Previous Year Questions- Coordinate Systems and Vector Calculus | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE) PDF Download

Q1: In the (x, y, z) coordinate system, three point-charges Q, Q and αQ are located in free space at (−1, 0, 0), (1, 0, 0) and (0, −1, 0) respectively. The value of α for the electric field to be zero at (0, 0.5, 0) is _____ (rounded off to 1 decimal places).       (2024)
(a) -1.61
(b) -2.36
(c) -2.87
(d) -3.25
Ans: (a)
Sol: From the figure,

Q2: In the figure, the electric field E and the magnetic field B point to x and z directions, respectively, and have constant magnitudes. A positive charge 'q' is released from rest at the origin. Which of the following statement(s) is/ are true.      (2023)
(a) The charge will move in the direction of z with constant velocity.
(b) The charge will al ways move on the y-z plane only.
(c) The trajectory of the charge will be a cycle.
(d) The charge will progress in the direction of y.
Ans: (a)

Q3: The vector function expressed by
represents a conservative field, where a_x, a_y, a_z are unit vectors along x, y and z directions, respectively. The values of constants k₁, k₂, k₃ are given by:     (2020)
(a) $𝑘1=3,𝑘2=3,𝑘3=7$k₁ = 3, k₂ = 3, k₃ = 7
(b) k₁ = 3, k₂ = 8, k₃ = 5
(c) $𝑘1=4,𝑘2=5,𝑘3=3$k₁ = 4, k₂ = 5, k₃ = 3
(d) k₁= 0, k₂ = 0, k₃ = 0
Ans: (c)
Sol: 
Q4: The figures show diagrammatic representations of vector fields respectively. Which one of the following choices is true?    (SET-2 (2017))
(a)
(b)
(c)
(d)
Ans: (c)
Sol: 
Q5: The line integral of the vector field  along a path from (0, 0, 0) to (1, 1, 1) parametrized by (t, t², t) is _____.        (SET-2 (2016))
(a) 4.41
(b) 2.26
(c) 6.56
(d) 8.34
Ans: (a)
Sol: 
Q6: In cylindrical coordinate system, the potential produced by a uniform ring charge is given by ψ = f(r, z), where f is a continuous function of r and z. Let  be the resulting electric field. Then the magnitude of      (SET-1  (2016))
(a) increases with r.
(b) is 0.
(c) is 3.
(d) decreases with z.
Ans: (b)
Sol: V is given as static field in time invariant.
Hence, ▽ × E = 0

Q7: Match the following.      (SET-2 (2015))
(a) P-2 Q-1 R-4 S-3
(b) P-4 Q-1 R-3 S-2
(c) P-4 Q-3 R-1 S-2
(d) P-3 Q-4 R-2 S-1
Ans: (b)
Sol: Stokes theorem
Gauss theorem
Divergence theorem
Cauchy integral theorem

Q8: Consider a function  where r is the distance from the origin and  is the unit vector in the radial direction. The divergence of this function over a sphere of radius R, which includes the origin, is      (SET-1  (2015))
(a) 0
(b) 2π
(c) 4π
(d) Rπ
Ans: (c)
Sol: From divergence theorem as we know,

Q9: The direction of vector A is radially outward from the origin, with ∣A∣ = krⁿ, where r² = x² + y² + z² and k is a constant. The value of n for which ▽⋅A = 0 is       (2012)
(a) -2
(b) 2
(c) 1
(d) 0
Ans: (a)
Sol: 
Q10: Divergence of the vector field
 is    (2007)
(a) $2𝑧\cos 𝑧2$2z cos z²
(b) $\sin 𝑥𝑦+2𝑧\cos 𝑧2$sinxy + 2z cos z²  
(c) xsinxy − cosz
(d) None of these
Ans: (a)
Sol: 
Divergence
Q11: Consider the following statements with reference to the equation (δp/δt)

1. This is a point form of the continuity equation.
2. Divergence of current density is equal to the decrease of charge per unit volume per unit at every point.
3. This is Max well's divergence equation
4. This represents the conservation of charge

Select the correct answer.     (2006)
(a) Only 2 and 4 are true
(b) 1, 2 and 3 are true
(c) 2, 3 and 4 are true
(d) 1, 2 and 4 are true
Ans: (d)

Q12: If  is the electric intensity,   is equal to      (2005)
(a)
(b)
(c) null vector
(d) Zero
Ans: (d)
Sol: Divergence of a curl field is always zero.
i.e.

Q13: Given a vector field  the divergence theorem states that     (2002)
(a)
(b)
(c)
(d)
Ans: (a)