GATE Overflow for GATE IN - Questions without answers in Electricity and Magnetism

GATE IN 2026 | Question: 5

Mon, 23 Feb 2026 13:37:50 +0000

An electric field has a potential of $V(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}} \mathrm{~V}$. A charge of $1$ coulomb placed at $(\hat{\imath}+\hat{\jmath}+\hat{k})$ experiences a force of

$$\vec{F}=(a \hat{\imath}+b \hat{\jmath}+c \hat{k}) \mathrm{N}$$

The values of $(a, b, c)$ are $\_\_\_\_$.

$a=\dfrac{1}{\sqrt{3}}, b=\dfrac{1}{\sqrt{3}}, c=\dfrac{1}{\sqrt{3}}$
$a=\dfrac{1}{3}, b=\dfrac{1}{3}, c=\dfrac{1}{3}$
$a=0, b=1, c=\dfrac{1}{\sqrt{3}}$
$a=0, b=1, c=\dfrac{1}{3}$

GATE IN 2026 | Question: 22

Mon, 23 Feb 2026 13:37:20 +0000

The potential difference between nodes $A$ and $B$ in a circuit is $v_{A}-v_{B}=5 \mathrm{~V}$. The work done in moving a charge of $1$ coulomb from point $B$ to $A$ is $\_\_\_\_$ $\mathrm{J}$. (answer in integer)

GATE IN 2026 | Question: 27

Mon, 23 Feb 2026 13:37:15 +0000

An electric field in free space is

$
\vec{E}=(2 x+5 y+6 z) \hat{\imath}+(5 x+4 y+10 z) \hat{\jmath}+(6 x+10 y+2 z) \hat{k} \mathrm{~V} / \mathrm{m}.$

The charge density is $\_\_\_\_$ $\mathrm{C} / \mathrm{m}^{3} .\left(\epsilon_{0}\right.$ is the permittivity of free space $)$

$8 \epsilon_{0}$
$10 \epsilon_{0}$
$6 \epsilon_{0}$
$4 \epsilon_{0}$

GATE IN 2026 | Question: 28

Mon, 23 Feb 2026 13:37:13 +0000

A straight thin wire carrying a current of $I=1 \mathrm{~A}$ in the direction $\widehat{n}=\dfrac{1}{\sqrt{6}} \hat{\imath}+\dfrac{2}{\sqrt{6}} \hat{\jmath}+\dfrac{1}{\sqrt{6}} \hat{k}$ is placed inside a magnetic field of $\vec{B}=(2 \hat{\imath}+2 \hat{k}) \mathrm{T}$. The force per unit length on the wire is $\_\_\_\_$ $\mathrm{N} / \mathrm{m}$.

$2 \sqrt{6} \hat{\imath}-2 \sqrt{6} \hat{k}$
$\sqrt{\dfrac{3}{2}} \hat{\imath}-\sqrt{\dfrac{3}{4}} \hat{\jmath}+\sqrt{\dfrac{3}{4}} \hat{k}$
$\dfrac{4}{\sqrt{6}} \hat{\imath}-\dfrac{4}{\sqrt{6}} \hat{k}$
$\sqrt{\dfrac{3}{2}} \hat{\imath}+\sqrt{\dfrac{3}{4}} \hat{\jmath}+\sqrt{\dfrac{3}{4}} \hat{k}$

GATE IN 2025 | Question: 9

Thu, 06 Mar 2025 17:18:40 +0000

An infinite sheet of uniform charge $\rho_{s}=10 \mathrm{C} / \mathrm{m}^{2}$ is placed on $z=0$ plane. The medium surrounding the sheet has a relative permittivity of $10$. The electric flux density, in $\mathrm{C} / \mathrm{m}^{2}$, at a point $\mathrm{P}(0,0,5)$, is

Note: $\hat{a}, \hat{b}$, and $\hat{c}$ are unit vectors along the $x, y$, and $z$ directions, respectively.

$5 \hat{c}$
$0.25 \hat{c}$
$10 \hat{c}$
$0.5 \hat{c}$

GATE IN 2025 | Question: 20

Thu, 06 Mar 2025 17:18:12 +0000

A $60 \: \mathrm{V}$ DC source with an internal resistance $R_{\text{i n t}}=0.5 \: \Omega$ is connected through a switch to a pair of infinitely long rails separated by $l=1 \mathrm{~m}$ as shown in the figure. The rails are placed in a constant, uniform magnetic field of flux density $B=0.5 \mathrm{~T}$, directed into the page. A conducting bar placed on these rails is free to move. At the instant of closing the switch, the force induced on the bar is

Note: Assume there is no friction between the bar and the rails. The resistances of the conducting bar and the rails are zero.

$60 \: \mathrm{N}$ in the direction of $\hat{x}$
$60\: \mathrm{N}$ opposite to the direction of $\hat{x}$
$120\: \mathrm{N}$ in the direction of $\hat{x}$
$120\: \mathrm{N}$ opposite to the direction of $\hat{x}$

GATE IN 2024 | Question: 5

Fri, 16 Feb 2024 18:41:04 +0000

The capacitor shown in the figure has parallel plates, with each plate having an area $A$. The thickness of the dielectric materials are $d_{1}$ and $d_{2}$ and their relative permittivities are $\varepsilon_{1}$ and $\varepsilon_{2}$, respectively. Assume that the fringing field effects are negligible and $\varepsilon_{0}$ is the permittivity of free space.

If $\mathrm{d}_{1}$ is decreased by $\delta \mathrm{d}_{1}$, the resultant capacitance becomes

$\dfrac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}_{1}-\delta \mathrm{d}_{1}+\frac{\mathrm{d}_{2}}{\varepsilon_{2}}}$
$\dfrac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}_{2}+\frac{\mathrm{d}_{1}}{\varepsilon_{2}}}$
$\dfrac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}_{2}-\delta \mathrm{d}_{2}+\frac{\mathrm{d}_{1}}{\varepsilon_{2}}}$
$\dfrac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}_{1}+\delta \mathrm{d}_{1}+\frac{\mathrm{d}_{2}}{\varepsilon_{2}}}$

GATE IN 2024 | Question: 10

Fri, 16 Feb 2024 18:41:03 +0000

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.

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

GATE IN 2024 | Question: 26

Fri, 16 Feb 2024 18:40:59 +0000

A wire of circular cross section with radius $a$ is shown in the figure. The current density is given by $\mathbf{J}=k s^{2}$, where $k$ is a constant, $s$ is the radial distance from the axis and $0 \leq s \leq a$.The total current $I$ in the wire is

$\dfrac{\pi k a^{4}}{2}$
$\dfrac{2 \pi k a^{3}}{3}$
$\dfrac{\pi k a^{3}}{2}$
$\dfrac{\pi k a^{4}}{4}$

GATE IN 2024 | Question: 53

Fri, 16 Feb 2024 18:40:53 +0000

Two magnetically coupled coils, when connected in series-aiding configuration, have a total inductance of $500 \mathrm{~mH}$. When connected in series-opposing configuration, the coils have a total inductance of $300 \mathrm{~mH}$. If the self-inductance of both the coils are equal, then the coupling coefficient is $\_\_\_\_\_\_$ (rounded off to two decimal places).

GATE IN 2023 | Question: 17

Mon, 22 May 2023 00:14:44 +0000

The force per unit length between two infinitely long parallel conductors, with a gap of $2 \mathrm{~cm} $ between them is $10~ \mu \mathrm{N} / \mathrm{m}.$ When the gap is doubled, the force per unit length will be____________$\mu \mathrm{N} / \mathrm{m}$ (rounded off to one decimal place).

GATE IN 2022 | Question: 49

Sun, 20 Mar 2022 17:33:55 +0000

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

GATE IN 2021 | Question: 3

Fri, 19 Feb 2021 15:48:41 +0000

An infinitely long line, with uniform positive charge density, lies along the $\text{z}$-axis. In cylindrical coordinate $\left ( r,\varnothing ,z \right )$, at any point $\vec{P}$ not on the $\text{z}$-axis, the direction of the electric field is

$\hat{r}$
$\hat{\varnothing }$
$\hat{z }$
$\frac{\left ( \hat{r}+\hat{z} \right )}{\sqrt{2}}$

GATE IN 2021 | Question: 12

Fri, 19 Feb 2021 15:48:39 +0000

A single-phase transformer has a magnetizing inductance of $\text{250 mH}$ and a core loss resistance of $300\: \Omega$, referred to primary side. When excited with a $\text{230 V}$, $\text{50 Hz}$ sinusoidal supply at the primary, the power factor of the input current drawn, with secondary on open circuit, is ______ (rounded off to two decimal places).

GATE IN 2021 | Question: 39

Fri, 19 Feb 2021 15:48:36 +0000

The figure below shows an electrically conductive bar of square cross-section resting on a plane surface. The bar of mass of $\text{1 kg}$ has a depth of $\text{0.5 m}$ along the $\text{y}$ direction. The coefficient of friction between the bar and the surface is $0.1$. Assume the acceleration due to gravity to be $\text{10 m/}$$s^{2}$. The system faces a uniform flux density $B=-1 \hat{z} T$. At time $t=0$, a current of $\text{10 A}$ is switched onto the bar and is maintained.

When the bar has moved by $\text{1 m}$, its speed in metre per second is ___________ (rounded off to one decimal place).

GATE IN 2021 | Question: 40

Fri, 19 Feb 2021 15:48:36 +0000

A toroid made of $\text{CRGO}$ has an inner diameter of $\text{10 cm}$ and an outer diameter of $\text{14 cm}$. The thickness of the toroid is $\text{2 cm}$. $200$ turns of copper wire is wound on the core $\mu_{o} = 4\pi\times10^{-7}$ $\text{H/m}$ and $\mu_{R}$ of $\text{CRGO}$ is $3000$. When a current of $\text{5 mA}$ flows through the winding, the flux density in the core in millitesla is ______________.

GATE2019 IN: 9

Sun, 10 Feb 2019 14:41:23 +0000

If each of the values of inductance, capacitance and resistance of a series LCR circuit are doubled, the Q-factor of the circuit would

reduce by a factor $\sqrt{2}$
reduce by a factor 2
increase by a factor $\sqrt{2}$
increase by a factor 2

GATE2015-64

Mon, 26 Mar 2018 18:31:55 +0000

A beam of monochromatic light passes through two glass slabs of the same geometrical thickness at normal incidence. The refractive index of the first slab is $1.5$ and that of the second, 2.0. The ratio of the time of passage of the beam through the first to the second slab is _____________.