Electrostatics · Electromagnetic Fields · GATE EE

Marks 1
20
Marks 2
26
Marks 5
4
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Marks 1

1

A uniform ring charge of radius $R$ carries a total charge $Q$. Which one of the following options correctly quantifies the magnitude of the force on a point charge of strength kept at the center of the ring? ( $\in$ is the permittivity of the medium))

GATE EE 2026
2

Which one of the following figures represents the radial electric field distribution $E_R$ caused by a spherical cloud of electrons with a volume charge density. $\rho=-3 \rho_0$ for $0 \leq R \leq a$ (both $\rho_0, a$ are positive and $R$ is the radial distance) and $\rho=0$ for $R>a$ ?

GATE EE 2025
3

A $1 \mu \mathrm{C}$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10 \mu \mathrm{C}$ is moved from $(0,10,0)$ to $(5,5,5)$ and subsequently to $(5,0,0)$, then the total work done is

$\_\_\_\_$ mJ . (Round off to 2 decimal places). Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ in SI units. All coordinates are in meters.

GATE EE 2021
4
A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x - y plane to be a conducting ground plane.

Take $${\varepsilon _0} = 8.85 \times {10^{ - 12}}$$ F/m.

The Z component of the E field at (0, 0, 0.1) is closest to
GATE EE 2018
5
Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed.
GATE EE 2017 Set 2
6
Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the particles are released but are constrained to move along the same straight line. Which of these will collide first?
GATE EE 2017 Set 1
7
Consider a function $$\overrightarrow f=\frac1{r^2}\widehat r$$ where r is the distance from the origin and $$\widehat r$$ is the unit vector in the radial direction. The divergence of the function over a sphere of radius R, which includes the origin, is
GATE EE 2015 Set 1
8
Match the following. GATE EE 2015 Set 2 Electromagnetic Fields - Electrostatics Question 40 English
GATE EE 2015 Set 2
9
Two semi-infinite dielectric regions are separated by a plane boundary at y = 0. The dielectric constants of region 1 (y< 0) and region 2 (y>0) are 2 and 5, respectively. Region 1 has uniform electric field $$\overrightarrow E=3{\widehat a}_x\;+\;4{\widehat a}_y\;+\;2{\widehat a}_z$$, where $${\widehat a}_x$$, $${\widehat a}_y$$, and $${\widehat a}_Z$$ are unit vectors along the x, y and z axes, respectively. The electric field in region 2 is
GATE EE 2015 Set 2
10
A hollow metallic sphere of radius r is kept at potential of 1 Volt. The total electric flux coming out of the concentric spherical surface of radius R(>r) is
GATE EE 2014 Set 3
11
A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is place symmetrically with respect to the plates. GATE EE 2014 Set 2 Electromagnetic Fields - Electrostatics Question 43 English If the potential difference between one of the plates and the nearest surface of dielectric interface is 2 Volts, then the ratio $$\varepsilon_1\;:\;\varepsilon_2$$ is
GATE EE 2014 Set 2
12
Divergence of the three-dimentional radial vector field $$\overrightarrow F$$ is
GATE EE 2010
13
Divergence of the vector field $$$\overrightarrow V\left(x,y,z\right)=-\left(x\cos xy\;+\;y\right)\;\widehat i\;+\;\left(y\cos xy\right)\;\widehat j\;+\;\left(\sin\;z^2\;+\;x^2\;+\;y^2\right)\widehat k$$$ is
GATE EE 2007
14
A parallel plate capacitor is shown in Fig. It is made of two square metal plates of $$400$$ $$mm$$ side. The $$14$$ $$mm$$ space between the plates is filled with two layers of dielectrics of $${\varepsilon _r} = 4,6\,\,mm$$ thick and $${\varepsilon _r} = 2,8\,\,mm$$ thick. Neglecting fringing of fields at the edges, the capacitance is GATE EE 2004 Electromagnetic Fields - Electrostatics Question 26 English
GATE EE 2004
15
Given a vector field $$\overrightarrow F ,$$ the divergence theorem states that
GATE EE 2002
16
In a uniform electric field, field lines and equipotentials
GATE EE 1997
17
If v, w, q stand for voltage, energy and charge, then v can be expressed
GATE EE 1996
18
In electrostatic field $$\nabla\times\overrightarrow E\equiv0$$
GATE EE 1994
19
Which of the following equations represents the Gauss's law in a homogeneous isotropic medium?
GATE EE 1992
20
An electrostatic potential is given by $$\phi=2x\sqrt y$$ volt in the rectangular co-ordinate system. The magnitude of the electric field at x = 1 m,y = 1 m is _________V/m
GATE EE 1992

Marks 2

1

A uniform spherical volume charge distribution of radius 2 m , centered at the origin, has a strength of $\frac{3}{\pi} \times 10^{-6} \mathrm{C} / \mathrm{m}^3$. A point charge of strength $\pi \times 8.854 \times 10^{-12} \mathrm{C}$ is moved from $(-3,0,-4)$ to $(0,0,4)$ in Cartesian coordinate system. The relative permittivity of the medium is 1 and the coordinate values are in meters. The work done during the process is $\_\_\_\_$ $\mu \mathrm{J}$. (Round off to two decimal places)

GATE EE 2026
2

An air filled cylindrical capacitor (capacitance $C_0$ ) of length $L$, with $a$ and $b$ as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its crosssectional view is shown in Figure (i). In order to increase the capacitance, a dielectric material of relative permittivity $\varepsilon_r$ is inserted inside $50 \%$ of the annular region as shown in figure (ii). The value of $\varepsilon_r$ for which the capacitance of the capacitor in figure (ii), becomes $5 C_0$ is

GATE EE 2025 Electromagnetic Fields - Electrostatics Question 5 English
GATE EE 2025
3

In the $(x, y, z)$ coordinate system, three point-charges $Q$, $Q$, and $\alpha Q$ are located in free space at $(-1, 0, 0)$, $(1, 0, 0)$, and $(0, -1, 0)$, respectively. The value of $\alpha$ for the electric field to be zero at $(0, 0.5, 0)$ is _________________ (rounded off to 1 decimal place).

GATE EE 2024
4

The closed curve shown in the figure is described by

$$r = 1 + \cos \theta $$, where $$r = \sqrt {{x^2} + {y^2}} ;x = r\cos \theta ,y = r\sin \theta $$

The magnitude of the line integral of the vector field $$F = - y\widehat i + x\widehat j$$ around the closed curve is ___________ (Round off to 2 decimal places).

GATE EE 2023 Electromagnetic Fields - Electrostatics Question 8 English

GATE EE 2023
5

A quadratic function of two variables is given as

$$f({x_1},{x_2}) = x_1^2 + 2x_2^2 + 3{x_1} + 3{x_2} + {x_1}{x_2} + 1$$

The magnitude of the maximum rate of change of the function at the point (1, 1) is ___________ (Round off to the nearest integer).

GATE EE 2023
6

As shown in the figure below, to concentric conducting spherical shells, centred at r = 0 and having radii r = c and r = d are maintained at potentials such that the potential V(r) at r = c is V1 and V(r) at r = d is V2. Assume that V(r) depends only on r, where r is the radial distance. The expression for V(r) in the region between r = c and r = d is

GATE EE 2022 Electromagnetic Fields - Electrostatics Question 10 English

GATE EE 2022
7

Consider a large parallel plate capacitor. The gap $d$ between the two plates is filled entirely with a dielectric slab of relative permittivity 5 . The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field $E_2$ in the gap to the original electric field $E_1$ is $\_\_\_\_$ .

GATE EE 2021
8
The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86 pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _____________ (up to 2 decimal places).
GATE EE 2018
9
A thin soap bubble of radius R = 1 cm, and thickness a = 3.3 µm(a << R), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r. The volume of the soap in the thin bubble is $$4\mathrm{πR}^2\mathrm a$$ and that of the drop is $$\frac43\mathrm{πr}^3$$. The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is __________. (Give the answer up to two decimal places.) GATE EE 2017 Set 2 Electromagnetic Fields - Electrostatics Question 36 English
GATE EE 2017 Set 2
10
Two electric charges q and -2q are placed at (0,0) and (6,0) on the x-y plane. The equation of the zero equipotential curve in the x-y plane is
GATE EE 2016 Set 1
11
A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strengths of air and glass are 30 kV/cm and 300 kV/cm, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is ______. GATE EE 2015 Set 1 Electromagnetic Fields - Electrostatics Question 33 English
GATE EE 2015 Set 1
12
Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +𝑄 is placed at a distance of 𝑑 from both sheets. The net force on the charge is $$\frac{Q^2}{4{\mathrm{πε}}_0}\frac{\overrightarrow K}{d^2}$$ , where $$\overrightarrow K$$ is given by GATE EE 2015 Set 2 Electromagnetic Fields - Electrostatics Question 34 English
GATE EE 2015 Set 2
13
A perfectly conducting metal plate is placed in x-y plane in a right handed coordinate system. A charge of $$+32{\mathrm{πε}}_0\sqrt2$$ columbs is placed at coordinate (0, 0, 2). $${\mathrm\varepsilon}_0$$ is the permittivity of free space. Assume $$\widehat i,\;\widehat j,\;\widehat k$$ to be unit vectors along x, y and z axes respectively. At the coordinate $$\left(\sqrt2,\sqrt2,0\right)$$, the electric field vector $$\overrightarrow E$$ (Newtons/Columb) will be GATE EE 2014 Set 3 Electromagnetic Fields - Electrostatics Question 32 English
GATE EE 2014 Set 3
14
A dielectric slab with 500 mm x 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform electric field of $$E=6{\widehat a}_x+8{\widehat a}_y$$ kV /mm. The relative permittivity of the dielectric material is equal to 2. The value of constant $$\varepsilon_0$$ is $$8.85\times10^{-12}\;F/m$$ . The energy stored in the dielectric in Joules is
GATE EE 2013
15
A capacitor is made with a polymeric dielectric having an $$\varepsilon_0$$ of 2.26 and a dielectric breakdown strength of 50 kV/cm. The permittivity of free space is 8.85 pF/m. If the rectangular plates of the capacitor have a width of 20 cm and a length of 40 cm, then the maximum electric charge in the capacitor is
GATE EE 2011
16
$$$F\left(x,y\right)=\left(x^2\;+\;xy\right)\;{\widehat a}_x\;+\;\left(y^2\;+\;xy\right)\;{\widehat a}_y$$$. Its line integral over the straight line from (x, y)=(0,2) to (2,0) evaluates to
GATE EE 2009
17
A capacitor consists of two metal plates each $$500 \times 500\,\,m{m^2}$$ and spaced $$6$$ $$mm$$ apart. The space between the metal plates is filled with a glass plate of $$4$$ $$mm$$ thickness and a layer of paper of $$2$$ $$mm$$ thickness. The relative permittivity of the glass and paper are $$8$$ and $$2$$ respectively. Neglecting the fringing effect, the capacitance will be (Given that $${\varepsilon _0} = 8.85 \times {10^{ - 12}}\,F/m$$ )
GATE EE 2008
18
Two point charges $${Q_1} = 10\,\,\mu C$$ and $${Q_2} = 20\,\,\mu C$$ are placed at coordinates $$(1,1,0)$$ and $$\left( { - 1, - 1,0} \right)$$ respectively. The total electric flux passing through a plane $$z=20$$ will be
GATE EE 2008
19
A solid sphere made of insulating material has a radius $$R$$ and has a total charge $$Q$$ distributed uniformly in its volume. What is the magnitude of the electric field intensity, $$E,$$ at distribution $$r\left( {0 < r < R} \right)$$ inside the sphere?
GATE EE 2007
20
A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ($${t_1}$$ and $${t_2}$$) as shown in Fig. The two different dielectric materials are separated by a conducting foil $$F.$$ The voltage of the conducting foil is GATE EE 2003 Electromagnetic Fields - Electrostatics Question 21 English
GATE EE 2003
21
A parallel plate capacitor has an electrode area of $$100$$ $$m{m^2}$$, with a spacing of $$0.1$$ $$mm$$ between the electrodes. The dielectric between the plates is air with a permittivity of $$8.85 \times {10^{ - 12}}\,\,F/m.$$ The charge on the capacitor is $$100$$ $$V$$. The stored energy in the capacitor is
GATE EE 2003
22
A point charge of $$+1$$ $$nC$$ is placed in a space with a permittivity of $$8.85 \times {10^{ - 12}}\,F/m$$ as shown in Fig. The potential difference $${V_{PQ}}$$ between two points $$P$$ and $$Q$$ at distance of $$40mm$$ and $$20$$ $$mm$$ respectively from the point charge is GATE EE 2003 Electromagnetic Fields - Electrostatics Question 22 English
GATE EE 2003
23
Given the potential function in free space to be $$V\left( x \right) = \left( {50{x^2} + 50{y^2} + 50{z^2}} \right)$$ volts, the magnitude (in volts /metre) and the direction of the electric field at a point $$\left( {1,\,\, - 1,\,\,1} \right),$$ where the dimensions are in metres, are
GATE EE 2001
24
The electric field $$\overrightarrow E $$ (in volts/metre) at the point $$(1, 1, 0)$$ due to a point charge of $$+1$$ $$\mu C$$ located at $$\left( { - 1,\,1,\,1} \right)$$ (coordinates in metres) is
GATE EE 2001
25
The capacitance of an isolated sphere of radius 10 cm in air is equal to _____ pF.
GATE EE 1997
26
The capacitance of the arrangement shown in Fig. is ................... $$pF$$ GATE EE 1997 Electromagnetic Fields - Electrostatics Question 13 English
GATE EE 1997

Marks 5

1
Show via the construction of a suitable Gaussian surface, that the capacitance of a spherical capacitor consisting of two concentric shells of radii $$a$$ and $$b$$ is given by $$C = 4\pi {\varepsilon _0}{{ab} \over {\left( {b - a} \right)}}$$ where $${\varepsilon _0}$$ is the free space permittivity.
GATE EE 2000
2
A charge $$+Q$$ is uniformly distributed throughout the volume of a dielectric sphere of radius $$R$$ and dielectric constant $$'{\varepsilon _R}'.$$ Based on Gauss law, determine the expressions for the electric field $$E$$ as a function of distance $$'r'$$ from the center of the sphere, within the ranges $$0 < r < R$$ and $$R \le r.$$ Indicate expression $$(s)$$ for the critical point $$(s)$$ on the sketch.
GATE EE 1999
3
An infinite number of charges, each equal to $$'q'$$ are placed along the $$x=1,x=2, x=4, x=8, x=16$$ and so on, Find the potential and electric field at point $$x=0,$$ due to these system of charges.
GATE EE 1998
4
Determine the electric field intensity at the point $$P$$ for the arrangement shown in Fig. GATE EE 1997 Electromagnetic Fields - Electrostatics Question 14 English
GATE EE 1997
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