ECE102 FE Quiz - Gecko PDF

1. The three coordinate axes mutually at right angles to each other, and call them the x, y, and z axes. A. Cartesian coordinate B. Cylindrical coordinate C. Spherical coordinate D. 3D coordinate Answer: A 2. Express the unit vector 𝑎𝑥 in spherical components at the po...

1. The three coordinate axes mutually at right angles to each other, and call them the x, y, and z axes. A. Cartesian coordinate B. Cylindrical coordinate C. Spherical coordinate D. 3D coordinate Answer: A 2. Express the unit vector 𝑎𝑥 in spherical components at the point: 𝑥 = 3, 𝑦 = 2, 𝑧 = −1 A. 0.80𝑎𝑟 − 0.22𝑎𝜃 − 0.55𝑎𝜙 B. 0.66𝑎𝑟 + 0.39𝑎𝜃 − 0.64𝑎𝜙 C. 0.59𝑎𝑟 − 0.38𝑎𝜃 − 0.72𝑎𝜙 D. 0.36𝑎𝑟 − 0.11𝑎𝜃 − 0.46𝑎𝜙 Answer: A 3. Time is classified as: A. Scalar B. Vector C. Magnitudinal D. CGS Answer: A 4. Magnetic field is classified as: A. Scalar B. Vector C. Magnitudinal D. CGS Answer: B 5. It is define as the vector force on a unit positive test charge and has a unit of volts per meter (𝑉/𝑚) or Newtons per Coulumb (𝑁/𝐶). A. Current field intensity B. Electric field intensity C. Electric flux density D. Current flux density Answer: B 6. It is defined as the product of the magnitude of A, the magnitude of B, and the cosine of the smaller angle between them. A. Cross product B. Dot product C. Both cross product and dot product  D. None of the choices Answer: B 7. It is equal to the product of the magnitudes of A, B, and the sine of the smaller angle between A and B. A. Cross product B. Dot product C. Both cross product and dot product D. None of the choices Answer: A 8. It is the three-dimensional version of the polar coordinate of analytic geometry A. Cartesian coordinate B. Cylindrical coordinate C. Spherical coordinate D. 3D coordinate Answer: B 9. Given the points 𝑀(0.1, −0.2, −0.1), 𝑁(−0.2, 0.1, 0.3), and 𝑃(0.4, 0, 0.1), find the angle between 𝑅𝑀𝑁 and 𝑅𝑀𝑃 A. 68° B. 78° C. 88° D. 98° Answer: B 10. Area is classified as A. Scalar B. Vector C. Magnitudinal D. CGS Answer: A 11. Find the vector component of 𝐹 = (10, −6, 5) that is parallel to 𝐺 = (0.1, 0.2, 0.3). A. (−0.93, −1.86, −2.79) B. (0.93, 1.86,2.79) C. (−0.93, 1.86, −2.79) D. (0.93, −1.86, 2.79) Answer: B 12. It is an axial or rotational vector whose magnitude is the maximum circulation of per unit area. A. Gradient of a scalar B. Curl of a vector C. Divergence of a vector  D. Laplacian of a scalar Answer: B 13. Express point 𝑃(3, 4, −6) in terms of cylindrical coordinate system. A. (5, 126.87°, −6) B. (5, 53.13°, −6) C. (7.81, 223.13°, −6) D. (7.81, 306.87°, −6) Answer: B 14. The force expressed by Coulomb’s Law is a/an ______ force, for each of the two charges experiences a force of the same magnitude, although opposite in direction. A. mutual B. equidistant C. opposite D. None of the choices Answer: A 15. A ______________ is not restricted in any way. It is completely defined by its magnitude and direction and can be drawn as any one of a set of equal length parallel lines. A. free vector B. line vector C. position vector D. reference vector Answer: A 16. Electric Field Density is classified as A. Scalar B. Vector C. Magnitudinal D. CGS Answer: B 17. Find the angle between the pairs of vectors; 𝒂 = 𝑎𝑥 − 𝑎𝑦 − 2𝑎𝑧 , 𝒃 = 2𝑎𝑥 + 𝑎𝑦 + 3𝑎𝑧. A. 60° B. 123.06° C. 160° D. 84.26° Answer: B 18. It is measured in Coulombs per square meter. A. Current field intensity B. Electric field intensity C. Electric flux density  D. Current flux density Answer: C 19. A ____________ is such that it can slide along its line of action, e.g. a mechanical force acting on a body. A. free vector B. line vector C. position vector D. reference vector Answer: B 20. At point 𝑃(−3, 4, 5), express the vector that extends from 𝑃 to 𝑄(2, 0, −1) in cylindrical coordinates. A. 1.6𝑎𝜌 + 6.2𝑎𝜙 − 5𝑎𝑧 B. −6.2𝑎𝜌 − 1.60𝑎𝜙 − 6𝑎𝑧 C. 6.2𝑎𝜌 + 1.60𝑎𝜙 − 6𝑎𝑧 D. −6.20𝑎𝜌 − 1.60𝑎𝜙 + 5𝑎𝑧 Answer: C 21. Calculate the distance between each pair of points (1, 0, 2) and (−2, 1, −3) A. 5.9161 B. 6.4031 C. 2.4495 D. 6 Answer: A 22. Determine an expression for 𝑎𝑦 in spherical coordinates at 𝑃(𝑟 = 4, 𝜃 = 0.2𝜋, 𝜙 = 0.8𝜋). A. 0.35𝑎𝑟 − 0.48𝑎𝜃 − 0.81𝑎𝜙 B. 0.35𝑎𝑟 + 0.48𝑎𝜃 − 0.81𝑎𝜙 C. −0.35𝑎𝑟 − 0.48𝑎𝜃 − 0.81𝑎𝜙 D. 0.35𝑎𝑟 + 0.48𝑎𝜃 + 0.81𝑎𝜙 Answer: B 23. Acceleration is classified as: A. Scalar B. Vector C. Magnitudinal D. CGS Answer: B 24. The surfaces 𝑟 = 2 and 4 , 𝜃 = 30° and 50° , and 𝜙 = 20° and 60° identify a closed surface. Find the enclose volume. A. 1.91 B. 2.91  C. 3.91 D. 4.91 Answer: B 25. Express the unit vector 𝑎𝑥 in spherical at the point; 𝜌 = 2.5, 𝜙 = 0.7 𝑟𝑎𝑑, 𝑧 = 1.5. A. 0.80𝑎𝑟 − 0.22𝑎𝜃 − 0.55𝑎𝜙 B. 0.66𝑎𝑟 + 0.39𝑎𝜃 − 0.64𝑎𝜙 C. 0.59𝑎𝑟 + 0.38𝑎𝜃 − 0.72𝑎𝜙 D. 0.36𝑎𝑟 + 0.11𝑎𝜃 − 0.46𝑎𝜙 Answer: B 26. Express the unit vector 𝑎𝑥 in spherical at the point; 𝜌 = 2.5, 𝜙 = 0.7 𝑟𝑎𝑑, 𝑧 = 1.5. A. 0.80𝑎𝑟 − 0.22𝑎𝜃 − 0.55𝑎𝜙 B. 0.66𝑎𝑟 + 0.39𝑎𝜃 − 0.64𝑎𝜙 C. 0.59𝑎𝑟 + 0.38𝑎𝜃 − 0.72𝑎𝜙 D. 0.36𝑎𝑟 + 0.11𝑎𝜃 − 0.46𝑎𝜙 Answer: C 27. It states that the total outward flux of a vector field through a closed surface is the same as the volume integral of the divergence. A. Gradient theorem B. Laplacian theorem C. Divergence theorem D. Stoke’s theorem Answer: C 28. Which of the following is not true about unit vectors? A. It has a magnitude of unity. B. It is equal to a particular vector divided by its magnitude. C. It is not a vector. D. None of the choices. Answer: C 29. The electric flux passing through any closed surface is equal to the total charge enclosed by that surface. A. Coulombs Law B. Gauss Law C. Newton First Law D. Faraday’s Law Answer: B 30. Calculate the distance of the points (−2, 1, −3) from the origin. A. 2.2361 B. 3.7416  C. 4.2426 D. 6 Answer: B 31. A uniform volume charge density of 80 𝜇𝐶/𝑚2 is present throughout the region 8 𝑚𝑚 < 𝑟 < 10 𝑚𝑚. Let 𝜌𝑣 = 0 for 0 < 𝑟 < 8 𝑚𝑚. Find the total charge inside the spherical surface 𝑟 = 10 𝑚𝑚. A. 161 𝑝𝐶 B. 162 𝑝𝐶 C. 163 𝑝𝐶 D. 164 𝑝𝐶 Answer: D 32. A ____________ occurs when the reference point is fixed. A. free vector B. line vector C. position vector D. reference vector Answer: A 33. Convert the point (3, 4, 5) from Cartesian to spherical coordinates A. (7.07, 45°, 53°) B. (0.707, 45°, 53°) C. (7.07, 54°, 63°) D. (0.707, 54°, 63°) Answer: A 34. Find the Cartesian coordinates of 𝐵(4, 25°, 120°) A. (0.845, 1.462, 3.625) B. (−0.845, 1.462, 3.625) C. (−8.45, 1.462, 3.625) D. (8.45, 1.462, 3.625) Answer: B 35. The circular coordinate system is also referred to as A. Cartesian system B. Cylindrical system C. Spherical system D. Space system Answer: B 36. The Cartesian system is also called as A. Circular coordinate system B. Rectangular coordinate system C. Spherical coordinate system  D. Space coordinate system Answer: B 37. The angular separation between the vectors 𝐴 = 4𝑖 + 3𝑗 + 5𝑘 and 𝐵 = 𝑖 − 2𝑗 + 2𝑘 is A. 65.8° B. 66.8° C. 67.8° D. 68.8° Answer: C 38. The polar form of Cartesian coordinates is A. Cylindrical coordinates B. Spherical coordinates C. Space coordinates D. 3D coordinates Answer: A 39. The Laplacian operator is A. ∇𝑉 B. ∇ ∙ 𝑉 C. ∇ × 𝑉 D. ∇2 𝑉 Answer: D 40. When two vectors are perpendicular, their A. Dot product is zero B. Cross product is zero C. Both are zero D. Cross product is unity Answer: A 41. 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 − 7𝑘 Answer: B 42. Del operator is also known as _____ A. Divergence operator B. Gradient operator C. Curl operator D. Laplacian operator Answer: B 43. Find the gradient of a function 𝑉 if 𝑉 = 𝑥𝑦𝑧 A. 𝑦𝑧 𝑎𝑥 + 𝑥𝑧 𝑎𝑦 + 𝑥𝑦 𝑎𝑧 B. 𝑦𝑧 𝑎𝑥 + 𝑥𝑦𝑎𝑦 + 𝑥𝑧 𝑎𝑧 C. 𝑥𝑦 𝑎𝑥 + 𝑦𝑧 𝑎𝑦 + 𝑥𝑧 𝑎𝑧 D. 𝑥𝑦𝑧 𝑎𝑥 + 𝑥𝑦 𝑎𝑦 + 𝑦𝑧 𝑎𝑧 Answer: A 44. Find the gradient of 𝑉 = 𝑥 2 sin 𝑦 cos 𝑧 A. 2𝑥 sin 𝑦 cos 𝑧 𝑎𝑥 + 𝑥 2 cos 𝑦 cos 𝑧 𝑎𝑦 − 𝑥 2 sin 𝑦 sin 𝑧 𝑎𝑧 B. 2𝑥 sin 𝑦 cos 𝑧 𝑎𝑥 + 𝑥 2 cos 𝑦 cos 𝑧 𝑎𝑦 + 𝑥 2 sin 𝑦 sin 𝑧 𝑎𝑧 C. 2𝑥 cos 𝑦 sin 𝑧 𝑎𝑥 + 𝑥 2 cos 𝑦 cos 𝑧 𝑎𝑦 − 𝑥 2 sin 𝑦 sin 𝑧 𝑎𝑧 D. 𝑥 sin 𝑦 cos 𝑧 𝑎𝑥 + 𝑥 2 cos 𝑦 cos 𝑧 𝑎𝑦 − 𝑥 2 sin 𝑦 sin 𝑧 𝑎𝑧 Answer: A 45. What is the value of 𝑎𝑧 ∙ 𝑎𝑟 A. 1 B. cos 𝜃 C. sin 𝜃 D. 0 Answer: B 46. Find the distance between 𝐴(10, 30°, 60°) and 𝐵(8, 60°, 90°) A. 4 B. 5 C. 6 D. 7 Answer: C 47. What is the value of 𝑎𝑟 ∙ 𝑎𝑥 ? A. sin 𝜃 cos 𝜙 B. sin 𝜃 sin 𝜙 C. cos 𝜃 cos 𝜃 D. cos 𝜃 cos 𝜙 Answer: A 48. The Curl operator is A. ∇𝑉 B. ∇ ∙ 𝑉 C. ∇ × 𝑉 D. ∇2 𝑉 Answer: C 49. The Divergence operator is A. ∇𝑉  B. ∇ ∙ 𝑉 C. ∇ × 𝑉 D. ∇2 𝑉 Answer: B 50. The Gradient operator is A. ∇𝑉 B. ∇ ∙ 𝑉 C. ∇ × 𝑉 D. ∇2 𝑉 Answer: A