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# Multiple choice question for engineering

## Set 1

1. The divergence of which quantity will be zero?
a) E
b) D
c) H
d) B

Answer: d [Reason:] The divergence of the magnetic flux density is always zero. This is because of the non existence of magnetic monopoles in a magnetic field.

2. Find the charge density when the electric flux density is given by 2x i + 3y j + 4z k.
a) 10
b) 9
c) 24
d) 0

Answer: b [Reason:] The charge density is the divergence of the electric flux density by Maxwell’s equation. Thus ρ = Div (D) and Div (D) = 2 + 3 + 4 = 9. We get ρ = 9 units.

3. Find the Maxwell equation derived from Faraday’s law.
a) Div(H) = J
b) Div(D) = I
c) Curl(E) = -dB/dt
d) Curl(B) = -dH/dt

Answer: c [Reason:] From the Faraday’s law and Lenz law, using Stoke’s theorem, we get Curl(E) = -dB/dt. This is the Maxwell’s first law of electromagnetics.

4. Find the Maxwell law derived from Ampere law.
a) Div(I) = H
b) Div(H) = J
c) Curl(H) = J
d) Curl(B) = D

Answer: c [Reason:] From the current density definition and Ohm’s law, the Ampere circuital law Curl(H) = J can be derived. This is Maxwell’s second law of electromagnetics.

5. The Faraday’s law states about which type of EMF?
a) Transformer EMF
b) Back EMF
c) Generator EMF
d) Secondary EMF

Answer: a [Reason:] The stationary loop in a varying magnetic field results in an induced emf due to the change in the flux linkage of the loop. This emf is called as induced or transformer EMF.

6. In which of the following forms can Maxwell’s equation not be represented?
a) Static
b) Differential
c) Integral
d) Harmonic

Answer: a [Reason:] Maxwell equations can be represented in differential/point form and integral form alternatively. Sometimes, it can be represented by time varying fields called harmonic form.

7. The charge build up in the capacitor is due to which quantity?
a) Conduction current
b) Displacement current
c) Convection current
d) Direct current

Answer: b [Reason:] The charge in the capacitor is due to displacement current. It is the current in the presence of the dielectric placed between two parallel metal plates.

8. In metals which of the following equation will hold good?
a) Curl(H) = J
b) Curl(J) = dD/dt
c) Curl(H) = D
d) Curl(J) = dB/dt

Answer: a [Reason:] Generally, the Curl(H) is the sum of two currents- conduction and displacement. In case of metals, it constitutes conduction J and in case of dielectrics, it constitutes the displacement current dD/dt.

9. Find the flux enclosed by a material of flux density 12 units in an area of 80cm.
a) 9.6
b) 12/80
c) 80/12
d) 12/0.8

Answer: a [Reason:] The total flux in a material is the product of the flux density and the area. It is given by flux = 12 x 0.8= 9.6 units.

10. Find the electric flux density of a material with charge density 16 units in unit volume.
a) 1/16
b) 16t
c) 16
d) 162

Answer: c [Reason:] The electric flux density from Maxwell’s equation is given by D = ∫ ρ dv. On substituting ρ = 16 and ∫dv = 1, we get D = 16 units.

## Set 2

1. The first Maxwell law is based on which law?
a) Ampere law
c) Lenz law
d) Faraday and Lenz law

Answer: d [Reason:] The first Maxwell equation states that Curl(E) = -dB/dt. It is based on the emf concept. Thus it is derived from the Faraday and Lenz law.

2. The benefit of Maxwell equation is that
a) Any parameter can be calculated
b) Antenna can be designed
c) Polarisation of the wave can be calculated
d) Transmission line constants can be found

Answer: a [Reason:] The Maxwell equation relates the parameters E, D, H, B. When one parameter is known the other parameters can be easily calculated. In other words, it is used to relate an electric field parameter with its equivalent magnetic field.

3. The correct sequence to find H, when D is given is
a) D-E-B-H
b) D-B-E-H
c) It cannot be computed from the data given
d) D-H

Answer: a [Reason:] There is no direct relation between D and H, so the option D-H is not possible. Using the formula D = εE, the parameter E can be computed from D. By Maxwell equation, Curl(E) = -dB/dt, the parameter B can be calculated. Using the formula B = μH, the parameter H can be calculated. Thus the sequence is D-E-B-H.

4. The curl of the electric field intensity is
a) Conservative
b) Rotational
c) Divergent
d) Static

Answer: b [Reason:] The curl of electric field intensity is Curl(E). From Maxwell law, the curl of E is a non-zero value. Thus E will be rotational.

5. Which of the following identities is always zero for static fields?
b) Curl(Div V)

Answer: d [Reason:] The curl of gradient of a vector is always zero. This is because the gradient of V is E and the curl of E is zero for static fields.

6. Find the Maxwell first law value for the electric field intensity is given by A sin wt az
a) 0
b) 1
c) -1
d) A

Answer: a [Reason:] The value of Maxwell first equation is Curl(E). The curl of E is zero. Thus for the given field, the value of Maxwell equation is zero. Thus the field is irrotational.

7. Find the electric field applied on a system with electrons having a velocity 5m/s subjected to a magnetic flux of 3.6 units.
a) 15
b) 18
c) 1.38
d) 0.72

Answer: b [Reason:] The electric field intensity is the product of the velocity and the magnetic flux density. Thus E = v x B, on substituting v = 5 and B = 3.6, we get E = 5 x 3.6 = 18 units.

8. Which of the following relations holds good?
a) Bq = ILE
b) E = ILBq
c) Eq = ILB
d) B = ILEq

Answer: c [Reason:] The force of a electrostatic field in given by F = Eq. The force on a conductor is given by F = BIL. In the case when a charge exists on a conductor, both the forces can be equated. Thus Eq = BIL is true.

9. When the Maxwell equation is expressed in frequency domain, then which substitution is possible?
a) d/dt = w/j
b) d/dt = j/w
c) d/dt = jw
d) Expression in frequency domain is not possible

Answer: c [Reason:] The conversion of time to frequency domain in Maxwell equation is given by the Fourier Transform. Differentiation in time gives jw in frequency domain. Thus d/dt = jw in frequency domain.

10. Calculate the emf of a material having a flux linkage of 2t2 at time t = 1second.
a) 2
b) 4
c) 8
d) 16

Answer: b [Reason:] The emf of a material is given by Vemf = -dλ/dt. On substituting λ = 2t2, the emf is 4t. At t = 1 sec, the emf will be 4 units.

11. Calculate the emf of a material having flux density 5sin t in an area of 0.5 units.
a) 2.5 sin t
b) -2.5 cos t
c) -5 sin t
d) 5 cos t

Answer: d [Reason:] The emf can be written as Vemf = -d(∫B.ds)/dt. It can be written as Vemf = -B= -5sin t, since the integration and differentiation gets cancelled.

12. To find D from B, sequence followed will be
a) B-E-D
b) B-H-D
c) E-H-D
d) E-B-D

Answer: a [Reason:] Using Maxwell equation, from B we can calculate E by Curl(E) = -dB /dt. From E, D can be calculated by D = εE. Thus the sequence is B->E->D.

## Set 3

1. Maxwell second equation is based on which law?
a) Ampere law
c) Lenz law
d) Coulomb law

Answer: a [Reason:] The second Maxwell equation is based on Ampere law. It states that the field intensity of a system is same as the current enclosed by it, i.e, Curl(H) = J.

2. The Maxwell second equation that is valid in any conductor is
a) Curl(H) = Jc
b) Curl(E) = Jc
c) Curl(E) = Jd
d) Curl(H) = Jd

Answer: a [Reason:] For conductors, the conductivity parameter σ is significant and only the conduction current density exists. Thus the component J = Jc and Curl(H) = Jc.

3. In dielectric medium, the Maxwell second equation becomes
a) Curl(H) = Jd
b) Curl(H) = Jc
c) Curl(E) = Jd
d) Curl(E) = Jd

Answer: a [Reason:] In dielectric medium conductivity σ will be zero. So the current density has only the displacement current density. Thus the Maxwell equation will be Curl(H) = Jd.

4. Find the displacement current density of a material with flux density of 5sin t
a) 2.5cos t
b) 2.5sin t
c) 5cos t
d) 5sin t

Answer: c [Reason:] The displacement current density is the derivative of the flux density. Thus Jd = dD/dt. Put D = 5sin t in the equation, we get Jd = 5cos t units.

5. Find the conduction current density of a material with conductivity 200units and electric field 1.5 units.
a) 150
b) 30
c) 400/3
d) 300

Answer: d [Reason:] The conduction current density is given by Jc = σE, where σ = 200 and E = 1.5. Thus we get, Jc = 200 x 1.5 = 300 units.

6. Calculate the conduction density of a material with resistivity of 0.02 units and electric intensity of 12 units.
a) 300
b) 600
c) 50
d) 120

Answer: b [Reason:] The conduction density is given by Jc = σE, where σ is the inverse of resistivity and it is 1/0.02 = 50. Thus we get, Jc = 50 x 12 = 600 units.

7. In the conversion of line integral of H into surface integral, which theorem is used?
a) Green theorem
b) Gauss theorem
c) Stokes theorem
d) It cannot be converted

Answer: c [Reason:] To convert line integral to surface integral, i.e, in this case from line integral of H to surface integral of J, we use the Stokes theorem. Thus the Maxwell second equation can be written as ∫H.dl = ∫∫J.ds.

8. An implication of the continuity equation of conductors is given by
a) J = σ E
b) J = E/σ
c) J = σ/E
d) J = jwEσ

Answer: a [Reason:] The continuity equation indicates the current density in conductors. This is the product of the conductivity of the conductor and the electric field subjected to it. Thus J = σE is the implication of the continuity equation for conductors.

9. Find the equation of displacement current density in frequency domain.
a) Jd = jwεE
b) Jd = jwεH
c) Jd = wεE/j
d) Jd = jεE/w

Answer: a [Reason:] The displacement current density is Jd = dD/dt. Since D = εE and in frequency domain d/dt = jw, thus we get Jd = jwεE.

10. The total current density is given as 0.5i + j – 1.5k units. Find the curl of the magnetic field intensity.
a) 0.5i – 0.5j + 0.5k
b) 0.5i + j -1.5k
c) i – j + k
d) i + j – k

Answer: b [Reason:] By Maxwell second equation, the curl of H is same as the sum of conduction current density and displacement current density. Thus Curl(H) = J = 0.5i + j – 1.5k units.

11. At dc field, the displacement current density will be
a) 0
b) 1
c) Jc
d) ∞

Answer: a [Reason:] The DC field refers to zero frequency. The conduction current is independent of the frequency, whereas the displacement current density is dependent on the frequency, i.e, Jd = jwεE. Thus at DC field, the displacement current density will be zero.

12. Both the conduction and displacement current densities coexist in which medium?
a) Only conductors in air
b) Only dielectrics in air
c) Conductors placed in any dielectric medium
d) Both the densities can never coexist

Answer: c [Reason:] Conduction density exists only for good conductors and displacement density is for dielectrics in any medium at high frequency. Thus both coexist when a conductor is placed in a dielectric medium.

## Set 4

1. The charge density of a electrostatic field is given by
a) Curl of E
b) Divergence of E
c) Curl of D
d) Divergence of D

Answer: d [Reason:] From the Gauss law for electric field, the volume charge density is the divergence of the electric flux density of the field. Thus Div(D) = ρv.

2. In the medium of free space, the divergence of the electric flux density will be
a) 1
b) 0
c) -1
d) Infinity

Answer: b [Reason:] In free space or air, the charge density will be zero. In other words, the conduction is possible in mere air medium. By gauss law, since the charge density is same as the divergence of D, the Div(D) in air/free space will be zero.

3. In a medium other than air, the electric flux density will be
a) Solenoidal
b) Curl free
c) Irrotational
d) Divergent

Answer: d [Reason:] In any medium other than the air, the conduction is possible, due to the charge carriers. Thus charge density is also non-zero. We can write from Gauss law that Div(D) is non-zero. When the divergence is said to be non-zero, the field is not solenoidal or called as divergent field.

4. For a solenoidal field, the surface integral of D will be,
a) 0
b) 1
c) 2
d) 3

Answer: a [Reason:] For a solenoidal field, the divergence will be zero. By divergence theorem, the surface integral of D and the volume integral of Div(D) is same. So as the Div(D) is zero for a solenoidal field, the surface integral of D is also zero.

5. In a dipole, the Gauss theorem value will be
a) 1
b) 0
c) -1
d) 2

Answer: b [Reason:] The Gauss theorem for an electric field is given by Div(D)= ρ. In a dipole only static charge exists and the divergence will be zero. Thus the Gauss theorem value for the dipole will be zero.

6. Find the electric flux density of a material whose charge density is given by 12 units in a volume region of 0.5 units.
a) 12
b) 24
c) 6
d) 48

Answer: c [Reason:] By Gauss law, Div(D) = ρv. To get D, integrate the charge density given. Thus D = ∫ρv dv, where ρv = 12 and ∫dv = 0.5. We get, D = 12 x 0.5 = 6 units.

7. From the Gauss law for electric field, we can compute which of the following parameters?
a) B
b) H
c) E
d) A

Answer: c [Reason:] From the Gauss law for electric field, we can find the electric flux density directly. On substituting, D= ε E, the electric field intensity can be calculated.

8. The charge density of a system with the position vector as electric flux density is
a) 0
b) 1
c) 2
d) 3

Answer: d [Reason:] The divergence of the electric flux density is the charge density. For a position vector xi + yj + zk, the divergence will be 1 + 1 + 1 = 3. Thus by Gauss law, the charge density is also 3.

9. The sequence for finding E when charge density is given is
a) E-D-ρv
b) E-B-ρv
c) E-H-ρv
d) E-V-ρv

Answer: a [Reason:] From the given charge density ρv, we can compute the electric flux density by Gauss law. Since, D = εE, the electric field intensity can also be computed. Thus the sequence is E-D-ρv.

10. The Gauss law employs which theorem for the calculation of charge density?
a) Green theorem
b) Stokes theorem
c) Gauss theorem
d) Maxwell equation

Answer: c [Reason:] The Gauss divergence theorem is given by ∫ D.ds = ∫Div(D).dv. From the theorem value, we can compute the charge density. Thus Gauss law employs the Gauss divergence theorem.

## Set 5

1. Which quantity is solenoidal in the electromagnetic theory?
a) Electric field intensity
b) Electric flux density
c) Magnetic field intensity
d) Magnetic flux density

Answer: d [Reason:] The divergence of the magnetic flux density is zero. This is the Maxwell fourth equation. As the divergence is zero, the quantity will be solenoidal or divergent less.

2. Which equation will be true, if the medium is considered to be air?
a) Curl(H) = 0
b) Div(H) = 0
c) Grad(H) = 0
d) Div(H) = 1

Answer: b [Reason:] From the Gauss law for magnetic field, the divergence of the magnetic flux density is zero. Also B = μH. Thus divergence of H is also zero, i.e, Div(H) = 0 is true.

3. Find the sequence to find B when E is given.
a) E-D-H-B
b) B-E-D
c) H-B-E-D
d) V-E-B

Answer: a [Reason:] From E, D can be computed as D = εE. Using the Ampere law, H can be computed from D. Finally, B can be calculated from H by B = μH.

4. The Gauss law for magnetic field is valid in
a) Air
b) Conductor
c) Dielectric
d) All cases

Answer: d [Reason:] The Gauss law for magnetic field states that the divergence of B is always zero. This is valid for all cases like free space, dielectric medium etc.

5. The sequence for finding H from E is
a) E-B-H
b) E-V-H
c) E-D-H
d) E-A-H

Answer: a [Reason:] From E, we can compute B using the Maxwell first law. Using B, the parameter H can be found since B = μH. Thus the sequence is E-B-H is true.

6. The reason for non existence of magnetic monopoles is
a) The magnetic field cannot be split
b) Due to permeability
c) Due to magnetization
d) Due to magnetostriction

Answer: a [Reason:] Practically monopoles do not exist, due to the connection between north and south poles. But theoretically, they exist. The reason for their non- existence practically is that, the magnetic field confined to two poles cannot be split or confined to a single pole.

7. The non existence of the magnetic monopole is due to which operation?
b) Divergence
c) Curl
d) Laplacian

Answer: b [Reason:] The Maxwell fourth law or the Gauss law for magnetic field states that the divergence of B is zero, implies the non existence of magnetic monopoles. Thus the operation involved is divergence.

8. Will dielectric breakdown lead to formation of magnetic monopole?
a) Yes
b) No

Answer: b [Reason:] When dielectric breakdown occurs, the material loses its dielectric property and becomes a conductor. When it is subjected to a magnetic field, north and south flux lines coexists, giving magnetic force. Thus there exists magnetic dipole. Suppose if the conductor is broken into very small pieces, still there exist a magnetic dipole in every broken part. In other words, when a piece is broken into half, there cannot exist a north pole in one half and a south pole in the other. Thus monopoles never exist.

9. Which equation will hold good for a magnetic material?
a) Line integral of H is zero
b) Surface integral of H is zero
c) Line integral of B is zero
d) Surface integral of B is zero