# Multiple choice question for engineering

## Set 1

1. The divergence of a vector is a scalar. State True/False.

a) True

b) False

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2. The divergence concept can be illustrated using Pascal’s law. State True/False.

a) True

b) False

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3. Compute the divergence of the vector xi + yj + zk.

a) 0

b) 1

c) 2

d) 3

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4. Find the divergence of the vector yi + zj + xk.

a) -1

b) 0

c) 1

d) 3

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5. Given D = e^{-x}sin y i – e^{-x}cos y j

Find divergence of D.

a) 3

b) 2

c) 1

d) 0

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^{-x}sin y) + Dy(-e

^{-x}cos y ) = -e

^{-x}sin y + e

^{-x}sin y = 0.

6. Find the divergence of the vector F= xe^{-x} i + y j – xz k

a) (1 – x)(1 + e^{-x})

b) (x – 1)(1 + e^{-x})

c) (1 – x)(1 – e)

d) (x – 1)(1 – e)

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^{-x}) + Dy(y)+Dz(-xz) = -xe

^{-x}+ e

^{-x}+ 1 – x = e

^{-x}(1 – x) + (1 – x) = (1 – x)(1 + e

^{-x}).

7. Determine the divergence of F = 30 i + 2xy j + 5xz^{2} k at (1,1,-0.2) and state the nature of the field.

a) 1, solenoidal

b) 0, solenoidal

c) 1, divergent

d) 0, divergent

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^{2}) = 0 + 2x + 10xz = 2x + 10xz Divergence at (1,1,-0.2) will give zero. As the divergence is zero, field is solenoidal. Alternate/Shortcut: Without calculation, we can easily choose option b, as by theory when the divergence is zero, the vector is solenoidal. Option b is the only one which is satisfying this condition.

8. Find whether the vector is solenoidal, E = yz i + xz j + xy k

a) Yes, solenoidal

b) No, non-solenoidal

c) Solenoidal with negative divergence

d) Variable divergence

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9. Find the divergence of the field, P = x^{2}yz i + xz k

a) xyz + 2x

b) 2xyz + x

c) xyz + 2z

d) 2xyz + z

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^{2}yz) + Dy(0) + Dz(xz) = 2xyz + x, which is option b. For different values of x,y,z the divergence of the field varies.

10. Identify the nature of the field, if the divergence is zero and curl is also zero.

a) Solenoidal, irrotational

b) Divergent, rotational

c) Solenoidal, irrotational

d) Divergent, rotational

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## Set 2

1. Choose the best definition of a dipole.

a) A pair of equal and like charges located at the origin

b) A pair of unequal and like charges located at the origin

c) A pair of equal and unlike charges separated by a small distance

d) A pair of unequal and unlike charges separated by a small distance

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2. The potential due to a dipole at a point P from it is the

a) Sum of potentials at the charges

b) Difference of potentials at the charges

c) Multiplication of potentials at the charges

d) Ratio of potentials at the charges

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3. Calculate the dipole moment of a dipole with equal charges 2C and -2C separated by a distance of 2cm.

a) 0.02

b) 0.04

c) 0.06

d) 0.08

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4. Find the angle at which the potential due a dipole is measured, when the distance from one charge is 12cm and that due to other is 11cm, separated to each other by a distance of 2cm.

a) 15

b) 30

c) 45

d) 60

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^{-1}(0.5) = 60.

5. Find the potential due the dipole when the angle subtended by the two charges at the point P is perpendicular.

a) 0

b) Unity

c) ∞

d) -∞

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^{2}). When the angle becomes perpendicular (θ = 90). The potential becomes zero since cos 90 will become zero.

6. For two charges 3C and -3C separated by 1cm and are located at distances 5cm and 7cm respectively from the point P, then the distance between their midpoint and the point P will be

a) 5.91

b) 12.6

c) 2

d) 9

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^{2}Now, r2 = 5 x 7 = 35. We get r = 5.91cm.

7. Calculate the distance between two charges of 4C forming a dipole, with a dipole moment of 6 units.

a) 1

b) 1.5

c) 2

d) 2.5

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8. The potential due to the dipole on the midpoint of the two charges will be

a) 0

b) Unity

c) ∞

d) -∞

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^{2}). Now it is given that potential on the midpoint, which means P is on midpoint, then the distance from midpoint and P will be zero. When r = 0 is put in the above equation, we get V = ∞. This shows that the potential of a dipole at its midpoint will be maximum/infinity.

9. Dipoles in any electric field undergo

a) Magnetism

b) Electromagnetism

c) Magnetisation

d) Polarisation

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10. Dipole moments are used to calculate the

a) Electric field intensity

b) Polarisation patterns

c) Strength of the dipole in the field

d) Susceptibility

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## Set 3

1. The lines of force are said to be

a) Real

b) Imaginary

c) Drawn to trace the direction

d) Not significant

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2. Electric flux density in electric field is referred to as

a) Number of flux lines

b) Ratio of flux lines crossing a surface and the surface area

c) Direction of flux at a point

d) Flux lines per unit area

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3. The electric flux density is the

a) Product of permittivity and electric field intensity

b) Product of number of flux lines and permittivity

c) Product of permeability and electric field intensity

d) Product of number of flux lines and permeability

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4. Which of the following correctly states Gauss law?

a) Electric flux is equal to charge

b) Electric flux per unit volume is equal to charge

c) Electric field is equal to charge density

d) Electric flux per unit volume is equal to volume charge density

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5. The Gaussian surface is

a) Real boundary

b) Imaginary surface

c) Tangential

d) Normal

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6. Find the flux density of a sheet of charge density 25 units in air.

a) 25

b) 12.5

c) 6.25

d) 3.125

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7. A uniform surface charge of σ = 2 μC/m^{2}, is situated at z = 2 plane. What is the value of flux density at P(1,1,1)m?

a) 10^{-6}

b) -10^{-6}

c) 10^{6}

d) -10^{6}

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^{-6}(-az)/2 = -10

^{-6}.

8. Find the flux density of line charge of radius (cylinder is the Gaussian surface) 2m and charge density is 3.14 units?

a) 1

b) 0.75

c) 0.5

d) 0.25

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9. If the radius of a sphere is 1/(4π)m and the electric flux density is 16π units, the total flux is given by,

a) 2

b) 3

c) 4

d) 5

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^{2}D from Gauss law. Ψ = 4π(1/16π

^{2}) X 16π = 4.

10. Find the electric field intensity of transformer oil (εr = 2 approx) with density 1/4π (in 10^{9} units)

a) 2.5

b) 3.5

c) 4.5

d) 5.5

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^{9}units.

## Set 4

1. Potential difference is the work done in moving a unit positive charge from one point to another in an electric field. State True/False.

a) True

b) False

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2. A point charge 2nC is located at origin. What is the potential at (1,0,0)?

a) 12

b) 14

c) 16

d) 18

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^{-9})/(4πε x 1) = 18 volts.

3. Six equal point charges Q = 10nC are located at 2,3,4,5,6,7m. Find the potential at origin.

a) 140.35

b) 141.35

c) 142.35

d) 143.35

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^{-9}/4πεo) (0.5 + 0.33 + 0.25 + 0.2 + 0.166 + 0.142) = 143.35 volts.

4. A point charge 0.4nC is located at (2, 3, 3). Find the potential differences between (2, 3, 3)m and (-2, 3, 3)m due to the charge.

a) 2.5

b) 2.6

c) 2.7

d) 2.8

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5. Find the potential of V = 60sin θ/r^{2} at P(3,60,25)

a) 5.774

b) 6.774

c) 7.774

d) 8.774

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^{2}, put r = 3m, θ = 60 and φ = 25, V = 60 sin 60/3

^{2}= 5.774 volts.

6. Given E = 40xyi + 20x^{2}j + 2k. Calculate the potential between two points (1,-1,0) and (2,1,3).

a) 105

b) 106

c) 107

d) 108

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^{2}dy + 2 dz), from (2,1,3) to (1,-1,0), we get Vpq on integrating from Q to P. Vpq = 106 volts.

7. The potential difference in an open circuit is

a) Zero

b) Unity

c) Infinity

d) Circuit does not exist open

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8. The potential taken between two points across a resistor will be

a) Positive

b) Negative

c) Zero

d) Infinity

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9. What is the potential difference between 10sinθcosφ/r^{2} at A(1,30,20) and B(4,90,60)?

a) 2.386

b) 3.386

c) 4.386

d) 5.386

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^{2}= 4.6985 and Potential at B, Vb = 10sin90cos60/4

^{2}= 0.3125. Potential difference between A and B is, Vab = 4.6985 – 0.3125 = 4.386 volts.

10. The voltage at any point in an ac circuit will be

a) Peak voltage

b) RMS voltage

c) Average voltage

d) Source voltage

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## Set 5

1. The permittivity is also called

a) Electrostatic energy

b) Dielectric constant

c) Dipole moment

d) Susceptibility

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2. Dielectric constant will be high in

a) Conductors

b) Semiconductors

c) Insulators

d) Superconductors

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3. Under the influence of electric field, the dielectric materials will get charged instantaneously. State True/False.

a) True

b) False

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4. Insulators perform which of the following functions?

a) Conduction

b) Convection

c) Provide electrical insulation

d) Allows current leakage at interfaces

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5. Which of the following properties distinguish a material as conductor, insulator and semiconductor?

a) Free electron charges

b) Fermi level after doping

c) Energy band gap

d) Electron density

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6. Semiconductors possess which type of bonding?

a) Metallic

b) Covalent

c) Ionic

d) Magnetic

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7. Find the susceptibility of a material whose dielectric constant is 2.26.

a) 1.26

b) 3.26

c) 5.1

d) 1

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8. The bound charge density and free charge density are 12 and 6 units respectively. Calculate the susceptibility.

a) 1

b) 0

c) 2

d) 72

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9. The susceptibility of free space is

a) 1

b) 0

c) 2

d) ∞

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10. When the electric field becomes zero, which of the following relations hold good?

a) E = P

b) D = P

c) B = P

d) H = P