Test: Vector Analysis- 2 - Electrical Engineering (EE) MCQ

Match List-I with List-ll and select the correct answer using the codes given below the lists:
List-I
A. Gauss’s divergence theorem
B. Stroke’s theorem
C. The divergence
D. The curl
List-ll

Assertion (A): Vector differential operator is a vector quantity and it signifies that certain operations of a differentiation are to be carried out on the scalar function following it.
Reason (R): Vector differential operator posses properties similar to ordinary vectors

Consider the following statements:
1. Divergence of a vector function at each point gives the rate per unit volume at which the physical entity is issuing from that point.
2. If a vector function ϕ represents temperature, then grad ϕ or ∇ϕ will represents rate of change of temperature with distance.
3. The curl of a vector function A gives the measure of the angular velocity at every point of the vector field.

Assertion (A): The Gauss’s divergence theorem permits us to express certain integrals by means of surface integrals.
Reason (R): Gauss’s divergence theorem states that “the surface integral of the curl of a vector field taken over any surface s is equal to the line integral of the vector field around the closed periphery (contour) of the surface.

If  is any vector field in cartesian co-ordinates system, then

If and , then

If S is any closed surface enclosing a volume V and then the value of (is a unit vector) will be equal to

Assertion (A): The laplacian operator of a scalar function ϕ can be defined as “Gradient of the divergence of the scalar ϕ”
Reason (R): Laplacian operator may be a “scalar laplacian" or a “vector laplacian'’ depending upon whether it is operated with a scalar function or a vector, respectively.

Match List-I (Terms) with List-II (Type) and select the correct answer using the codes given below the lists:
List-I
A. Curl= 0
B. Div = 0
C. Div grad (ϕ) = 0
D. Div div (ϕ) = 0
List-ll
1. Laplace equation
2. Irrotational 
3. Solenoidal
4. Not defined
Codes:
    A B C D
(a) 2 3 1 4
(b) 4 1 3 2
(c) 2 1 3 4
(d) 4 3 1 2

Which of the following relations are not correct?​

If uF = ∇_v, where u and v are scalar fields and F is a vector field, then F. curl F is equal to

A vector field which has a vanishing divergence is called as ____________ 

Which of the following statements is not true of a phasor?​

Match List-I (Physical quantities) with List-ll (Dimensions) and select the correct answer using the codes given below the lists:
List-I
A. Electric potential
B. Magnetic flux
C. Magnetic field intensity
D. Magnetic flux density
List-ll
1. MT^-2I^-1
2. ML²T^-3I^-1 
3. IL^-1
4. ML²T^-2I^-1
Codes:
    A B C D
(a) 2 4 3 1
(b) 4 2 3 1
(c) 1 2 1 3
(d) 4 2 1 3

Which of the following statements is not true regarding vector algebra?

A  rigid body is rotating with an angular velocity of ω where,  and v is the line velocity. If is the position vector given by  then the value of curl  will be equal to

If  then which of the following relation will hold true?