Maxwell's Equations - Electromagnetics - Electronics & Communication Engineering Previous Year Questions

1

2007 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2007

If C is a closed curve enclosing a surface S, then the magnetic field intensity H, the current density J and the electric flux density D are related by

A

\(\oint_C \vec{H} \cdot d\vec{s} = \oint_S \left(\vec{J} + \frac{\partial \vec{D}}{\partial t}\right) \cdot d\vec{l}\)

B

\(\oint_C \vec{H} \cdot d\vec{l} = \iint_S \left(\vec{J} + \frac{\partial \vec{D}}{\partial t}\right) \cdot d\vec{s}\)

C

\(\iint_S \vec{H} \cdot d\vec{s} = \oint_C \left(\vec{J} + \frac{\partial \vec{D}}{\partial t}\right) \cdot d\vec{l}\)

D

\(\oint_C \vec{H} \cdot d\vec{l} = \iint_S \left(\vec{J} + \frac{\partial \vec{D}}{\partial t}\right) \cdot d\vec{s}\)

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2

2008 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2008

For static electric and magnetic fields in an inhomogeneous source-free medium, which of the following represents the correct form of two of Maxwell's equations?

A

\(\nabla \cdot \mathbf{E} = 0\) and \(\nabla \times \mathbf{B} = 0\)

B

\(\nabla \cdot \mathbf{E} = 0\) and \(\nabla \cdot \mathbf{B} = 0\)

C

\(\nabla \times \mathbf{E} = 0\) and \(\nabla \cdot \mathbf{B} = 0\)

D

\(\nabla \times \mathbf{E} = 0\) and \(\nabla \times \mathbf{B} = 0\)

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3

2009 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2009

Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y-z plane and parallel to the y-axis. The other wire is in the x-y plane and parallel to the x-axis. Which components of the resulting magnetic field are non-zero at the origin ?

A

\(x, y, z\) components

B

\(x, y\) components

C

\(y, z\) components

D

\(x, z\) components

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4

2009 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2009

If a vector field \(\vec{V}\) is related to another vector field \(\vec{A}\) through \(\vec{V} = \nabla \times \vec{A}\), which of the following is true ? Note: \(C\) and \(S_C\) refer to any closed contour and any surface whose boundary is \(C\).

A

\(\oint_C \vec{V} \cdot d\vec{l} = \iint_{S_C} \vec{A} \cdot d\vec{S}\)

B

\(\oint_C \vec{A} \cdot d\vec{l} = \iint_{S_C} \vec{V} \cdot d\vec{S}\)

C

\(\oint_C \nabla \times \vec{V} \cdot d\vec{l} = \iint_{S_C} \nabla \times \vec{A} \cdot d\vec{S}\)

D

\(\oint_C \nabla \times \vec{A} \cdot d\vec{l} = \iint_{S_C} \vec{V} \cdot d\vec{S}\)

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5

2009 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2009

A magnetic field in air is measured to be \[ \vec{B} = B_0 \left( \frac{x}{x^2 + y^2} \hat{y} - \frac{y}{x^2 + y^2} \hat{x} \right) \] What current distribution leads to this field ? [Hint: The algebra is trivial in cylindrical coordinates.]

A

\(\vec{J} = -\frac{B_0 \hat{z}}{\mu_0} \left( \frac{1}{x^2 + y^2} \right), \; r \neq 0\)

B

\(\vec{J} = -\frac{B_0 \hat{z}}{\mu_0} \left( \frac{2}{x^2 + y^2} \right), \; r \neq 0\)

C

\(\vec{J} = 0 \, , \; r \neq 0\)

D

\(\vec{J} = \frac{B_0 \hat{z}}{\mu_0} \left( \frac{1}{x^2 + y^2} \right), \; r \neq 0\)

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6

2011 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2011

A current sheet $\vec{J} = 10\hat{a}_y \,\text{A/m}$ lies on the dielectric interface $x = 0$ between two dielectric media with $\epsilon_{r1} = 5$, $\mu_{r1} = 1$ in Region-1 ($x < 0$) and $\epsilon_{r2} = 2$, $\mu_{r2} = 2$ in Region-2 ($x > 0$). If the magnetic field in Region-1 at $x = 0^-$ is $\vec{H}_1 = 3\hat{a}_x + 30\hat{a}_y \,\text{A/m}$, the magnetic field in Region-2 at $x = 0^+$ is

A

$\vec{H}_2 = 1.5\hat{a}_x + 30\hat{a}_y - 10\hat{a}_z \,\text{A/m}$

B

$\vec{H}_2 = 3\hat{a}_x + 30\hat{a}_y - 10\hat{a}_z \,\text{A/m}$

C

$\vec{H}_2 = 1.5\hat{a}_x + 40\hat{a}_y \,\text{A/m}$

D

$\vec{H}_2 = 3\hat{a}_x + 30\hat{a}_y + 10\hat{a}_z \,\text{A/m}$

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7

2012 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2012

The magnetic field at a distance \( r \) from the center of the wire is proportional to

A

\(r \) for \(r < a \) and \(1/r^2 \) for \(r > a \)

B

\(0 \) for \(r < a \) and \(1/r \) for \(r > a \)

C

\(r \) for \(r < a \) and \(1/r \) for \(r > a \)

D

\(0 \) for \(r < a \) and \(1/r^2 \) for \(r > a \)

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8

2012 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2012

A hole of radius \( b \) (\( b < a \)) is now drilled along the length of the wire at a distance \( d \) from the center of the wire as shown below. The magnetic field inside the hole is

A

uniform and depends only on \(d \)

B

uniform and depends only on \(b \)

C

uniform and depends on both \(b \) and \(d \)

D

non uniform

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9

2013 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2013 [Session 1]

The divergence of the vector field \( \vec{A} = x\hat{a}_x + y\hat{a}_y + z\hat{a}_z \) is

A

0

B

1/3

C

1

D

3

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10

2014 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2014 [Session 1]

The force on a point charge \(+q\) kept at a distance \(d\) from the surface of an infinite grounded metal plate in a medium of permittivity \(\epsilon\) is

A

0

B

\(\frac{q^2}{16\pi\epsilon d^2}\) away from the plate

C

\(\frac{q^2}{16\pi\epsilon d^2}\) towards the plate

D

\(\frac{q^2}{4\pi\epsilon d^2}\) towards the plate

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11

2014 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2014 [Session 3]

A region shown below contains a perfect conducting half-space and air. The surface current \(\boldsymbol{K}_s\) on the surface of the perfect conductor is \(\boldsymbol{K}_s = \hat{\boldsymbol{z}} 2\) amperes per meter. The tangential \(\boldsymbol{H}\) field in the air just above the perfect conductor is

A

(\hat{x} + \hat{z})2\text{ amperes per meter}

B

\(\hat{x}2\text{ amperes per meter}\)

C

\(-\hat{z}2\text{ amperes per meter}\)

D

\(\hat{z}2\text{ amperes per meter}\)

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12

2014 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2014 [Session 4]

The electric field (assumed to be one-dimensional) between two points A and B is shown. Let ψ_A and ψ_B be the electrostatic potentials at A and B, respectively. The value of ψ_B − ψ_A in Volts is __________

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13

2014 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2014 [Session 4]

If E⃗ = −(2y³ − 3yz²)x̂ − (6xy² − 3xz²)ŷ + (6xyz)ẑ is the electric field in a source free region, a valid expression for the electrostatic potential is

A

xy³ − yz²

B

2xy³ − xyz²

C

y³ + xyz²

D

2xy³ − 3xyz²

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14

2016 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2016 [Session 1]

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m², −4 nC/m² and ρ_s, respectively. The value of ρ_s (nC/m²) required to ensure that the electric flux density D = 0 at radius 10 m is ______

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15

2016 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2016 [Session 1]

The current density in a medium is given by \( \vec{J} = \frac{400 \sin\theta}{2\pi(r^2 + 4)} \hat{a}_r \text{ Am}^{-2} \) The total current and the average current density flowing through the portion of a spherical surface \( r = 0.8 \text{ m}, \frac{\pi}{12} \le \theta \le \frac{\pi}{4}, 0 \le \phi \le 2\pi \) are given, respectively, by

A

15.09 A, 12.86 Am^-2

B

18.73 A, 13.65 Am^-2

C

12.86 A, 9.23 Am^-2

D

10.28 A, 7.56 Am^-2

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16

2016 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2016 [Session 2]

A uniform and constant magnetic field \( \mathbf{B} = \hat{z}B \) exists in the \( \hat{z} \) direction in vacuum. A particle of mass \( m \) with a small charge \( q \) is introduced into this region with an initial velocity \( \mathbf{v} = \hat{x}v_x + \hat{z}v_z \). Given that \( B, m, q, v_x \) and \( v_z \) are all non-zero, which one of the following describes the eventual trajectory of the particle?

A

Helical motion in the \(\hat{z} \) direction.

B

Circular motion in the \(xy \) plane.

C

Linear motion in the \(\hat{z} \) direction.

D

Linear motion in the \(\hat{x} \) direction.

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17

2016 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2016 [Session 2]

The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that the energy stored in it is \(E\) when the plate separation is \(d\). The capacitor is then isolated electrically and the plates are moved such that the plate separation becomes \(2d\).
At this new plate separation, what is the energy stored in the capacitor, neglecting fringing effects?

A

2E

B

\(\sqrt{2}E\)

C

E

D

E/2

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18

2016 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2016 [Session 2]

A positive charge \(q\) is placed at \(x = 0\) between two infinite metal plates placed at \(x = -d\) and at \(x = +d\) respectively. The metal plates lie in the \(yz\) plane.
The charge is at rest at \(t = 0\), when a voltage \(+V\) is applied to the plate at \(-d\) and voltage \(-V\) is applied to the plate at \(x = +d\). Assume that the quantity of the charge \(q\) is small enough that it does not perturb the field set up by the metal plates. The time that the charge \(q\) takes to reach the right plate is proportional to

A

\(d / V\)

B

\(\sqrt{d} / V\)

C

\(d / \sqrt{V}\)

D

\(\sqrt{d} / \sqrt{V}\)

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19

2016 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2016 [Session 3]

Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?

A

\(\nabla \cdot \vec{B} = 0 \)

B

\(\nabla \cdot \vec{D} = \rho_v \)

C

\(\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} \)

D

\(\nabla \times \vec{H} = \sigma \vec{E} + \frac{\partial \vec{D}}{\partial t} \)

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20

2017 · Electronics & Communication Engineering · Electromagnetics · Maxwell's Equations

Electronics & Communication Engineering (EC) 2017

Two conducting spheres S1 and S2 of radii a and b (b > a) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure. For some charge placed on this structure, the potential and surface electric field on S1 are Va and Ea, and that on S2 are Vb and Eb, respectively. Then, which of the following is CORRECT?

A

Vₐ = Vb and Eₐ < Eb

B

Vₐ > Vb and Eₐ > Eb

C

Vₐ = Vb and Eₐ > Eb

D

Vₐ > Vb and Eₐ = Eb

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