b2 – b1a2)K. Using the formula, the answer can be calculated.

Discussion

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The magnetic field intensity is said to be(a) Divergent(b) Curl free(c) Solenoidal(d) RotationalI have been asked this question in an interview for job.Enquiry is from Vector Properties in section Vector Analysis and Applications of Electromagnetic Theory

The curl of gradient of a vector is non-zero. State True or False.(a) True(b) FalseThis question was addressed to me during an online exam.My doubt is from Vector Properties in section Vector Analysis and Applications of Electromagnetic Theory

The divergence of curl of a vector is zero. State True or False.(a) True(b) FalseThe question was asked in final exam.I want to ask this question from Vector Properties topic in portion Vector Analysis and Applications of Electromagnetic Theory

The Laplacian operator is actually(a) Grad(Div V)(b) Div(Grad V)(c) Curl(Div V)(d) Div(Curl V)I have been asked this question in an online interview.My enquiry is from Vector Properties in portion Vector Analysis and Applications of Electromagnetic Theory

The del operator is called as(a) Gradient(b) Curl(c) Divergence(d) Vector differential operatorThis question was posed to me in an internship interview.This key question is from Vector Properties topic in portion Vector Analysis and Applications of Electromagnetic Theory

The relation between vector potential and field strength is given by(a) Gradient(b) Divergence(c) Curl(d) Del operatorThis question was addressed to me in a job interview.My doubt stems from Vector Properties topic in division Vector Analysis and Applications of Electromagnetic Theory

Find the projection of A on B. Given A = 10j + 3k and B = 4j + 5k.(a) 6(b) 6.25(c) 6.5(d) 6.75I have been asked this question in a job interview.This is a very interesting question from Position and Distance Vectors in portion Vector Analysis and Applications of Electromagnetic Theory

Distance and position vectors rely on field strength. State True/False.(a) True(b) FalseI have been asked this question in exam.My question is based upon Position and Distance Vectors topic in portion Vector Analysis and Applications of Electromagnetic Theory

The distance vector can be used to compute which of the following?(a) Dot product(b) Cross product(c) Unit normal vector(d) AreaI have been asked this question in unit test.My enquiry is from Position and Distance Vectors in chapter Vector Analysis and Applications of Electromagnetic Theory

The work-electric field relation is given by(a) Volume integral(b) Surface integral(c) Line integral(d) Relation impossibleThe question was asked in quiz.I need to ask this question from Position and Distance Vectors topic in portion Vector Analysis and Applications of Electromagnetic Theory

The divergence of distance vector is(a) 0(b) 3(c) 2(d) 1I got this question in final exam.The doubt is from Position and Distance Vectors topic in section Vector Analysis and Applications of Electromagnetic Theory

The dot product of two vectors is a scalar. The cross product of two vectors is a vector. State True/False.(a) True(b) FalseThe question was asked in homework.I'm obligated to ask this question of Dot and Cross Product in division Vector Analysis and Applications of Electromagnetic Theory