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# Multiple choice question for engineering

## Set 1

1. The Cartesian system is also called as
a) Circular coordinate system
b) Rectangular coordinate system
c) Spherical coordinate system
d) Space coordinate system

Answer: b [Reason:] The other name for Cartesian is rectangular system, which is given by (x,y,z).

2. The volume of a parallelepiped in Cartesian is
a) dV = dx dy dz
b) dV = dx dy
c) dV = dy dz
d) dV = dx dz

Answer: a [Reason:] The volume of a parallelepiped is given by product of differential length, breadth and height.

3. A charge is placed in a square container. The position of the charge with respect to the origin can be found by
a) Spherical system
b) Circular system
c) Cartesian system
d) Space coordinate system

Answer: c [Reason:] Since the container possesses dimensions of a square (length, breadth and height), it can be found by Cartesian system.

4. The scalar factor of Cartesian system is unity. State True/False.
a) True
b) False

Answer: a [Reason:] The range of Cartesian system is one to infinity. Thus the minimum scalar value of the system is unity.

5. The angular separation between the vectors A = 4i + 3j + 5k and B = i – 2j + 2k is (in degrees)
a) 65.8
b) 66.8
c) 67.8
d) 68.8

Answer: c [Reason:] The dot product the vector is 8. Angle of separation is cos θ = 8/ (7.07 X 3) = 0.377 and θ = cos-1(0.377) = 67.8.

6. The Cartesian coordinates can be related to cylindrical coordinates and spherical coordinates. State True/False.
a) True
b) False

Answer: a [Reason:] All the coordinate systems are inter-convertible and all the vector operations are applicable to it.

7. Transform the vector A = 3i – 2j – 4k at P(2,3,3) to cylindrical coordinates
a) -3.6j – 4k
b) -3.6j + 4k
c) 3.6j – 4k
d) 3.6j + 4k

Answer: a [Reason:] Convert the Cartesian form to cylindrical form by formula and substitute the points to get -3.6j – 4k.

8. The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by
a) (7,64.62,71.57)
b) (7,-64.62,-71.57)
c) (7,-64.62,71.57)
d) (7,64.62,-71.57)

Answer: d [Reason:] Substitute the points in the vector and convert the Cartesian to cylindrical form to get radius as 7, plane angle1 as 64.62 and plane angle2 as -71.57.

9. Which of the following criteria is used to choose a coordinate system?
a) Distance
b) Intensity
c) Magnitude
d) Geometry

Answer: d [Reason:] The coordinate system is chosen based on the geometry of the given problem. From a point charge +Q, the electric field spreads in all 360 degrees. The calculation of electric field in this case will be spherical system.

10. Vector transformation followed by coordinate point substitution and vice-versa, both given the same result. Choose the best answer.
a) Possible, when the vector is constant
b) Possible, when the vector is variable
c) Possible in all cases
d) Not possible

Answer: a [Reason:] The order of vector transformation and point substitution will not affect the result, only when the vector is a constant.

## Set 2

1. When two vectors are perpendicular, their
a) Dot product is zero
b) Cross product is zero
c) Both are zero
d) Both are not necessarily zero

Answer: a [Reason:] Dot product of two perpendicular vectors is given by A.B = |a||b|cos 90, which is zero. Thus, dot product is zero and vectors are perpendicular.

2. The cross product of the vectors 3i + 4j – 5k and –i + j – 2k is,
a) 3i – 11j + 7k
b) -3i + 11j + 7k
c) -3i – 11j – 7k
d) -3i + 11j – 7k

Answer: b [Reason:] Cross product of two vectors is, A X B = (a2*b3 – b2*a3)i – (a1*b3 – b1*a3)j + (a1*b2 – b1*a2)k. Using the formula, the answer can be calculated.

3. Which of the following are not vector functions in Electromagnetics?
b) Divergence
c) Curl
d) There is no non- vector functions in Electromagnetics

Answer: d [Reason:] Since all the coordinates in electromagnetic are space coordinates, direction and magnitude both are important. Thus all functions are vector only.

4. The work done of vectors force F and distance d, separated by angle θ can be calculated using,
a) Cross product
b) Dot product
c) Addition of two vectors
d) Cannot be calculated

Answer: b [Reason:] Force is a vector quantity, whereas distance is scalar. Work is defined as the product of force and distance, which is given by dot product.

5. Find whether the vectors are parallel, (-2,1,-1) and (0,3,1)
a) Parallel
b) Collinearly parallel
c) Not parallel
d) Data insufficient

Answer: c [Reason:] Two vectors are parallel when their cross product is zero. Since their cross product is 4i + 2j – 6k (non-zero), the vectors are not parallel.

6. Lorentz force is based on,
a) Dot product
b) Cross product
c) Both dot and cross product
d) Independent of both

Answer: b [Reason:] Lorentz force is given by, F = q (v x B).Thus cross product is the answer.

7. Electromagnetic forces are defined by
a) Fleming’s right hand rule
b) Fleming’s left hand rule
d) Ampere law

Answer: b [Reason:] The three left hand fingers denote electric field, magnetic field and wave propagation in free space, analogous to force, magnetic field and current respectively in any conductor.

8. The dot product of two vectors is a scalar. The cross product of two vectors is a vector. State True/False.
a) True
b) False

Answer: a [Reason:] Dot product is an algebraic operation that takes two equal length sequences and returns a scalar. Cross product is a binary operation that calculates area of two vectors, thus vector quantity.

9. Which of the Pythagorean Theorem is valid in Electromagnetics?
a) |dot product| + |dot product| = 1
b) |cross product| – |cross product| = 1
c) |dot product|2 + |cross product|2 = 1
d) |dot product| + |cross product| = 0

Answer: c [Reason:] Option c gives |cos|2 + |sin|2 = 1, which is the right answer.

10. Which of the following is not true?
a) A . (B . C) = scalar value
b) A . (B x C) = scalar value
c) A x (B . C) = scalar value
d) A x (B x C) = vector value

Answer: c [Reason:] Cross product of dot product of two vectors is a vector value.

## Set 3

1. The electrostatic energy in an electric field does not depend on which of the following?
a) Magnitude of charges
b) Permittivity
c) Applied electric field
d) Flux lines

Answer: c [Reason:] The energy in an electric field directly magnitude of charges. Thus electric field and flux density are also dependent. But the applied field affects only the polarisation and it is independent of the energy in the field.

2. Calculate the energy in an electric field with flux density 6 units and field intensity of 4 units.
a) 12
b) 24
c) 36
d) 48

Answer: a [Reason:] The energy in an electric field is given by, W = 0.5 x D x E, where D = 6 and E = 4. We get W = 0.5 x 6 x 4 = 12 units.

3. Calculate the energy in an electric field with permittivity of 56 and field intensity of 36π(in μJ)
a) 3.16
b) 5.16
c) 7.16
d) 9.16

Answer: a [Reason:] The energy in an electric field is given by, W = 0.5 x D x E. Since D = εE, we get W = 0.5 x ε x E2. On substituting the data, we get 3.16 microjoule.

4. Equipotential surface is a
a) Real surface
b) Complex surface
c) Imaginary surface
d) Not existing surface

Answer: c [Reason:] Equipotential surface is an imaginary surface in an electric field of a given charge distribution in which all the points on the surface are at the same electric potential.

5. The work done in moving a test charge from one point to another in an equipotential surface is zero. State True/False.
a) True
b) False

Answer: a [Reason:] Since the electric potential in the equipotential surface is the same, the work done will be zero.

6. When curl of a path is zero, the field is said to be conservative. State True/False.
a) True
b) False

Answer: a [Reason:] By Stoke’s theorem, when curl of a path becomes zero, then ∫ E.dl = 0. In other words the work done in a closed path will always be zero. Fields having this property is called conservative or lamellar fields.

7. If the electric potential is given, which of the following cannot be calculated?
a) Electrostatic energy
b) Electric field intensity
c) Electric flux density
d) Permittivity

Answer: a [Reason:] Using potential, we can calculate electric field directly by gradient operation. From E, the flux density D can also be calculated. Thus it is not possible to calculate energy directly from potential.

8. Superconductors exhibit which of the following properties?
a) Ferromagnetism
b) Polarisation
c) Diamagnetism
d) Ferrimagnetism

Answer: c [Reason:] Since superconductors have very good conductivity at low temperatures (σ->∞), they have nearly zero resistivity and exhibit perfect diamagnetism.

9. Debye is the unit used to measure
a) Permittivity
b) Electric dipole moment
c) Magnetic dipole moment
d) Susceptibility

Answer: b [Reason:] Debye is the standard unit for measurement of electric dipole moment. 1 Debye = 3.336 x 10-30 Coulomb-meter.

10. Ceramic materials possess which of the following properties?
a) Brittle and low dielectric constant
b) Rigid and low dielectric constant
c) Brittle and high dielectric constant
d) Rigid and high dielectric constant

Answer: c [Reason:] Ceramic materials are generally brittle. Since these materials are used in capacitors, they have higher dielectric constant than polymer. With respect to energy, they possess high electrostatic energy due to very high dielectric constant (W α ε).

## Set 4

1. Find the force that exists in an electromagnetic wave.
a) Electrostatic force
b) Magnetostatic force
c) Lorentz force
d) Electromotive force

Answer: c [Reason:] In an electromagnetic wave, the force of the electric and magnetic field both coexist. This is given by F = qE + q(v x B). It is called Lorentz force.

2. In an field having a force of 12N and distance 20cm, the torque will be
a) 0.24
b) 2.4
c) 24
d) 12/20

Answer: b [Reason:] The torque is defined as the product of the force and distance in a field. Thus T = F x d = 12 x 0.2 = 2.4 units.

3. Find the torque in a conductor having current 2A, flux density 50 units, length 15cm and distance of 8m.
a) 120
b) 240
c) 800
d) 350

Answer: a [Reason:] The torque on a conductor is given by T = BILd, where L x d is the area of the conductor. Thus the torque will be, T = 50 x 2 x 0.15 x 8 = 120 units.

4. The distance of the conductor when the area and length of the conductor is 24m2 and 13.56m.
a) 1.76
b) 2.67
c) 1.52
d) 2.15

Answer: a [Reason:] We know that the surface integral is the area component which is the product of two dimensions given by length and distance in a conductor. Thus A = L x d. To get d, d = A/L = 24/13.56 = 1.76 units.

5. The torque on a conductor with flux density 23 units, current 1.6A and area 6.75 units will be
a) 248.4
b) 192.6
c) 175.4
d) 256.9

Answer: a [Reason:] The maximum torque on a conductor will be at perpendicular angle ie, at 90. The torque will be given as T = BIA, where B = 23, I = 1.6 and A = 6.75.Thus we get, T = 23 x 1.6 x 6.75 = 248.4 units.

6. Consider the conductor to be a coil of turns 60 and the flux density to be 13.5 units, current 0.12A and area 16units. The torque will be
a) 1555.2
b) 1222.5
c) 525.1
d) 255.6

Answer: a [Reason:] For a single turn or loop, the torque will be BIA. For N turns, the torque will be T = NBIA, where N = 60, B = 13.5, I = 0.12 and A = 16. Thus T = 60 x 13.5 x 0.12 x 16 = 1555.2 units.

7. The torque of a conductor is defined only in the case when
a) The field is perpendicular to the loop
b) The plane of the loop is parallel to the field
c) The plane of the loop is perpendicular to the current direction
d) The field and the current direction are same

Answer: b [Reason:] The torque of a conductor is given by T = NBIA. This equation of the conductor is valid only when the plane of the loop is parallel to the magnetic field applied to it.

8. Find the angle at which the torque is minimum.
a) 30
b) 45
c) 60
d) 90

Answer: d [Reason:] The torque of a conductor loop is given by T = BIA cos θ. The torque is minimum refers to zero torque. This is possible only when the angle is 90 or perpendicular.

9. The magnetic moment and torque are related as follows
a) T = BM
b) B = TM
c) M = TB
d) T = M

Answer: a [Reason:] The torque is defined as the product of the magnetic flux density and the magnetic moment. It is given by T = BM, where M = IA is the magnetic moment.

10. Calculate the magnetic moment when a field of B= 51 units is subjected to a torque of 20 units.
a) 0.39
b) 4.2
c) 2.55
d) 3.21

Answer: a [Reason:] The magnetic moment is given by the ratio of the torque and the magnetic flux density. Thus M = T/B, where T = 20 and B = 51 units. We get M = 20/51 = 0.39 units.

## Set 5

1. Find the curl of E when B is given as 15t.
a) 15
b) -15
c) 7.5
d) -7.5

Answer: b [Reason:] From Maxwell first law, we get Curl of E as the negative derivative of B with respect to time. Thus Curl(E) = -dB/dt. On substituting B= 15t and differentiating, Curl(E) = -15 units.

2. The charge build up in a capacitor is due to
a) Conduction current density
b) Displacement current density
c) Polarisation
d) Magnetization

Answer: b [Reason:] The capacitor consists of a dielectric placed between two conducting plates, subjected to a field. The current due to a dielectric is always due to the displacement current density.

3. The surface integral of which parameter is zero?
a) E
b) D
c) B
d) H

Answer: c [Reason:] The divergence of the magnetic flux density is always zero. By Stokes theorem, the surface integral of B is same as the volume integral of the divergence of B. Thus the surface integral of B is also zero.

4. Harmonic electromagnetic fields refer to fields varying sinusoidally with respect to time. State True/False.
a) True
b) False

Answer: a [Reason:] Fields that varying sinusoidally with respect to time are called as harmonic fields. An example for harmonic fields is A sin wt.

5. When electric potential is null, then the electric field intensity will be
a) 0
b) 1
c) dA/dt
d) –dA/dt

Answer: d [Reason:] The electric field intensity is given by E = -Grad(V)- dA/dt, where V is the electric potential and A is the magnetic vector potential. When V is zero, then E = -dA/dt.

6. The gradient of the magnetic vector potential can be expressed as
a) –με dV/dt
b) +με dE/dt
c) –με dA/dt
d) +με dB/dt

Answer: a [Reason:] The gradient of A is the ratio of the negative gradient of electric potential to the speed of light c. We can write c = 1/√(με). Thus grad(A) = -με dV/dt is the required expression.

7. Find the time constant of a capacitor with capacitance of 2 microfarad having an internal resistance of 4 megaohm.
a) 2
b) 0.5
c) 8
d) 0.25

Answer: c [Reason:] The time constant of capacitor is given by T = RC, where R = 4×106 and C = 2×10-6. Thus T = 4×106 x2x10-6 = 8 seconds.

8. Which components exist in an electromagnetic wave?
a) Only E
b) Only H
c) Both E and H
d) Neither E or H

Answer: c [Reason:] In an electromagnetic wave, the electric and magnetic components coexist. They propagate perpendicular to each other and to the direction of propagation in space.

9. The propagation of the electromagnetic waves can be illustrated by
b) Ampere law
c) Flemming rule
d) Coulomb law