Electrostatics - I - ELECTROMAGNETICS MCQs

Multiple Choice Questions 8 Pages

Savitribai Phule Pune University

electrical engineering

Contributed by

Yadu Deshmukh

DEPARTMENT OF ELECTRONICS AND TELECOMMUNICATION
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SUBJECT: ELECTROMAGNETICS
MCQ Unit 1- Electrostatics – I
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
2) 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
3) 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
4) The cylindrical coordinate system is also referred to as
a) Cartesian system
b) Circular system
c) Spherical system
d) Space system
5) 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 system
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6) 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)
7) 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)
8) 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
9) 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
10) The distance vector is obtained in
a) Cartesian coordinate system
b) Spherical coordinate system
c) Circular coordinate system
d) Space coordinate system
10) 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
11) Find whether the vectors are parallel, (-2,1,-1) and (0,3,1)
a) Parallel
b) Collinearly parallel
c) Not parallel
d) Data insufficient
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12) The divergence of distance vector is
a) 0
b) 3
c) 2
d) 1
13) The polar form of Cartesian coordinates is
a) Circular coordinates
b) Spherical coordinates
c) Cartesian coordinates
d) Space coordinates
14) The distance vector can be used to compute which of the following?
a) Dot product
b) Cross product
c) Unit normal vector
d) Area
15) 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
16) The del operator is called as
a) Gradient
b) Curl
c) Divergence
d) Vector differential operator
17) The relation between vector potential and field strength is given by
a) Gradient
b) Divergence
c) Curl
d) Del operator
18) The Laplacian operator is actually
a) Grad(Div V)
b) Div(Grad V)
c) Curl(Div V)
d) Div(Curl V)
19) A vector is said to be solenoidal when its
a) Divergence is zero
b) Divergence is unity
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c) Curl is zero
d) Curl is unity
20) The magnetic field intensity is said to be
a) Divergent
b) Curl free
c) Solenoidal
d) Rotational
21) 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
22) 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
23) The divergence theorem converts
a) Line to surface integral
b) Surface to volume integral
c) Volume to line integral
d) Surface to line integral
24) Find the charged enclosed by a sphere of charge density ρ and radius a.
a) ρ (4πa
2
)
b) ρ(4πa
3
/3)
c) ρ(2πa
2
)
d) ρ(2πa
3
/3)
25) Evaluate Gauss law for D = 5r
2
/4 i in spherical coordinates with r = 4m and θ = π/2 as
volume integral.
a) 600
b) 588.9
c) 577.8
d) 599.7
26) Compute divergence theorem for D = 5r
2
/4 i in spherical coordinates between r = 1 and r
= 2 in volume integral.
a) 80 π
b) 5 π
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c) 75 π
d) 85 π
27) Compute the Gauss law for D = 10ρ
3
/4 i, in cylindrical coordinates with ρ = 4m, z = 0
and z = 5, hence find charge using volume integral.
a) 6100 π
b) 6200 π
c) 6300 π
d) 6400 π
28) Using volume integral, which quantity can be calculated?
a) area of cube
b) area of cuboid
c) volume of cube
d) distance of vector
29) Compute the charge enclosed by a cube of 2m each edge centered at the origin and
with the edges parallel to the axes. Given D = 10y
3
/3 j.
a) 20
b) 70/3
c) 80/3
d) 30
30) Find the value of divergence theorem for the field D = 2xy i + x
2
j for the rectangular
parallelepiped given by x = 0 and 1, y = 0 and 2, z = 0 and 3.
a) 10
b) 12
c) 14
31) The mathematical perception of the gradient is said to be
a) Tangent
b) Chord
c) Slope
d) Arc
32) Divergence of gradient of a vector function is equivalent to
a) Laplacian operation
b) Curl operation
c) Double gradient operation
d) Null vector
33) The gradient of xi + yj + zk is
a) 0
b) 1
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c) 2
d) 3
34) Curl of gradient of a vector is
a) Unity
b) Zero
c) Null vector
d) Depends on the constants of the vector
35) The gradient can be replaced by which of the following?
a) Maxwell equation
b) Volume integral
c) Differential equation
d) Surface integral
36) Surface integral is used to compute
a) Surface
b) Area
c) Volume
d) density
37) Find the value of divergence theorem for A = xy
2
i + y
3
j + y
2
z k for a cuboid given by
0<x<1, 0<y<1 and 0<z<1.
a) 1
b) 4/3
c) 5/3
d) 2
38) Find the value of divergence theorem for the field D = 2xy i + x
2
j for the rectangular
parallelepiped given by x = 0 and 1, y = 0 and 2, z = 0 and 3.
a) 10
b) 12
c) 14
d) 16
39) Gauss theorem uses which of the following operations?
a) Gradient
b) Curl
c) Divergence
d) Laplacian
40) Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x
2
+ y
2
+
z
2
= 9.
a) 120π
b) 180π
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c) 240π
d) 300π
41) The Gauss divergence theorem converts
a) line to surface integral
b) line to volume integral
c) surface to line integral
d) surface to volume integral
42) The divergence theorem for a surface consisting of a sphere is computed in which
coordinate system?
a) Cartesian
b) Cylindrical
c) Spherical
d) Depends on the function
43) Find the Gauss value for a position vector in Cartesian system from the origin to one
unit in three dimensions.
a) 0
b) 3
c) -3
d) 1
44) If a function is described by F = (3x + z, y
2
− sin x
2
z, xz + ye
x5
), then the divergence
theorem value in the region 0<x<1, 0<y<3 and 0<z<2 will be
a) 13
b) 26
c) 39
d) 51
45) Find the divergence theorem value for the function given by (e
z
, sin x, y
2
)
a) 1
b) 0
c) -1
d) 2
46) Coulomb is the unit of which quantity?
a) Field strength
b) Charge
c) Permittivity
d) Force
47) Coulomb law is employed in
a) Electrostatics
b) Magnetostatics
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c) Electromagnetics
d) Maxwell theory
48) Find the force between 2C and -1C separated by a distance 1m in air(in newton).
a) 18 X 10
6

b) -18 X 10
6

c) 18 X 10
-6

d) -18 X 10
-6
49) Find the force of interaction between 60 stat coulomb and 37.5 stat coulomb spaced
7.5cm apart in transformer oil(εr=2.2) in 10
-4
N,
a) 8.15
b) 5.18
c) 1.518
d) 1.815
50) Find the force between two charges when they are brought in contact and separated by
4cm apart, charges are 2nC and -1nC, in μN.
a) 1.44
b) 2.44
c) 1.404
d) 2.404
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