VECTOR CALCULUS

MULTIPLE CHOICE QUESTION:

1. A scalar quantity has __________.

a. magnitude

b. direction

c. both (a) and (b)

d. none of these

2. Which of the following is/are scalar quantity(s)?

a. distance

b. density

c. temperature

d. all of these

3. Which of the following is not a scalar quantity?

a. entropy

b. displacement

c. volume

d. mas

4. A vector quantity has __________.

a. magnitude

b. direction

c. both (a) and (b)

d. none of these

5. Which of the following is/are vector quantity(s)?

a. force

b. electric field intensity

c. acceleration

d. all of these

6. A unit vector has its magnitude as ____________.

a. 0

b. 1

c. ∞

d. none of these

7. A unit vector has _______ direction to that of the main vector.

a. same

b. opposite

c. normal upwards

d. normal downwards

8. A vector   in Cartesian coordinates is represented by ____________.

a. (Px, Pφ, Pz)

b. (Px, Py, Pz)

c. (Px, Pφ, Pθ)

d. none of these

9. ________ of two vectors uses the Law of Parallelogram.

a. multiplication

b. division

c. addition

d. all of these

10. demonstrates _________.

a. Commutative Law

b. Associative Law

c. Distributive Law

d. Law of Parallelogram

11. Multiplication of two vectors is __________.

a. vector

b. scalar

c. either vector or scalar

d. cannot say

12. If two vectors are orthogonal, then their scalar product is __________.

a. 1

b. 0

c. ∞

d. 100

13. ___________ Product is governed by the Right-Hand Screw Rule.

a. vector

b. scalar

c. simple mathematical

d. none of these

14. The vector product obeys the __________ law.

a. Commutative

b. Associative

c. Distributive

d. Parallelogram

15. Which of the following is/are in correct?

a.

b.

c.

d. none of these

16.

e.

f.

g. both (a) and (b)

h. none of these

16.

a.

b.

c.

d. none of these

17. The cross product of the same vector to itself is _ ___________.

a. 0

b. 1

c. ∞

d. 100

18. ____________ product of two unit vectors is the third unit vector.

a. vector

b. scalar

c. both (a) and (b)

d. none of these

19. 'r' in Cylindrical coordinates corresponding to Cartesian coordinate (3, 4, 5) is ____________.

a. 12

b. 7

c. 10

d. 5

20. In a Cartesian coordinate system, axes x, y and z are at __________ to each other.

a. 45°

b. 90°

c. 120°

d. 180°

21. Cartesian coordinates are represented in terms of ___________.

a. (r, φ, z)

b. (r, θ, φ)

c. (x, y, z)

d. all of these

22. Cylindrical coordinates are represented in terms of ____________.

a. (r, φ, z)

b. (r, θ, φ)

c. (x, y, z)

d. all of these

23. Spherical coordinates are represented in terms of ___________.

a. (r, φ, z)

b. (r, θ, φ)

c. (x, y, z)

d. all of these

24. In Cylindrical coordinate systems, unit vector   is __________.

a. directed outwards radially

b. normal to cylindrical surface at a point

c. both (a) and (b)

d. none of these

25. Unit vector   is at ________ to φ = constant plane.

a. 90°

b. 180°

c. 270°

d. 360°

26. Cylindrical coordinate 'r' is related to the Cartesian coordinate as __________.

a. (x, y)

b. (x + y)

c. (x2/y2)

d. (x2 + y2)1/2

27. Cylindrical coordinate 'z' is related to the Cartesian coordinate as __________.

a. tan−1(y/x)

b. z

c. xy/z

d. cot z

28. Dot multiplication   is equal to __________.

a. sin φ

b. cos φ

c. −sin φ

d. −cos φ

29. In a Spherical coordinate system, φ is ____________.

a. angle of elevation

b. azimuthal angle

c. distant from the origin to the point

d. all of these

30. Spherical coordinate system is a _________.

a. right-handed syste.

b. left-handed system

c. both (a)and (b)

d. none of these

31. Cross product aΦ × ar is equal to _____________.

a. aΦ

b. -aΦ

c. 1

d. 0

32. In a Spherical coordinate system, φ is given as _________.

a. y/x

b. x/y

c. tan−1(y/x)

d. tan−1(x/y)

33. In a Spherical coordinate system, r is given as ___________.

a. (x + y + z)

b. (x2 + y2 + z2)

c. (x2 + y2 + z2)1/2

d.

34. Dot product aΦ.ar is equal to ____________.

a. aΦ

b. -aΦ

c. 1

d. 0

35. For transformation from the Cartesian coordinate system to Spherical coordinate system,  should be equal to ____________.

a. cos θ

b. − cos θ

c. sin θ

d. − sin θ

36. In terms of Spherical coordinate system variables, y of Cartesian coordinate system is given as __________.

a. r sin θ cos φ

b. r sin θ sin φ

c. r cos θ sin φ

d. r cos θ cos φ

37. In a Spherical coordinate system, unit vector aΦ is perpendicular to the shifted ________ plane.

a. x−y

b. y−z

c. x−z

d. none of these

38. In the Cylindrical coordinate system, z ranges between ____________.

a. 0 and 1

b. −∞ and 0

c. 0 and −∞

d. −∞ and ∞

39. In the Cylindrical coordinate system, φ ranges from _____________.

a. 0 to less than π

b. 0 to less than 2π

c. 0 to less than 3π

d. 0 to less than 4π

ELECTROSTATICS

1. Maxwell's equations involve_______.

a. Charge density

b. Current density

c. Magnetic intensity

d. All of these

2. As per Coulomb's Law, force between two point charges is____

3. ε0 is ________ F/m.

a. 8.854 × 10−12

b. 6.654 × 10−12

c. 8.854 × 10−10

d. 6.654 × 10−10

4. Electric field intensity   is related to force   and charge q as __________.

5. Electric dipole is a pair of __________ and __________ point charges.

a. Equal and same

b. Unequal and same

c. Equal and opposite

d. Unequal and opposite

6. Magnitude of dipole moment | | is given as __________.

a. qd

b. q/d

c. d/q

d. None of these

7. Electric field intensity   due to volume charge is given as __________.

8. Electric flux density________medium.

a. Depends on

b. Independent of

c. Both (a) and (b)

d. None of these

9. Electric potential energy V is given as _________.

10.As per Gauss's Law, the total electric flux φ through a closed surface and the total charge qencby that surface are related as________.

10. If work done Wmn is zero, then VN and VM are related as _______.

a. VN + VM = 0

b. VN − VM = 0

c. 2VN + VM = 0

d. VN + 2VM = 0

11. According to Maxwell's first equation, _______.

12. Charge distribution symmetry can be of _______ type.

a. Spherical

b. Cylindrical

c. Planar

d. All of these

13. Curl of electrostatic field is __________.

a. ∞

b. 1

c. 0

d. None of these

14. As per Stoke's Theorem,   = _________.

a. ∞

b. 1

c. 0

d. None of these

15. Potential energy _____ if a test charge is moved from a lower potential point to a higher potential point.

a. Remains the same

b. Increases

c. Decreases

d. Becomes zero

16. Continuity equation is given as ___________.

17. If both the mediums are dielectrics, then boundary condition is given as ___________.

18. Poisson's equation is given as __________.

19. In the case of a linear material medium, _________ equation can be derived easily from Gauss' law.

a. Poisson

b. Laplace

c. Both (a) and (b)

d. None of these

20. According to the method of images, the tangential component of electric field to conductor surface is __________.

a. Unity

b. Zero

c. Infinity

d. None of these

MAGNETOSTATICS

1. Steady magnetic fields are governed by __________ law.

a. Biot–Savart's

b. Ampere's Circuital

c. Both (a) and (b)

d. None of these

2. There will be force of attraction between two current-carrying conductors if the currents are in __________ direction.

a. Same

b. Opposite

c. None of these

d. Cannot say

3. Lorentz force equation comprises __________ and __________ forces.

a. Electric, magnetic

b. Mechanical, chemical

c. Both (a) and (b)

d. None of these

4. Magnetic dipole moment is a product of __________.

a. Current and area

b. Area and its direction

c. Current, area and its direction

d. None of these

5. According to Faraday's __________ Law, as long as changes happen in magnetic flux, induced emf persists.

a. First

b. Second

c. Third

d. Fourth

6. According to __________ Law, induced current acts to produce an opposing flux.

a. Bio–Savart's

b. Lenz's

c. Ampere's

d. Faraday's

7. In terms of current density, Biot–Savart's Law is expressed as __________.

8. Biot–Savart's Law can be applied to __________ length current-carrying conductors.

a. Large

b. Medium

c. Small

d. Very small

9. According to Ampere's Circuital Law, field intensity   at a point at distance R from a very long straight filament conductor-carrying current I is given as

10. Ampere's Circuital Law is analogous to __________ Law in electrostatics.

a. Lenz's

b. Gauss's

c. Biot–Savart's

d. Faraday's

11. Ampere's Circuital Law can be applied __________ the conductor.

a. Inside

b. Outside

c. Both (a) and (b)

d. None of these

12. Magnetic flux density is the same as __________.

a. Magnetic induction

b. Magnetic field strength

c. Both (a) and (b)

d. None of these

13. Total flux passing through a closed surface held in a magnetic field is __________.

a. Infinity

b. Zero

c. Unity

d. None of these

14. Which of the following is true for electrostatics?

15. __________ gradient of magnetic scalar potential gives magnetic field intensity.

a. Positive

b. Negative

c. Double

d. Integral

16. Magnetic vector potential for volume current is expressed as __________.

17. __________ can be obtained from vector magnetic potential .

18. Magnetization is given as __________.

19. Magnetization volume current density in magnetic materials is due to __________.

a. Applied non-uniform magnetic field

b. Non-uniform magnetic susceptibility of material

c. Both (a) and (b)

d. None of these

20. According to the Law of refraction __________.

21. Energy density WH is given as __________.

MAXWELLS EQUATION

1. Maxwell's equations shelter on __________ law(s).

a. Faraday's

b. Gauss's

c. Ampere's

d. All of these

2. Conduction current through a wire is __________ displacement current in capacitor.

a. Same as

b. Different from

c. Twice of

d. None of these

3. In empty space, conduction current is __________.

a. Infinity

b. Unity

c. Zero

d. None of these

4. As per Maxwell's first equation __________.

a.  

b.  

c.  

d.  

5. Maxwell's second equation gives __________.

a.  

b.  

c.  

d.  

6. According to Ampere's Circuital Law __________.

a.  

b.  

c.  

d. None of these

7. Maxwell's third equation gives __________.

a.  

b.  

c.  

d.  

8. Maxwell's fourth equation gives __________.

a.  

b.  

c.  

d.  

9. emf is closed __________ integral of non-conservational electric field that is generated by battery.

a. Line

b. Surface

c. Volume

d. None of these

10. Maxwell's equations in __________ form give unformation at points of discontinuity in electromagnetic fields.

a. Differential

b. Integral

c. Algebraic

d. None of these

11. Which of the following is a boundary condition?

a.  

b.  

c.  

d. None of these

12. Another boundary condition using Maxwell's equations is given as __________.

a. Htan '1' + Htan '2' = 0

b. Htan '1' − Htan '2' = 0

c. Htan '1' + Htan '2' = Js

d. Htan '1'− Htan '2' = Js

13. At the point of discontinuity, __________ component of magnetic flux density is continuous.

a. Tangential

b. Normal

c. None of these

d. Cannot say

14. For those surfaces where surface charge density is __________ normal component of electric flux density is continuous.

a. Infinity

b. Unity

c. Zero

d. None of these

15. Which of the following vector form of boundary condition is incorrect?

a.  

b.  

c.  

d. None of these

16. Waves are used in __________.

a. TV

b. Radio

c. Radar

d. All of these

17. Current through a capacitor is expressed as __________.

a.  

b.  

c.  

d.  

18. Displacement current density   ____________ current passing through a capacitor.

a. Represents

b. Does not represent

c. Is the same as

d. None of these

19. Line integral of an electric field around a closed path is __________.

a. infinity

b. unity

c. zero

d. None of these

20. __________ are caused by accelerated charges

a. Time-varying fields

b. Waves

c. Both (a) and (b)

d. None of these

ELECTROMAGNETIC WAVES

1. At the Brewster angle, polarization ______________.

a. Cannot be reflected

b. Is reflected at 30°

c. Is reflected at 90°

d. None of these

2. Wave number has units of____________.

a. Radians

b. Meter

c. Radians/meter

d. None of these

3. Wave speed in terms of frequency f and wavelength λ is expressed as _________.

a. f/λ

b. λ/f

c. λ f

d. (λ + f)

4. For a lossy dielectric medium, ____________.

a. σ = 0

b. σ ≠ 0

c. None of these

d. Cannot say

5. Wave attenuation is given as ______________.

a. e+βx

b. e-βx

c. e+αx

d. e−αx

6. In the case of a perfect dielectric medium, phase constant ______________ as conductivity increases.

a. Increases

b. Decreases

c. Remains unchanged

d. None of these

7. Phase velocity is given as _________.

a. ωβ

b. βω

c. β/ω

d. None of these

8. For a good conductor ________________.

9. For a good dielectric medium ____________.

10. In good conductors, rate of attenuation is __________.

a. Small

b. Large

c. Infinity

d. Zero

11. Poynting Vector   is obtained as

12. Power density has _________________.

a. A DC component

b. A second harmonic component

c. Both (a) and (b)

d. None of these

13. Reflection coefficient Γ is __________.

a. ≥100

b. = 10

c. ≤ 1

d. None of these

14. Which of the following expressions is correct?

a. (1 + Γ) = τ

b. (1 + τ) = Γ

c. (1 + Γ) τ = 0

d. (1 + τ)Γ = 0

15. Transmission coefficient is given as __________.

16. Standing wave consists of two travelling waves of ____________ amplitudes and _____________ is direction.

a. Unequal, same

b. Unequal, opposite

c. Equal, same

d. Equal, opposite

17. Standing wave ratio S is given as __________.

18. SNR ranges from ______.

a. 0 to 1

b. 1 to 10

c. 10 to 100

d. 1 to ∞

19. As per Snell's Law _______.

20. Brewster's angle is given as tan θB = ____________.

d. None of these