Electrostatic Fields and Capacitance - Electricity and Magnetism - Instrumentation Engineering Previous Year Questions

1

2010 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2010

The electric charge density in the region \(R: x^2 + y^2 \leq 1, y \leq 0\) is given as \(\sigma(x,y) = 1\) C/m², where \(x\) and \(y\) are in meters. The total charge (in coulomb) contained in the region \(R\) is

A

\(4\pi\)

B

\(2\pi\)

C

\(\pi/2\)

D

0

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2

2013 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2013 [Session 1]

For a vector $E$, which one of the following statements is NOT TRUE?

A

If $\nabla \cdot E = 0$, $E$ is called solenoidal.

B

If $\nabla \times E = 0$, $E$ is called conservative.

C

If $\nabla \times E = 0$, $E$ is called irrotational.

D

If $\nabla \cdot E = 0$, $E$ is called irrotational.

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3

2013 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2013 [Session 2]

For a vector \( E \), which one of the following statements is NOT TRUE?

A

If \(\nabla \cdot E = 0 \), \(E \) is called solenoidal.

B

If \(\nabla \times E = 0 \), \(E \) is called conservative.

C

If \(\nabla \times E = 0 \), \(E \) is called irrotational.

D

If \(\nabla \cdot E = 0 \), \(E \) is called irrotational.

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4

2013 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2013 [Session 3]

For a vector E, which one of the following statements is NOT TRUE?

A

If ∇·E = 0, E is called solenoidal.

B

If ∇×E = 0, E is called conservative.

C

If ∇×E = 0, E is called irrotational.

D

If ∇·E = 0, E is called irrotational.

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5

2024 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2024

The capacitor shown in the figure has parallel plates, with each plate having an area A. The thickness of the dielectric materials are d₁ and d₂ and their relative permittivities are ε₁ and ε₂, respectively. Assume that the fringing field effects are negligible and ε₀ is the permittivity of free space.
If d₁ is decreased by δd₁, the resultant capacitance becomes

A

\(\frac{\varepsilon_0 A}{d_1 - \delta d_1 + \frac{d_2}{\varepsilon_2}}\)

B

\(\frac{\varepsilon_0 A}{d_2 + \frac{d_1}{\varepsilon_2}}\)

C

\(\frac{\varepsilon_0 A}{d_2 - \delta d_2 + \frac{d_1}{\varepsilon_2}}\)

D

\(\frac{\varepsilon_0 A}{d_1 + \delta d_1 + \frac{d_2}{\varepsilon_2}}\)

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6

2024 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2024

The capacitance formed between two concentric spherical metal shells having radii \(x\) and \(y\) with \(y > x\) is

Note: \(\epsilon\) is the permittivity of the medium between the shells.

A

\(4\pi\epsilon\left(\frac{xy}{y-x}\right)\)

B

\(4\pi\epsilon\left(\frac{x^2}{y-x}\right)\)

C

\(4\pi\epsilon\left(\frac{y^2}{y-x}\right)\)

D

\(4\pi\epsilon\left(\frac{y^2-xy}{x}\right)\)

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7

2025 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2025

An infinite sheet of uniform charge ρs = 10 C/m² is placed on z = 0 plane. The medium surrounding the sheet has a relative permittivity of 10. The electric flux density, in C/m², at a point P(0, 0, 5), is Note: â, b̂, and ĉ are unit vectors along the x, y, and z directions, respectively.

A

5 ĉ

B

0.25 ĉ

C

10 ĉ

D

0.5 ĉ

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8

2021 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2021

An infinitely long line, with uniform positive charge density, lies along the z-axis. In cylindrical coordinates \( (r, \theta, z) \), at any point \( P \) not on the z-axis, the direction of the electric field is

A

\(\hat{r} \)

B

\(\hat{\theta} \)

C

\(\hat{z} \)

D

\(\frac{\hat{r} + \hat{z}}{\sqrt{2}} \)

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9

2022 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2022

A capacitor is constructed using two concentric spheres and air as the dielectric medium (permittivity of air = \(8.854 \times 10^{-12}\) F/m). The radii of the inner and outer spheres are \(a=10\) cm and \(b=15\) cm, respectively. The capacitance (in picofarads) is ______ (round off to 2 decimal places)

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10

2026 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2026

An electric field has a potential of \[ V(x, y, z) = \sqrt{x^2 + y^2 + z^2} \] V.
A charge of 1 coulomb placed at \[ (\hat{i} + \hat{j} + \hat{k}) \] experiences a force of
\[ \vec{F} = (a\hat{i} + b\hat{j} + c\hat{k}) \] N
The values of \[ (a, b, c) \] are _____.

A

\(a = \frac{1}{\sqrt{3}}, b = \frac{1}{\sqrt{3}}, c = \frac{1}{\sqrt{3}} \)

B

\(a = \frac{1}{3}, b = \frac{1}{3}, c = \frac{1}{3} \)

C

\(a = 0, b = 1, c = \frac{1}{\sqrt{3}} \)

D

\(a = 0, b = 1, c = \frac{1}{3} \)

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11

2026 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2026

The potential difference between nodes A and B in a circuit is v_A − v_B = 5 V. The work done in moving a charge of 1 coulomb from point B to A is ____ J. (answer in integer)

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12

2026 · Instrumentation Engineering · Electricity and Magnetism · Electrostatic Fields and Capacitance

Instrumentation Engineering (IN) 2026

An electric field in free space is
E = (2x + 5y + 6z)i + (5x + 4y + 10z)j + (6x + 10y + 2z)k V/m.
The charge density is ____ C/m³. (ε₀ is the permittivity of free space)

A

8ε₀

B

10ε₀

C

6ε₀

D

4ε₀

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