# Multiple choice question for engineering

## Set 1

1. The electric field intensity is defined as

a) Force per unit charge

b) Force on a test charge

c) Force per unit charge on a test charge

d) Product of force and charge

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2. Find the force on a charge 2C in a field 1V/m.

a) 0

b) 1

c) 2

d) 3

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3. Find the electric field intensity of two charges 2C and -1C separated by a distance 1m in air.

a) 18 X 10^{9}

b) 9 X 10^{9}

c) 36 X 10^{9}

d) -18 X 10^{9}

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

^{9}E = F/q = 18 X 10

^{9}/2 = 9 X 10

^{9}.

4. What is the electric field intensity at a distance of 20cm from a charge 2 X 10^{-6} C in vacuum?

a) 250,000

b) 350,000

c) 450,000

d) 550,000

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^{-6})/(4∏ X εo X 0.2

^{2}) = 450,000 V/m.

5. Determine the charge that produces an electric field strength of 40 V/cm at a distance of 30cm in vacuum(in 10^{-8}C)

a) 4

b) 2

c) 8

d) 6

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^{2}) Q = (4000 X 0.3

^{2})/ (9 X 10

^{9}) = 4 X 10

^{-8}C.

6. The field intensity of a charge defines the impact of the charge on a test charge placed at a distance. It is maximum at d = 0cm and minimises as d increases. State True/False

a) True

b) False

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7. Electric field of an infinitely long conductor of charge density λ, is given by E = λ/(2πεh).aN. State True/False.

a) True

b) False

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8. Electric field intensity due to infinite sheet of charge σ is

a) Zero

b) Unity

c) σ/ε

d) σ/2ε

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^{2}+a

^{2})) Here, h is the distance of the sheet from point P and a is the radius of the sheet. For infinite sheet, α = 90. Thus E = σ/2ε.

9. For a test charge placed at infinity, the electric field will be

a) Unity

b) +∞

c) Zero

d) -∞

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^{2}) When distance d is infinity, the electric field will be zero, E= 0.

10. In electromagnetic waves, the electric field will be perpendicular to which of the following?

a) Magnetic field intensity

b) Wave propagation

c) Both H and wave direction

d) It propagates independently

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## Set 2

1. Convert the point (3,4,5) from Cartesian to spherical coordinates

a) (7.07,45⁰,53⁰)

b) (0.707,45⁰,53⁰)

c) (7.07,54⁰,63⁰)

d) (0.707,54⁰,63⁰)

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^{2}+y

^{2}+z

^{2}) = √50 = 7.07 Θ = cos

^{-1}(z/r) = cos

^{-1}(5/5√2) = 45⁰ Φ = tan

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

^{-1}(4/3) = 53⁰.

2. Example of spherical system in the following is

a) Charge in space

b) Charge in box

c) Charge in dielectric

d) Uncharged system

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3. Spherical systems are employed in waveguides. State True/False

a) True

b) False

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4. Choose which of following condition is not required for a waveguide to exist.

a) The dimensions should be in accordance with desired frequency

b) Cut-off frequency should be minimum 6GHz

c) The shape should be spherical

d) No specific condition is required for waveguide design

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5. Find the spherical coordinates of A(2,3,-1)

a) (3.74, 105.5⁰, 56.13⁰)

b) (3.74, 105.5⁰, 56.31⁰)

c) (3.74, 106.5⁰, 56.13⁰)

d) (3.74, 106.5⁰, 56.31⁰)

### View Answer

^{2}+y

^{2}+z

^{2}) = √14 = 3.74 Θ = cos

^{-1}(z/r) = cos

^{-1}(-1/3.74) = 105.5⁰ Φ = tan

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

^{-1}(3/2) = 56.31⁰.

6. Find the Cartesian coordinates of B(4,25⁰,120⁰)

a) (0.845, 1.462, 3.625)

b) (-0.845, 1.462, 3.625)

c) (-8.45, 2.462, 6.325)

d) (8.45, 2.462, 6.325)

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7. The area of sphere can be computed from the sphere volume. State True/False.

a) True

b) False

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8. Given B= (10/r)i+( rcos θ) j+k in spherical coordinates. Find Cartesian points at (-3,4,0)

a) -2i + j

b) 2i + k

c) i + 2j

d) –i – 2k

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^{2}+y

^{2}+z

^{2}) = √25 = 5 Θ = cos

^{-1}(z/r) = 1 Φ = tan

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

^{-1}(-4/3) Thus, B = -2i + j.

9. The scalar factor of spherical coordinates is

a) 1, r, r sin θ

b) 1, r, r

c) r, r, 1

d) r, 1, r

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10. Transform the vector (4,-2,-4) at (1,2,3) into spherical coordinates.

a) 3.197i – 2.393j + 4.472k

b) -3.197i + 2.393j – 4.472k

c) 3.197i + 2.393j + 4.472k

d) -3.197i – 2.393j – 4.472k

### View Answer

^{2}+y

^{2}+z

^{2}) = 3.74 Θ = cos

^{-1}(z/r) = cos

^{-1}(3/3.74) = 36.7⁰ Φ = tan

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

^{-1}(2/1) = 63.4⁰ A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sin θ)j + (-4 sin φ – 2 cos φ)k On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.

## Set 3

1. In conductors, which condition will be true?

a) σ/ωε > 1

b) σωε > 1

c) σ/ωε < 1

d) σωε < 1

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2. For metals, the conductivity will be

a) 0

b) 1

c) -1

d) Infinity

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3. In conductors, which two parameters are same?

a) Wavelength and phase constant

b) Phase and attenuation constant

c) Attenuation constant and skin depth

d) Skin depth and wavelength

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4. Calculate the velocity of wave propagation in a conductor with frequency 5 x 10^{8} rad/s and phase constant of 3 x 10^{8} units.

a) 3/5

b) 15

c) 5/3

d) 8

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5. Calculate the wavelength of the wave with phase constant of 3.14 units.

a) 1

b) 2

c) 0.5

d) 4

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6. For dielectrics, which two components will be in phase?

a) E and wave direction

b) H and wave direction

c) Wave direction and E x H

d) E and H

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7. In perfect conductors, the phase shift between the electric field and magnetic field will be

a) 0

b) 30

c) 45

d) 90

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8. The expression for phase constant is given by

a) Phase constant β = ωμε

b) Phase constant ω = με

c) Phase constant β = ω√(με)

d) Phase constant β = 1/ωμε

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9. In waveguides, which of the following conditions will be true?

a) V > c

b) V < c

c) V = c

d) V >> c

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10. The attenuation constant in lossless dielectrics will be

a) 0

b) 1

c) -1

d) ∞

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## Set 4

1. For a dielectric, the condition to be satisfied is

a) σ/ωε > 1

b) σ/ωε < 1

c) σ = ωε

d) ωε = 1

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2. For a perfect dielectric, which parameter will be zero?

a) Conductivity

b) Frequency

c) Permittivity

d) Permeability

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3. Calculate the phase constant of a wave with frequency 12 rad/s and velocity 3×10^{8} m/s(in 10^{-8} order)

a) 0.5

b) 72

c) 4

d) 36

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^{8}and ω = 12, we get β = 12/(3×10

^{8}) = 4 x 10

^{-8}m/s.

4. For a lossless dielectric, the attenuation will be

a) 1

b) 0

c) -1

d) Infinity

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5. Calculate the velocity of a wave with frequency 2 x10^{9} rad/s and phase constant of 4 x 10^{8} units.

a) 0.5

b) 5

c) 0.2

d) 2

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^{9}/ 4 x 10

^{8}= 5 units.

6. Which of the following is the correct relation between wavelength and the phase constant of a wave?

a) Phase constant = 2π/wavelength

b) Phase constant = 2π x wavelength

c) Phase constant = 1/(2π x wavelength)

d) Phase constant = wavelength/2π

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7. In lossy dielectric, the phase difference between the electric field E and the magnetic field H is

a) 90

b) 60

c) 45

d) 0

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8. The intrinsic impedance is the ratio of square root of

a) Permittivity to permeability

b) Permeability to permittivity

c) Phase constant to wavelength

d) Wavelength to phase constant

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9. Calculate the skin depth of a material with attenuation constant of 2 units.

a) 2

b) 1

c) 0.5

d) 4

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10. Calculate the phase constant of a wave with skin depth of 2.5 units.

a) 5/2

b) 5

c) 2

d) 2/5

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11. An example for lossless propagation is

a) Dielectric waveguide propagation

b) Conductor propagation

c) Cavity resonator propagation

d) It is not possible

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12. Skin depth phenomenon is found in which materials?

a) Insulators

b) Dielectrics

c) Conductors

d) Semiconductors

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## Set 5

1. The magnetic energy of a magnetic material is given by

a) BH/2

b) B/2H

c) H/2B

d) B/H

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^{2}or B

^{2}/2μ.

2. The induced emf in a material opposes the flux producing it. This is

a) Faraday law

b) Ampere law

c) Lenz law

d) Curie law

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3. The energy in a magnetic material is due to which process?

a) Emf

b) Magnetization

c) Magnetostriction

d) Polarization

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4. The flux lines of two energised coils overlapping on each other will give

a) Series aiding

b) Shunt aiding

c) Series opposing

d) Shunt opposing

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5. The resistance in a magnetic material is called as

a) Capacitance

b) Inductance

c) Reluctance

d) Magnetic resistance

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6. Calculate the reluctance of the material with a mmf of 3.5 units and flux of 7units.

a) 32.5

b) 10.5

c) 0.5

d) 2

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7. Which of the following relations is correct?

a) NI = Sφ

b) NS = Iφ

c) Nφ = SI

d) NI = S/φ

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8. Calculate the reluctance of a material with length 2π x 10^{-4} in air with area 0.5.

a) 1

b) 10

c) 100

d) 1000

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^{-4}, A = 0.5 and μ = 4π x 10

^{-7}, we get S = 10

^{3}/(2×0.5) = 1000 units.

9. Ampere turn is equivalent to which element?

a) Sφ

b) S/φ

c) φ/S

d) S

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10. The line integral of the magnetic field intensity is given by

a) Turns

b) Flux density

c) MMF

d) Current element