Vector Analysis and Applications MCQs ( Electromagnetic Theory ) MCQs – Electromagnetic Theory MCQs
Latest Electromagnetic Theory MCQs
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Electromagnetic Theory MCQs – Vector Analysis and Applications MCQs ( Electromagnetic Theory ) MCQs
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Dot and Cross Product
1. 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 zero
Answer: a
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.
2. 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
Explanation: Cross product of two vectors is, A X B = (a2*b3 – b2*a3)i – (a1*b3 – b1*a3)j + (a1*b2 – b1*a2)k. Using the formula, the answer can be calculated.
3. Which of the following are not vector functions in Electromagnetics?
a) Gradient
b) Divergence
c) Curl
d) There is no non- vector functions in Electromagnetics
Answer: d
Explanation: Since all the coordinates in electromagnetic are space coordinates, direction and magnitude both are important. Thus all functions are vector only.
4. 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 calculated
Answer: b
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.
5. Find whether the vectors are parallel, (-2,1,-1) and (0,3,1)
a) Parallel
b) Collinearly parallel
c) Not parallel
d) Data insufficient
Answer: c
Explanation: 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.
6. Lorentz force is based on,
a) Dot product
b) Cross product
c) Both dot and cross product
d) Independent of both
Answer: b
Explanation: Lorentz force is given by, F = q (v x B).Thus cross product is the answer.
7. Electromagnetic forces are defined by
a) Fleming’s right hand rule
b) Fleming’s left hand rule
c) Faraday’s law
d) Ampere law
Answer: b
Explanation: 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.
8. The dot product of two vectors is a scalar. The cross product of two vectors is a vector. State True/False.
a) True
b) False
Answer: a
Explanation: 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.
9. 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| = 0
Answer: c
Explanation: Option c gives |cos|2 + |sin|2 = 1, which is the right answer.
10. Which of the following is not true?
a) A . (B . C) = scalar value
b) A . (B x C) = scalar value
c) A x (B . C) = scalar value
d) A x (B x C) = vector value
Answer: c
Explanation: Cross product of dot product of two vectors is a vector value.
Position and Distance Vectors
1. The distance vector is obtained in
a) Cartesian coordinate system
b) Spherical coordinate system
c) Circular coordinate system
d) Space coordinate system
Answer: d
Explanation: Vector formed by connecting two points in space is distance vector. Thus, it is obtained in space coordinate system.
2. The divergence of distance vector is
a) 0
b) 3
c) 2
d) 1
Answer: b
Explanation: The distance vector of any coordinates is generally, r = xi + yj + zk. The divergence of r is 1 + 1 + 1 = 3.
3. 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 – k
Answer: a
Explanation: 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.
General Concepts And Constraints In Design Of Rotating Machines MCQs
4. 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)/1.414
Answer: a
Explanation: 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.
5. The polar form of Cartesian coordinates is
a) Circular coordinates
b) Spherical coordinates
c) Cartesian coordinates
d) Space coordinates
Answer: a
Explanation: The radius in the polar coordinates is the Pythagorean triplet-(r,x,y).Thus it is the circular coordinates.
6. The work-electric field relation is given by
a) Volume integral
b) Surface integral
c) Line integral
d) Relation impossible
Answer: c
Explanation: The work done is given by, W = -Q ∫E dl. Thus it is line integral.
7. The distance vector can be used to compute which of the following?
a) Dot product
b) Cross product
c) Unit normal vector
d) Area
Answer: c
Explanation: The distance vector is the distance between two points on space, thus the unit normal vector is computed using the distance vector.
8. Distance and position vectors rely on field strength. State True/False.
a) True
b) False
Answer: a
Explanation: Position or distance of a vector is dependent on the field strength.
9. Find the projection of A on B. Given A = 10j + 3k and B = 4j + 5k.
a) 6
b) 6.25
c) 6.5
d) 6.75
Answer: b
Explanation: Projection of A on B = (A . B)/|B|. Thus the answer is 40/6.4= 6.25.
10. The vector product of two vectors is given by area of the parallelogram. State True/False.
a) True
b) False
Answer: a
Explanation: The vector product of two vectors is A X B = AB sin θ. n, where n is the unit normal vector to the plane given by A and B. Their magnitude is given by |A X B|, which is the area of parallelogram.
Vector Properties
1. The del operator is called as
a) Gradient
b) Curl
c) Divergence
d) Vector differential operator
Answer: d
Explanation: The Del operator is used to replace the differential terms, thus called vector differential operator in electromagnetics.
2. The relation between vector potential and field strength is given by
a) Gradient
b) Divergence
c) Curl
d) Del operator
Answer: a
Explanation: The vector potential and field is given by, E = -Del (V).
3. The Laplacian operator is actually
a) Grad(Div V)
b) Div(Grad V)
c) Curl(Div V)
d) Div(Curl V)
Answer: b
Explanation: The Laplacian operator is the divergence of gradient of a vector, which is also called del2V operator.
4. The divergence of curl of a vector is zero. State True or False.
a) True
b) False
Answer: a
Explanation: The curl of a vector is the circular flow of flux. The divergence of circular flow is considered to be zero.
5. The curl of gradient of a vector is non-zero. State True or False.
a) True
b) False
Answer: b
Explanation: The differential flow of flux in a vector is a vector. The curl of this quantity will be zero.
6. 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 = 1
Answer: c
Explanation: By standard proof, Div (u X v) = v . Curl(u) – u . Curl (v).
7. A vector is said to be solenoidal when its
a) Divergence is zero
b) Divergence is unity
c) Curl is zero
d) Curl is unity
Answer: a
Explanation: When the divergence of a vector is zero, it is said to be solenoidal /divergent-free.
8. The magnetic field intensity is said to be
a) Divergent
b) Curl free
c) Solenoidal
d) Rotational
Answer: c
Explanation: By Maxwell’s equation, the magnetic field intensity is solenoidal due to the absence of magnetic monopoles.
9. 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, irrotational
Answer: b
Explanation: Since the path is not divergent, it is solenoidal and the path has curl, thus rotational.
10. When a vector is irrotational, which condition holds good?
a) Stoke’s theorem gives non-zero value
b) Stoke’s theorem gives zero value
c) Divergence theorem is invalid
d) Divergence theorem is valid
Answer: b
Explanation: Stoke’ theorem is given by, ∫ A.dl = ∫ (Curl A). ds, when curl is zero(irrotational), the theorem gives zero value.