27 + Interview Questions in Coordinate Systems And Transforms in Electromagnetic Theory Page 1 InterviewSolution

1.	The scalar factor of spherical coordinates is(a) 1, r, r sin θ(b) 1, r, r(c) r, r, 1(d) r, 1, rI have been asked this question by my school teacher while I was bunking the class.My question comes from Spherical Coordinate System in division Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Right choice is (a) 1, r, r SIN θ The EXPLANATION is: The radius varies from unity to infinity, the plane ANGLE from zero to 360 ⁰ and the z plane from (-∞, ∞) .

Discussion

2.	The area of sphere can be computed from the sphere volume. State True/False.(a) True(b) FalseThis question was posed to me in an online interview.Question is from Spherical Coordinate System in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Right option is (a) True To EXPLAIN: On double integrating the differential volume, the AREA can be COMPUTED for a sphere.

Discussion

3.	Given B= (10/r)i+( rcos θ) j+k in spherical coordinates. Find Cartesian points at (-3,4,0)(a) -2i + j(b) 2i + k(c) i + 2j(d) –i – 2kThe question was posed to me during an online exam.The query is from Spherical Coordinate System topic in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer» CORRECT option is (a) -2I + j Explanation: R = √(x^2+y^2+z^2) = √25 = 5 Θ = cos^-1(z/r) = 1 Φ = tan^-1(y/x) = tan^-1(-4/3) Thus, B = -2i + j.

Discussion

4.	Find the Cartesian coordinates of B(4,25⁰,120⁰)(a) (0.845, 1.462, 3.625)(b) (-0.845, 1.462, 3.625)(c) (-8.45, 2.462, 6.325)(d) (8.45, 2.462, 6.325)This question was addressed to me in an online interview.My question is taken from Spherical Coordinate System topic in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Correct OPTION is (B) (-0.845, 1.462, 3.625) To ELABORATE: x = r sin θ cos φ = 4 sin25⁰ cos 120⁰ = -0.845 y = r sin θ sin φ = 4 sin 25⁰ sin 120⁰ = 1.462 z = r cos θ = 4 cos 25⁰ = 3.625.

Discussion

5.	Find the spherical coordinates of A(2,3,-1)(a) (3.74, 105.5⁰, 56.13⁰)(b) (3.74, 105.5⁰, 56.31⁰)(c) (3.74, 106.5⁰, 56.13⁰)(d) (3.74, 106.5⁰, 56.31⁰)This question was addressed to me in an online quiz.My question comes from Spherical Coordinate System in division Coordinate Systems and Transforms of Electromagnetic Theory
Answer» RIGHT CHOICE is (B) (3.74, 105.5⁰, 56.31⁰) EXPLANATION: R = √(x^2+y^2+z^2) = √14 = 3.74 Θ = cos^-1(z/r) = cos^-1(-1/3.74) = 105.5⁰ Φ = tan^-1(y/x) = tan^-1(3/2) = 56.31⁰.

Discussion

6.	Choose which of following condition is not required for a waveguide to exist.(a) The dimensions should be in accordance with desired frequency(b) Cut-off frequency should be minimum 6GHz(c) The shape should be spherical(d) No specific condition is required for waveguide designThis question was addressed to me in an online interview.This intriguing question originated from Spherical Coordinate System topic in portion Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Right option is (c) The shape should be spherical To EXPLAIN: A WAVEGUIDE need not be spherical, it has to be rectangular or CIRCULAR, as it violates the propagation of the wave.

Discussion

7.	Spherical systems are employed in waveguides. State True/False(a) True(b) FalseI got this question during an interview.I'm obligated to ask this question of Spherical Coordinate System in portion Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Right choice is (B) False For explanation: There is no WAVEGUIDE DESIGNED spherically to AVOID absorption, rather than PROPAGATION.

Discussion

8.	Convert the point (3,4,5) from Cartesian to spherical coordinates(a) (7.07,45⁰,53⁰)(b) (0.707,45⁰,53⁰)(c) (7.07,54⁰,63⁰)(d) (0.707,54⁰,63⁰)The question was posed to me during an online interview.The question is from Spherical Coordinate System in chapter Coordinate Systems and Transforms of Electromagnetic Theory
Answer» RIGHT OPTION is (a) (7.07,45⁰,53⁰) BEST EXPLANATION: R = √(x^2+y^2+z^2) = √50 = 7.07 Θ = cos^-1(z/r) = cos^-1(5/5√2) = 45⁰ Φ = tan^-1(y/x) = tan^-1(4/3) = 53⁰.

Discussion

9.	Example of spherical system in the following is(a) Charge in space(b) Charge in box(c) Charge in dielectric(d) Uncharged systemThis question was addressed to me during an online exam.This intriguing question comes from Spherical Coordinate System in portion Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Correct OPTION is (a) Charge in space To EXPLAIN: From a point charge +Q, the electric field spreads in all 360 degrees. The calculation of electric field in this CASE will be spherical system. THUS it is charge in the space.

Discussion

10.	Transform the spherical system B = (10/r)i + (10cos θ)j + k into cylindrical form at (5, π/2, -2)(a) 2.467i + j + 1.167k(b) 2.467i – j + 1.167k(c) 2.467i – j – 1.167k(d) 2.467i + j – 1.167kThis question was addressed to me in quiz.My question comes from Cylindrical Coordinate System in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Correct choice is (a) 2.467i + j + 1.167k The best explanation: The equivalent cylindrical FORM is given by, B = (10sin θ/r + rcos2θ)i + j + (10cos θ/r –r sin θ cos θ)k At (5, π/2, -2), r = √(5^2+-2^2) = √29 sin θ = 5/√29 and cos θ = -2/√29 Thus, B = 2.467i + j + 1.167k.

Discussion

11.	Rectangular waveguides dominate the circular waveguides. Find the reason.(a) Low cut-off frequency(b) Easy to design(c) More wave propagation(d) The statement is falseI have been asked this question in a job interview.This intriguing question originated from Cylindrical Coordinate System topic in chapter Coordinate Systems and Transforms of Electromagnetic Theory
Answer» CORRECT choice is (b) Easy to design To EXPLAIN I would say: Due to linear design, the desired dimensions can be easily CONSTRUCTED using RECTANGULAR waveguides than circular ones.

Discussion

12.	Charges filled inside a cylindrical will possess flux in which direction?(a) Upwards(b) Downwards(c) Laterally outwards(d) InwardsThe question was posed to me in quiz.This interesting question is from Cylindrical Coordinate System in portion Coordinate Systems and Transforms of Electromagnetic Theory
Answer» The CORRECT choice is (C) Laterally outwards The explanation: The flux DUE to the charges will ACT outside the CYLINDER. Since the cylinder possesses curved surfaces, it will flow laterally outwards.

Discussion

13.	The pressure inside a piston cylinder is a variable of(a) Radius(b) Plane angle(c) Z plane distance(d) Constant, not a variableThe question was posed to me in class test.This intriguing question originated from Cylindrical Coordinate System in chapter Coordinate Systems and Transforms of Electromagnetic Theory
Answer» The CORRECT option is (c) Z PLANE DISTANCE The best explanation: Pressure varies up and down in a cylinder due to SUCTION. Thus it is dependent on the z plane distance of the cylinder.

Discussion

14.	Cylindrical system is employed in waveguides. State True/False.(a) True(b) FalseThe question was posed to me in quiz.Query is from Cylindrical Coordinate System topic in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Correct answer is (a) True To elaborate: CYLINDRICAL SYSTEMS are employed in circular waveguides, WHEREAS CARTESIAN systems are employed in RECTANGULAR waveguides.

Discussion

15.	A charge located at point p (5,30⁰,2) is said to be in which coordinate system?(a) Cartesian system(b) Cylindrical system(c) Spherical system(d) Space systemThis question was addressed to me by my college professor while I was bunking the class.I want to ask this question from Cylindrical Coordinate System topic in division Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Right option is (b) Cylindrical SYSTEM To EXPLAIN: The cylindrical system is of the form (ρ, φ, z), which relates the POINT GIVEN in the question.

Discussion

16.	Cylindrical systems have the following scalar values respectively(a) 1, ρ ,1(b) 1, 1, 1(c) 0,1,0(d) 1,0,0I got this question by my college professor while I was bunking the class.This question is from Cylindrical Coordinate System in portion Coordinate Systems and Transforms of Electromagnetic Theory
Answer» RIGHT answer is (a) 1, ρ ,1 For explanation: The range of radius is one to unity, that of plane angle is one to 360 DEGREE and that of z plane is one to INFINITY. Thus the MINIMUM scalar FACTOR has to be 1, ρ , 1.

Discussion

17.	Transform the vector B=yi+(x+z)j located at point (-2,6,3) into cylindrical coordinates.(a) (6.325,-71.57,3)(b) (6.325,71.57,3)(c) (6.325,73.57,3)(d) (6.325,-73.57,3)This question was posed to me in an interview.The query is from Cylindrical Coordinate System topic in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer» RIGHT OPTION is (a) (6.325,-71.57,3) To ELABORATE: ρ = √(x^2+y^2) = √40 = 6.325 Φ = tan^-1(y/x) = tan^-1(-6/2) = -71.57 z = 3.

Discussion

18.	The cylindrical coordinate system is also referred to as(a) Cartesian system(b) Circular system(c) Spherical system(d) Space systemI had been asked this question during an interview for a job.I'm obligated to ask this question of Cylindrical Coordinate System in division Coordinate Systems and Transforms of Electromagnetic Theory
Answer» The correct choice is (B) Circular SYSTEM The BEST I can explain: The cylindrical coordinates(r,φ,z) is also called as circular system and is used for SYSTEMS with circular DIMENSIONS.

Discussion

19.	Which of the following criteria is used to choose a coordinate system?(a) Distance(b) Intensity(c) Magnitude(d) GeometryI had been asked this question in a job interview.My doubt is from Cartesian Coordinate System in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Correct CHOICE is (d) Geometry To elaborate: The coordinate SYSTEM is CHOSEN based on the geometry of the given problem. From a POINT charge +Q, the electric field spreads in all 360 DEGREES. The calculation of electric field in this case will be spherical system.

Discussion

20.	The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by(a) (7,64.62,71.57)(b) (7,-64.62,-71.57)(c) (7,-64.62,71.57)(d) (7,64.62,-71.57)This question was posed to me in class test.Asked question is from Cartesian Coordinate System in division Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Right choice is (d) (7,64.62,-71.57) Explanation: SUBSTITUTE the POINTS in the vector and CONVERT the Cartesian to cylindrical form to GET radius as 7, plane angle1 as 64.62 and plane angle2 as -71.57.

Discussion

21.	Transform the vector A = 3i – 2j – 4k at P(2,3,3) to cylindrical coordinates(a) -3.6j – 4k(b) -3.6j + 4k(c) 3.6j – 4k(d) 3.6j + 4kI got this question in an online interview.The above asked question is from Cartesian Coordinate System in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer»

Discussion

22.	The Cartesian coordinates can be related to cylindrical coordinates and spherical coordinates. State True/False.(a) True(b) FalseI have been asked this question at a job interview.Asked question is from Cartesian Coordinate System topic in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Correct CHOICE is (a) True For explanation I would say: All the coordinate SYSTEMS are inter-convertible and all the VECTOR operations are applicable to it.

Discussion

23.	The angular separation between the vectors A = 4i + 3j + 5k and B = i – 2j + 2k is (in degrees)(a) 65.8(b) 66.8(c) 67.8(d) 68.8I got this question during an interview.The question is from Cartesian Coordinate System in division Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Right ANSWER is (c) 67.8 For explanation I would say: The DOT product the VECTOR is 8. Angle of SEPARATION is cos θ = 8/ (7.07 X 3) = 0.377 and θ = cos^-1(0.377) = 67.8.

Discussion

24.	The scalar factor of Cartesian system is unity. State True/False.(a) True(b) FalseI got this question during a job interview.This is a very interesting question from Cartesian Coordinate System topic in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer» RIGHT ANSWER is (a) True The explanation: The range of CARTESIAN system is one to infinity. Thus the minimum SCALAR value of the system is unity.

Discussion

25.	A charge is placed in a square container. The position of the charge with respect to the origin can be found by(a) Spherical system(b) Circular system(c) Cartesian system(d) Space coordinate systemThis question was addressed to me during an online exam.My question is from Cartesian Coordinate System topic in section Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Correct option is (C) Cartesian system To explain I would say: SINCE the container possesses dimensions of a SQUARE (length, BREADTH and height), it can be found by Cartesian system.

Discussion

26.	The Cartesian system is also called as(a) Circular coordinate system(b) Rectangular coordinate system(c) Spherical coordinate system(d) Space coordinate systemI got this question in an internship interview.Asked question is from Cartesian Coordinate System in portion Coordinate Systems and Transforms of Electromagnetic Theory
Answer» Correct option is (b) Rectangular coordinate system The best I can EXPLAIN: The other name for CARTESIAN is rectangular system, which is given by (X,y,Z).

Discussion

27.	The volume of a parallelepiped in Cartesian is(a) dV = dx dy dz(b) dV = dx dy(c) dV = dy dz(d) dV = dx dzThis question was posed to me in exam.My question is from Cartesian Coordinate System topic in division Coordinate Systems and Transforms of Electromagnetic Theory
Answer» CORRECT choice is (a) DV = dx DY dz The best explanation: The volume of a parallelepiped is given by product of differential LENGTH, breadth and height.

Discussion

Explore topic-wise InterviewSolutions in .

The area of sphere can be computed from the sphere volume. State True/False.(a) True(b) FalseThis question was posed to me in an online interview.Question is from Spherical Coordinate System in section Coordinate Systems and Transforms of Electromagnetic Theory

Spherical systems are employed in waveguides. State True/False(a) True(b) FalseI got this question during an interview.I'm obligated to ask this question of Spherical Coordinate System in portion Coordinate Systems and Transforms of Electromagnetic Theory

Cylindrical system is employed in waveguides. State True/False.(a) True(b) FalseThe question was posed to me in quiz.Query is from Cylindrical Coordinate System topic in section Coordinate Systems and Transforms of Electromagnetic Theory

Which of the following criteria is used to choose a coordinate system?(a) Distance(b) Intensity(c) Magnitude(d) GeometryI had been asked this question in a job interview.My doubt is from Cartesian Coordinate System in section Coordinate Systems and Transforms of Electromagnetic Theory

The angular separation between the vectors A = 4i + 3j + 5k and B = i – 2j + 2k is (in degrees)(a) 65.8(b) 66.8(c) 67.8(d) 68.8I got this question during an interview.The question is from Cartesian Coordinate System in division Coordinate Systems and Transforms of Electromagnetic Theory

The scalar factor of Cartesian system is unity. State True/False.(a) True(b) FalseI got this question during a job interview.This is a very interesting question from Cartesian Coordinate System topic in section Coordinate Systems and Transforms of Electromagnetic Theory

The volume of a parallelepiped in Cartesian is(a) dV = dx dy dz(b) dV = dx dy(c) dV = dy dz(d) dV = dx dzThis question was posed to me in exam.My question is from Cartesian Coordinate System topic in division Coordinate Systems and Transforms of Electromagnetic Theory