WorksheetsTERM TEST - ELECTROMAGNETICS
Total questions: 110
Worksheet time: 55mins
Name
Class
Date
1.
Which of the following is correct?
a)
A. Green’s Theorem is a particular case of Stokes Theorem
b)
B. Stokes Theorem is a particular case of Green’s Theorem
c)
C. Not Attempted
d)
D. None of the Above
2.
Green’s Theorem relates a double integral over a region to a?
a)
A. indefinite integral
b)
B. surface integral
c)
C. volume integral
d)
D. line integral
3.
Green’s Theorem is used to?
a)
A. transform the line integral in xy - plane to a surface integral on the same xy - plane
b)
B. transform double integrals into triple integral in a region v
c)
C. transform surface integral into line integral
d)
D. None of the Above
4.
Pick the correct statement from the ff:
a)
A. Stoke’s theorem is a particular form of Green’s Theorem
b)
B. Green’s theorem and Stokes Theorem are entirely differcent
c)
C. Green’s theorem and Stoke’s theorem are same
d)
D. Green’s Theorem is particular form of Stoke’s Theorem
5.
Green’s Theorem doesn’t relate a double integral over a region to a?
a)
A. indefinite integral
b)
B. surface integral
c)
C. volume integral
d)
D. line integral
e)
E. All except line integral
6.
Mathematically, the functions in Green’s theorem will be?
a)
A. Continuous partial derivatives
b)
B. Continuous derivatives
c)
C. Discrete derivatives
d)
D. Discrete partial derivatives
7.
Which of the following is not an application of Green’s theorem?
a)
A. Volume of plane figures
b)
B. Centroid of plane figures
c)
C. Area surveying
d)
D. Solving two dimensional flow integrals
8.
The path traversal in calculating the Green’s theorem is
a)
A. Anticlockwise
b)
B. Inwards
c)
C. Clockwise
d)
D. Outwards
9.
If two functions A and B are discrete, their Green’s value for a region of circle of radius a in the positive quadrant is?
a)
A. ∞
b)
B. -∞
c)
C. 0
d)
D. Does not exist
10.
Applications of Green’s theorem are meant to be in?
a)
A. Two dimensional
b)
B. Three dimensional
c)
C. One dimensional
d)
D. Four dimensional
11.
The Green’s theorem can be related to which of the following theorems mathematically?
a)
A. Gauss divergence theorem
b)
B. Stoke’s theorem
c)
C. Euler’s theorem
d)
D. Leibnitz’s theorem
12.
The Shoelace formula is a shortcut for the Green’s theorem.
a)
A. True
b)
B. False
c)
C. Shortcut to Euler’s theorem
d)
D. None of the mentioned
13.
States that a line integral around the boundary of the plane region D can be computed as the double integral over the region D.
a)
A. Green’s Theorem
b)
B. Stokes Theorem
c)
C. Euler’s Theorem
d)
D. None of the mentioned
14.
What is Green's theorem primarily concerned with in vector calculus?
a)
A. The relationship between circulation and flux of a vector field in a plane
b)
B. The relationship between magnetic and electric fields
c)
C. The relationship between pressure and velocity fields in fluid dynamics
d)
D. The relationship between the gradient and the curl of a scalar field
15.
Which of the following is an application of Green’s theorem?
a)
A. Solving two dimensional flow integrals
b)
B. Area surveying
c)
C. Volume of plane figures
d)
D. Both A and B
16.
Use Green’s Theorem to evaluate ∮Cxydx+x2y3dy where C is the triangle with vertices (0,0)(0,0), (1,0)(1,0), (1,2)(1,2) with positive orientation.
a)
A. 2/3
b)
B. 5/9
c)
C. 6/7
d)
D. 9/10
17.
Evaluate ∮Cy3dx−x3dywhere C is the positively oriented circle of radius 2 centered at the origin.
a)
A. -24π
b)
B. -48π
c)
C. -72π
d)
D. -96π
18.
Evaluate ∮Cy3dx−x3dy where C are the two circles of radius 2 and radius 1 centered at the origin with positive orientation.
a)
A. -45π/2
b)
B. -55π/2
c)
C. -65π/2
d)
D. -75π/2
19.
Use Green’s Theorem to find the area of a disk of radius a.
a)
A. πa^2
b)
B. 2πa^2
c)
C. 3πa^2
d)
D. 4πa^2
20.
Use Greens Theorem to evaluate the line integral∫C5ydx−4xdy over the region connecting the points (0,0),(2,0),(2,4) oriented clockwise
a)
A. 63
b)
B. 54
c)
C. 45
d)
D. 36
21.
Del operator is also known as ___
a)
a. Divergence Operator
b)
b. Gradient Operator
c)
c. Curl Operator
d)
d. Laplacian Operator
22.
The gradient is taken on a ____
a)
a. tensor
b)
b. vector
c)
c. scalar
d)
d. anything
23.
Divergence and Curl of a vector field are ___
a)
a. Scalar & Vector
b)
b. Vector & Scalar
c)
c. Scalar & Scalar
d)
d. Vector & Vector
24.
A vector field with a vanishing curl is called as ___
a)
a. Irrotational
b)
b. Solenoidal
c)
c. Rotational
d)
d. Cycloidal
25.
A vector field has a vanishing divergence is called as ___
a)
a. Solenoidal Field
b)
b. Rotational Field
c)
c. Irrotational Field
d)
d. Hemispheroidal Field
26.
What is the divergence of the vector field 𝑭=3𝑥^2𝑖+5𝑥𝑦^2 𝑗+𝑥𝑦𝑧^3 𝑘 at the point (1,2,3)?
a)
a. 89
b)
b. 80
c)
c. 124
d)
d. 100
27.
If 𝑊=𝑥𝑦+𝑦𝑧+𝑧, find the directional derivative of 𝑊 at (1,-2,0) in the direction towards the point (3,6,9).
a)
a. -0.6
b)
b. -0.7
c)
c. -0.8
d)
d. -0.9
28.
Find the gradient of 𝑉 if 𝑉=𝑥𝑦𝑧.
a)
a. 𝑦𝑧𝑖+𝑥𝑧𝑗+𝑥𝑦𝑘
b)
b. 𝑦𝑧𝑖+𝑥𝑦𝑗+𝑥𝑧𝑘
c)
c. x𝑦𝑖+𝑦𝑧𝑗+𝑥𝑧𝑘
d)
d. x𝑦𝑧𝑖+𝑥𝑦𝑗+𝑦𝑧𝑘
29.
The value of 𝐶𝑢𝑟𝑙(𝒓) if 𝒓=𝑥𝑖+𝑦𝑗+𝑧𝑘
a)
a. 0
b)
b. 1
c)
c. 3
d)
None of the above
30.
The value of 𝑑𝑖𝑣(𝒓) if 𝒓=𝑥𝑖+𝑦𝑗+𝑧𝑘
a)
a. 0
b)
b. 1
c)
c. 3
d)
d. None of the above
31.
The function 𝑭=𝑦𝑧𝑖+𝑥𝑧𝑗+𝑥𝑦𝑘 is
a)
a. Irrotational
b)
b. Solenoidal
c)
c. Both
d)
d. None of the above
32.
The function 𝑭=(𝑥+3𝑦)𝑖+(𝑦−3𝑧)𝑗+(𝑥−2𝑧)𝑘 is
a)
a. Irrotational
b)
b. Solenoidal
c)
c. Both
d)
d. None of the above
33.
Evaluate the directional derivative of the function 𝑓=𝑥^2−𝑦^2+2𝑧^2 at the point P(1,2,3) in the direction of PQ where Q has coordinates (5,0,4)
a)
a. 28
b)
b. 28/11
c)
c. 28/17
d)
d. None of these
34.
What is the greatest rate of increases of 𝑢=𝑥𝑦𝑧^2 at the point (1,0,3)?
a)
a. -9
b)
b. 9
c)
c. 7
d)
d. None of these
35.
The directional derivative of the function 𝑓(𝑥,𝑦,𝑧)=𝑥𝑦^2+𝑦𝑧^3 at the point (2,-1,1) in the direction of the vector 𝑖+2𝑗+2𝑘 is
a)
a. 11/3
b)
b. 3/11
c)
c. -11/3
d)
d. -3/11
36.
The divergence of the curl is zero
a)
a. True
b)
b. False
c)
c. Maybe
d)
d. Needs more information
37.
The curl of gradient is 1
a)
a. True
b)
b. False
c)
c. Maybe
d)
d. Needs more information
38.
The gradient of scalar function 𝐴=5𝑥^2𝑦−5𝑦^2𝑧+𝑧^2𝑥 at the point P(1,1,1) is
a)
a. 11𝑖−5𝑗−3𝑘
b)
b. 11𝑖+5𝑗−3𝑘
c)
c. 11𝑖−5𝑗+3𝑘
d)
d. 11𝑖+5𝑗+3𝑘
39.
If 𝑭=𝑥^2𝑦𝑖+2𝑥𝑧𝑗+2𝑦𝑧𝑘, then the value of 𝑑𝑖𝑣(𝑐𝑢𝑟𝑙 𝑭) is
a)
a. 1
b)
b. 2
c)
c. 0
d)
d. -1
40.
What is the directional derivative if 𝑓(𝑥,𝑦)=𝑥𝑦 at point P(-2,0) in the direction of 𝒗=1/2𝑖+√3/2𝑗
a)
a. √3
b)
b. 2√3
c)
c. −√3
d)
d. √2
41.
If two vectors have same direction but different magnitude then they are called as
a)
a. Unlike Vectors
b)
b. Like Vectors
c)
c. Collinear Vectors
d)
d. None of the Above
42.
Cross product can be used to calculate
a)
a. Angle between two vectors
b)
b. Area of triangle
c)
c. Area of Parallelogram
d)
d. All of the above
43.
Gradient of a scalar field V indicates ___________.
a)
a. magnitude of maximum space rate of change of V
b)
b. direction of maximum space rate of change of V
c)
c. both A and B
d)
d. None of the above
44.
If divergence of a vector field is zero at a point, then it means that __________.
a)
a. flux in the vector field at that point is zero.
b)
b. net outward flux in the vector filed at that point is zero.
c)
c. rate of change of flux in the vector filed at that point is zero
d)
d. None of the above.
45.
Solenoidal vector field means ________.
a)
a. Divergence free vector field
b)
b. Incompressible vector field
c)
c. Transverse electric field
d)
d. All of the above
46.
The mathematical perception of the gradient is said to be
a)
a. Tangent
b)
b. Slope
c)
c. Arc
d)
d. Chord
47.
___________ relates surface integral with closed line integral.
a)
a. Divergence theorem
b)
b. Gauss theorem
c)
c. Stoke theorem
d)
d. Both a and b
48.
If the result of a mathematical operation is a vector, then the operation cannot be ___________.
a)
a. Gradient
b)
b. Curl
c)
c. Cross Product
d)
d. Divergence
49.
On taking product of two vectors and the direction of the resultant vector will be _______.
a)
a. Along
b)
b. Behind
c)
c. Perpendicular to the plane formed by and as per right-hand rule
d)
d. Perpendicular to the plane formed by and as per left-hand rule
50.
Which of the following operations is used to find the magnitude of a vector?
a)
a. Dot product
b)
b. Cross product
c)
c. Scalar product
d)
d. Norm operation
51.
The dot product of two perpendicular vectors is:
a)
a. Always zero
b)
b. Always positive
c)
c. Always negative
d)
d. Can be zero or positive
52.
The cross product of two vectors results in a vector that is __________.
a)
a. Perpendicular to both input vectors
b)
b. Parallel to both input vectors
c)
c. Collinear with one of the input vectors
d)
d. In the plane formed by the input
53.
What is the result of the dot product of two parallel vectors?
a)
a. Zero
b)
b. A scalar
c)
c. A vector
d)
d. Undefined
54.
Which property holds true for the cross product of two vectors?
a)
a. Commutative
b)
b. Associative
c)
c. Distributive
d)
d. None of the above
55.
What does the magnitude of the cross product of two vectors represent geometrically?
a)
a. The area of the parallelogram formed by the vectors
b)
b. The volume of the parallelepiped formed by the vectors
c)
c. The angle between the vectors
d)
d. The length of the vectors
56.
What is the magnitude of the vector a=3i-4j+12k?
a)
a. 13
b)
b. 14
c)
c. 15
d)
d. 16
57.
Find the angle between the vectors a = 3i + 2j + 6k and b = 2i + 4j – 4k.
a)
a. −𝟑/𝟓
b)
b. 𝟑/𝟓
c)
c. 𝟒/𝟐𝟏
d)
d. −𝟓/𝟐𝟏
58.
Find the sine of the angle between vectors 𝑖+2 𝑗+3 𝑘 𝑎𝑛𝑑 3 𝑖−4 𝑗+2 𝑘
a)
a. 𝑠𝑖𝑛𝜃=9√5 / √14√29
b)
b. 𝑠𝑖𝑛𝜃= 19√2 / √5√29
c)
c. 𝑠𝑖𝑛𝜃= 4√7 / √5√29
d)
d. 𝑠𝑖𝑛𝜃= 7√4 / √5√29
59.
Find the dot product of these two vector, 𝑎=3𝑖+2𝑗−6𝑘 and 𝑏=4𝑖−3𝑗+𝑘
a)
a. 6
b)
b. 5
c)
c. 4
d)
d. 0
60.
Does [𝑎×𝑏,𝑏×𝑐,𝑐×𝑎]=[𝑎 𝑏 𝑐]?
a)
a. Yes
b)
b. No, [𝑎×𝑏,𝑏×𝑐,𝑐×𝑎] is equal to [𝑎 𝑏 𝑐]^2
c)
c. No, [𝑎×𝑏,𝑏×𝑐,𝑐×𝑎] is equal to [𝑎 𝑏 𝑐]^3
d)
d. No, [𝑎×𝑏,𝑏×𝑐,𝑐×𝑎] is equal to [𝑎 𝑏 𝑐]
61.
Based on the conclusion, in what way does Electromagnetic Waves and Visible Light related to one another?
a)
a. they are indeed compatible
b)
b. they are similar
c)
c. they have distinctive differences
62.
Maxwell was the ____ person to calculate the speed of propagation of electromagnetic waves.
a)
a. Second
b)
b. Fourth
c)
c. Third
d)
d. First
63.
Vector Field is also known as?
a)
a. Magnetism
b)
b. Vector
c)
c. Magnetic Field
d)
d. Gauss Law
64.
Zero is the divergence of the magnetic field.
a)
a. Yes
b)
b. True
c)
c. No
d)
d. Not always
65.
Assigning an arrow pointing in a certain direction to every point in the region of space.
a)
a. Gauss
b)
b. Faraday’s Law
c)
c. Magnetism
d)
d. Vector Field
66.
Around what kind of object does magnetic field can represent as Vector Field?
a)
a. Magnetic
b)
b. Vector
c)
c. Iron
d)
d. Heat
67.
Closed surface integral of magnetic flux density is always equal to total scalar magnetic flux, enclosed within that surface of any shape or size lying in a medium.
a)
Maxwell’s Equation
b)
b. Gauss Law on Magnetostatics
c)
c. Magnetostatics
d)
d. Gauss Law
68.
How many equations does Maxwell have?
a)
a. Five
b)
b. Six
c)
c. Four
d)
d. One
69.
To which does the second equation focuses?
a)
a. Electromagnetic Waves
b)
b. Electromagnetics
c)
c. Electro field
d)
d. Electromagnet
70.
What is often applied to Vector Field?
a)
a. Density
b)
b. Divergence
c)
c. Divergense
71.
Assertion (A): Electronic and Ionic polarization in a polyatomic gas are independent of temperature.
Reason (R): The orientation polarization is independent of temperature.
a)
a. Both A and R are true and R is the correct explanation of A
b)
b. Both A and R are true, but R is not a correct explanation of A
c)
c. A is true but R is false.
d)
d. A is false but R is true.
72.
The space outside or surrounding an electric charge where it has a force of attraction or repulsion.
a)
a. Electric field
b)
b. Magnetic field
c)
c. Electromagnetic field
d)
d. Electric flux
73.
A combination of two charges, with equal charge magnitude but opposite signs.
a)
a. Magnetic dipole
b)
b. Static dipole
c)
c. Dynamic dipole
d)
d. Electric dipole
74.
The imaginary lines representing the electric field
a)
a. Electric field
b)
b. Electric flux
c)
c. Electric flux density
d)
d. Electric lines of force
75.
A dielectric material must be ____
a)
a. Insulator
b)
b. Resistor
c)
c. Electric field
d)
d. None of the above
76.
At a point may be defined as equal to the lines of force passing normally through a unit cross section at that point.
a)
a. Electric Intensity
b)
b. Magnetic flux density
c)
c. Electric flux
d)
d. None of the above
77.
Which material has the highest value of dielectric constant?
a)
a. Glass
b)
b. Oil
c)
c. Vacuum
d)
d. Ceramics
78.
When the dielectric is homogeneous, the potential gradient is
a)
a. Uniform
b)
b. Non-Uniform
c)
c. Zero
d)
d. Any of the above
79.
Which of the following has the least value of dielectric constant?
a)
a. Ceramics
b)
b. Oil
c)
c. Glass
d)
d. Paper
80.
Which of the following capacitors is
marked for polarity?
a)
a. Air
b)
b. Paper
c)
c. Mica
d)
d. Electrolytic
81.
The potential gradient across the material of low permittivity is than across the material of high permittivity.
a)
a. Smaller
b)
b. Greater
c)
c. both (a) and (b)
d)
d. None of the above
82.
Dielectric strength ____ with increasing thickness
a)
a. Increases
b)
b. Decreases
c)
c. Remains unaltered
d)
d. None of the above
83.
A dielectric is subjected to an alternating field. The dielectric losses have the potential to
a)
a. real part of dielectric constant
b)
b. imaginary part of dielectric constant
c)
c. both real and imaginary parts of dielectric constant
d)
d. either real or imaginary part of the dielectric constant
84.
In a polyatomic gas, the types of polarization which exist together are.
a)
a. electronic and orientational
b)
b. electronic and ionic
c)
c. ionic and orientational
d)
d. electronic, orientational, and ionic
85.
A capacitor consists of two ____
a)
a. Insulators only
b)
b. Conductors only
c)
c. Conductors separated by an insulator.
d)
d. Insulators separated by conductor.
86.
A capacitance of 100uf is connected in series with a resistance of 800 ohms. The time constant of the circuit is
a)
a. 0.2 s
b)
b. 0.4 s
c)
c. 0.6 s
d)
d. 0.8 s
87.
A capacitor having a capacitance of 5uF is charged to a potential difference of 10,000V. The energy stored in the capacitor is
a)
a. 50 joules
b)
b. 150 joules
c)
c. 200 joules
d)
d. 250 joules
88.
Two infinite parallel plates 10mm apart have maintained between them a potential difference of 100V. The acceleration of an electron placed between them is
a)
a. 0.56 x10^15 m/s^2
b)
b. 1.5 x10^15 m/s^2
c)
c. 1.6 x10^15 m/s^2
d)
d. 1.76 x10^15 m/s^2
89.
Calculate the electric field intensity 10cm from a charge Q= 5nC
a)
a. 450 N/C
b)
b. 900 N/C
c)
c. 4.5x10^3 N/C
d)
d. 9.0x10^3 N/C
90.
Three charges of +5C, -6C, and +7C are inside a sphere, what is the total electric flux passing through the surface of the sphere?
a)
a. 5 Coulombs
b)
b. 6 Coulombs
c)
c. 7 Coulombs
d)
d. 8 Coulombs
91.
What law states that, the line integral of the magnetic field around some closed loop is equal to 'μ0' times the algebraic sum of the currents which pass through the loop.
a)
A. Ampere’s Circuital
b)
B. Biot-Savart’s
c)
C. Kirchoff’s Voltage
d)
D. Lorentz’s
92.
Which law is an equation that describes the magnetic field created by a current-carrying wire, and allows you to calculate its strength at various points?
a)
A. Ampere’s Circuital
b)
B. Biot-Savart’s
c)
C. Kirchoff’s Voltage
d)
D. Lorentz’s
93.
Biot-Savart's law in magnetic field is analogous to which law in electric field?
a)
A. Gauss law
b)
B. Faraday's law
c)
C. Coulomb’s law
d)
D. Ampere's law
94.
If the flow of electric current is parallel to the magnetic field, at what value will the force be?
a)
A. Zero
b)
B. Infinity
c)
C. Maximum
d)
D. Half the original
95.
Tesla is a unit of what?
a)
A. Field Strength
b)
B. Inductance
c)
C. Flux density
d)
D. Flux
96.
A magnetic field exists around____.
a)
A. Iron
b)
B. Copper
c)
C. Aluminum
d)
D. Moving charges
97.
If a coil carrying current is placed in a uniform magnetic field, then which of the following will be produced?
a)
A. emf is produced
b)
B. Torque is produced
c)
C. Force is produced
d)
D. Torque and force is produced
98.
Magnetic vector potential for a line current will be inversely proportional to ____.
a)
A. Current
b)
B. Current density
c)
C. Distance
d)
D. Field intensity
99.
If the cross-sectional area of a magnetic field increases, but the flux remains the same, the flux density ___.
a)
A. increases
b)
B. decreases
c)
C. remains the same
d)
D. doubles
100.
When a solenoid is activated, the force that moves the plunger is _____.
a)
A. an electromagnetic field
b)
B. a permanent magnetic field
c)
C. a varying voltage
d)
D. a steady current
101.
What is the magnetic field outside a solenoid?
a)
A. Infinity
b)
B. Half the value of the field inside
c)
C. Double the value of the field inside
d)
D. Zero
102.
If a long hollow copper pipe carries a direct current, the magnetic field associated with the current will be____.
a)
A. Inside the pipe only
b)
B. Outside the pipe only
c)
C. Neither inside nor outside the pipe
d)
D. Both inside and outside the pipe
103.
A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field ____.
a)
A. is zero only along the axis of the pipe
b)
B. is zero at any point inside the pipe
c)
C. is maximum at the center and minimum at the edges
d)
D. is uniform throughout the pipe but not zero
104.
A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. What will happen to the magnetic field lines inside the cylinder?
a)
A. Bend closer to cylinder axis
b)
B. Bend far away from the cylinder axis
c)
C. Remains uniform as before
d)
D. Ceases to exist inside the cylinder
105.
A length L of wire carries a steady current 1 A. It is bent first to form a coil of 1 turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the center caused by the same current is_.
a)
A. One fourth of its first value
b)
B. Same as of its first value
c)
C. Four times of its first value
d)
D. Half of its first value
106.
If flux density is 10 Wb/m^2 and the area of the coil is 2 m^2, what is its flux?
a)
A. 20 Wb
b)
B. 10 Wb
c)
C. 5 Wb
d)
D. 40 Wb
107.
What is the flux density when the flux is 5.5 μWb and the cross-sectional area is 6 × 10^–3 m^2?
a)
A. 917 uT
b)
B. 91.7 uT
c)
C. 91 T
d)
D. 9.7 T
108.
The magnetic field at a distance r from a long wire carrying current I is 0.4 T. What is the magnetic field at a distance 2r?
a)
A. 0.2 T
b)
B. 0.1 T
c)
C. 0.8 T
d)
D. 1.6 T
109.
A coil of diameter 0.2 m is formed by a 6.28 m long wire and a current of 1 A is passed in it. What will be the magnetic induction at its center?
a)
A. 6.28 × 10^-5 T
b)
B. 0
c)
C. 6.28 T
d)
D. 6.28 × 10^-3 T
110.
What will be the magnetic field of a finite current element with 1 A current and height 1/2π m?
a)
A. 1 A/m
b)
B. 2 A/m
c)
C. 0.5 A/m
d)
D. 0.25 A/m
100 %
