# Multiple choice question for engineering

## Set 1

1. Coulomb is the unit of which quantity?

a) Field strength

b) Charge

c) Permittivity

d) Force

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2. Coulomb law is employed in

a) Electrostatics

b) Magnetostatics

c) Electromagnetics

d) Maxwell theory

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3. Find the force between 2C and -1C separated by a distance 1m in air(in newton).

a) 18 X 10^{6}

b) -18 X 10^{6}

c) 18 X 10^{-6}

d) -18 X 10^{-6}

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^{2}) = -2 X 9/(10

^{-9}X 12) = -18 X 10

^{9}.

4. Two charges 1C and -4C exists in air. What is the direction of force?

a) Away from 1C

b) Away from -4C

c) From 1C to -4C

d) From -4C to 1C

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5. Find the force of interaction between 60 stat coulomb and 37.5 stat coulomb spaced 7.5cm apart in transformer oil(εr=2.2) in 10^{-4} N,

a) 8.15

b) 5.18

c) 1.518

d) 1.815

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^{9}) C F = (1.998 X 1.2488 X 10

^{-16})/(4∏ X 8.854 X 10

^{-12}X 2.2 X (7.5 X 10

^{-2})

^{2}) = 1.815 X 10

^{-4}N.

6. Find the force between two charges when they are brought in contact and separated by 4cm apart, charges are 2nC and -1nC, in μN.

a) 1.44

b) 2.44

c) 1.404

d) 2.404

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7. The Coulomb law is an implication of which law?

a) Ampere law

b) Gauss law

c) Biot Savart law

d) Lenz law

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8. Two small diameter 10gm dielectric balls can slide freely on a vertical channel. Each carry a negative charge of 1μC. Find the separation between the balls if the lower ball is restrained from moving.

a) 0.5

b) 0.4

c) 0.3

d) 0.2

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^{-3}X 9.81 = 9.81 X 10

^{-2}N. On calculating r by substituting charges, we get r = 0.3m.

9. A charge of 2 X 10^{-7} C is acted upon by a force of 0.1N. Determine the distance to the other charge of 4.5 X 10^{-7} C, both the charges are in vacuum.

a) 0.03

b) 0.05

c) 0.07

d) 0.09

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^{2}) , substituting q1, q2 and F, r2 = q1q2/(4∏εoF) = We get r = 0.09m.

10. For a charge Q1, the effect of charge Q2 on Q1 will be,

a) F1 = F2

b) F1 = -F2

c) F1 = F2 = 0

d) F1 and F2 are not equal

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## Set 2

1. Curl is defined as the angular velocity at every point of the vector field. State True/False.

a) True

b) False

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2. The curl of curl of a vector is given by,

a) Div(Grad V) – (Del)^{2}V

b) Grad(Div V) – (Del)^{2}V

c) (Del)^{2}V – Div(Grad V)

d) (Del)^{2}V – Grad(Div V)

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^{2}V is a standard result of the curl operation.

3. Which of the following theorem use the curl operation?

a) Green’s theorem

b) Gauss Divergence theorem

c) Stoke’s theorem

d) Maxwell equation

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4. The curl of a curl of a vector gives a

a) Scalar

b) Vector

c) Zero value

d) Non zero value

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5. Find the curl of the vector and state its nature at (1,1,-0.2)

F = 30 i + 2xy j + 5xz^{2} k

a) √4.01

b) √4.02

c) √4.03

d) √4.04

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^{2}j + 2y k. At (1,1,-0.2), Curl F = -0.2 j + 2 k. |Curl F| = √(-0.2

^{2}+2

^{2}) = √4.04.

6. Is the vector is irrotational. E = yz i + xz j + xy k

a) Yes

b) No

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7. Find the curl of A = (y cos ax)i + (y + e^{x})k

a) 2i – ex j – cos ax k

b) i – ex j – cos ax k

c) 2i – ex j + cos ax k

d) i – ex j + cos ax k

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8. Find the curl of the vector A = yz i + 4xy j + y k

a) xi + j + (4y – z)k

b) xi + yj + (z – 4y)k

c) i + j + (4y – z)k

d) i + yj + (4y – z)k

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9. Curl cannot be employed in which one of the following?

a) Directional coupler

b) Magic Tee

c) Isolator and Terminator

d) Waveguides

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10. Which of the following Maxwell equations use curl operation?

a) Maxwell 1st and 2nd equation

b) Maxwell 3rd and 4th equation

c) All the four equations

d) None of the equations

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## Set 3

1. The real part of the propagation constant is the

a) Attenuation constant

b) Phase constant

c) Permittivity

d) Permeability

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2. The phase constant of a wave is given by

a) ω√(LC)

b) ω√(L/C)

c) ω√(C/L)

d) ω√(1/LC)

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3. The cut off frequency of the dominant mode in a TE wave in the line having a and b as 2.5 cm and 1 cm respectively is

a) 4.5 GHz

b) 5 GHz

c) 5.5 GHz

d) 6 GHz

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_{10}. The cut off frequency will be mc/2a, where m = 1 and a = 0.025 are given. On substituting, we get the frequency as 1 x 3 x 10

^{8}/2 x 0.025 = 6 GHz.

4. The cut off frequency of the TE_{01} mode will be

a) mc/2a

b) mc/2b

c) nc/2a

d) nc/2b

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5. The condition which will satisfy the dimensions of the waveguide is

a) a = b

b) a > b

c) a < b

d) ab = 0

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6. The cut off wavelength of the TE_{10} mode having a broad wall dimension of 5cm is

a) 0.1

b) 1

c) 10

d) 0.01

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7. The broad wall dimension of a waveguide having a cut off frequency of 7.5 GHz is

a) 1

b) 2

c) 3

d) 4

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8. The sin θ in the waveguide refers to the ratio of the

a) Frequency to wavelength

b) Wavelength to frequency

c) Cut off frequency to frequency

d) Frequency to cut off frequency

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9. Is the transmission of a frequency 5 GHz possible in waveguides?

a) Yes

b) No

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10. The dimension for a waveguide in dominant mode with a cut off wavelength of 2 units is

a) 2

b) 4

c) 6

d) 8

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11. The waveguides are used in a transmission line for

a) Increasing transmission coefficient

b) Increasing reflection coefficient

c) Decreasing transmission coefficient

d) Decreasing reflection coefficient

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12. The attenuation coefficient of the wave having a resistance of 15 ohm in a 50 ohm line is

a) 15

b) 1.5

c) 0.15

d) 0.015

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_{o}. On substituting for R = 15 and Z

_{o}= 50, we get α = 15/(2 x 50) = 0.15 units.

## Set 4

1. The cylindrical coordinate system is also referred to as

a) Cartesian system

b) Circular system

c) Spherical system

d) Space system

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2. Transform the vector B=yi+(x+z)j located at point (-2,6,3) into cylindrical coordinates.

a) (6.325,-71.57,3)

b) (6.325,71.57,3)

c) (6.325,73.57,3)

d) (6.325,-73.57,3)

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^{2}+y

^{2}) = √40 = 6.325 Φ = tan

^{-1}(y/x) = tan

^{-1}(-6/2) = -71.57 z = 3.

3. Cylindrical systems have the following scalar values respectively

a) 1, ρ ,1

b) 1, 1, 1

c) 0,1,0

d) 1,0,0

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4. A charge located at point p (5,30⁰,2) is said to be in which coordinate system?

a) Cartesian system

b) Cylindrical system

c) Spherical system

d) Space system

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5. Cylindrical system is employed in waveguides. State True/False.

a) True

b) False

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6. The pressure inside a piston cylinder is a variable of

a) Radius

b) Plane angle

c) Z plane distance

d) Constant, not a variable

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7. Charges filled inside a cylindrical will possess flux in which direction?

a) Upwards

b) Downwards

c) Laterally outwards

d) Inwards

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8. Rectangular waveguides dominate the circular waveguides. Find the reason.

a) Low cut-off frequency

b) Easy to design

c) More wave propagation

d) The statement is false

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9. Transform the spherical system B = (10/r)i + (10cos θ)j + k into cylindrical form at (5, π/2, -2)

a) 2.467i + j + 1.167k

b) 2.467i – j + 1.167k

c) 2.467i – j – 1.167k

d) 2.467i + j – 1.167k

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^{2}+-2

^{2}) = √29 sin θ = 5/√29 and cos θ = -2/√29 Thus, B = 2.467i + j + 1.167k.

10. Convert the given rectangular coordinates A(2,3,1) into corresponding cylindrical coordinates

a) (3.21,56.31,1)

b) (3.21,57.31,0)

c) (3.61,57.31,0)

d) (3.61,56.31,1)

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^{2}+y

^{2}) = √13 = 3.61 Φ = tan

^{-1}(y/x) = 56.31 z = 1 Thus, A = (3.61,56.31,1).

## Set 5

1. A dielectric is always an insulator. But an insulator is not necessarily a dielectric. State True/False.

a) True

b) False

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2. Identify a good dielectric.

a) Iron

b) Ceramics

c) Plastic

d) Magnesium

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3. A dielectric can be made a conductor by

a) Compression

b) Heating

c) Doping

d) Freezing

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4. Find the dielectric constant for a material with electric susceptibility of 4.

a) 3

b) 5

c) 8

d) 16

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5. For a dielectric which of the following properties hold good?

a) They are superconductors at high temperatures

b) They are superconductors at low temperatures

c) They can never become a superconductor

d) They have very less dielectric breakdown voltage

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6. The magnetic field which destroys the superconductivity is called

a) Diamagnetic field

b) Ferromagnetic field

c) Ferrimagnetic field

d) Critical field

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7. The magnetic susceptibility in a superconductor will be

a) Positive

b) Negative

c) Zero

d) Infinity

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8. The superconducting materials will be independent of which of the following?

a) Magnetic field

b) Electric field

c) Magnetization

d) Temperature

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9. Find the mean free path of an electron travelling at a speed of 18m/s in 2 seconds.

a) 9

b) 36

c) 0.11

d) 4.5

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10. Find the velocity of an electron when its kinetic energy is equal to one electron volt (in 10^{5}m/s).

Given charge of an electron e = 1.6 x 10^{-19} and mass of an electron m = 9.1 x 10^{-31}.

a) 3.9

b) 4.9

c) 5.9

d) 6.9

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^{2}/2 = eV. Put e and m in the equation to get velocity v = 5.9 x 10

^{5}m/s.