Previous Year Questions- Coordinate Systems and Vector Calculus

# 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)
Sol: As per Answer key of IIT Official : MTA (Marks to All)
Given :

Q3: The vector function expressed by
represents a conservative field, where ax, ay, az 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, k= 0, k= 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 r= 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) $2𝑧cos⁡𝑧2$2z cos z2
(b) $sin⁡𝑥𝑦+2𝑧cos⁡𝑧2$sinxy + 2z cos z
(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

(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)

The document Previous Year Questions- Coordinate Systems and Vector Calculus | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Electromagnetic Fields Theory (EMFT).
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## FAQs on Previous Year Questions- Coordinate Systems and Vector Calculus - Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE)

 1. What is the significance of coordinate systems in electrical engineering?
Ans. Coordinate systems play a crucial role in electrical engineering as they provide a framework for describing the position and orientation of various components in a circuit or system. Commonly used coordinate systems in electrical engineering include Cartesian, polar, and cylindrical coordinates.
 2. How do vector calculus concepts such as gradient, divergence, and curl apply to electrical engineering problems?
Ans. Vector calculus concepts are extensively used in electrical engineering to analyze electromagnetic fields, circuits, and devices. The gradient represents the rate of change of a scalar field, divergence measures the tendency of a vector field to converge or diverge, and curl indicates the rotation of a vector field.
 3. Can you explain the concept of vector fields and their applications in electrical engineering?
Ans. In electrical engineering, vector fields represent physical quantities such as electric and magnetic fields that vary in magnitude and direction at different points in space. Understanding vector fields is essential for analyzing circuit behavior, electromagnetic interactions, and signal propagation.
 4. How are coordinate transformations used in electrical engineering calculations?
Ans. Coordinate transformations are employed in electrical engineering to convert between different coordinate systems, such as converting Cartesian coordinates to polar coordinates. This is particularly useful when analyzing systems with complex geometries or when simplifying mathematical expressions.
 5. What is the role of divergence theorem and Stokes' theorem in electrical engineering applications?
Ans. The divergence theorem and Stokes' theorem are fundamental principles in vector calculus that are frequently utilized in electrical engineering to relate surface integrals to volume integrals and line integrals to surface integrals, respectively. These theorems are essential for analyzing electromagnetic fields, circuits, and systems.

## Electromagnetic Fields Theory (EMFT)

11 videos|50 docs|73 tests

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