# Maxwell Equations · Electromagnetics · GATE ECE

Start Practice## Marks 1

GATE ECE 2024

Let $\hat{i}$ and $\hat{j}$ be the unit vectors along $x$ and $y$ axes, respectively and let $A$ be a positive constant. Which one of the following st...

GATE ECE 2022

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is 2s...

GATE ECE 2017 Set 2

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 ...

GATE ECE 2016 Set 3

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

GATE ECE 2016 Set 2

A uniform and constant magnetic field
$$B=\widehat zB$$
exists in the
$$\widehat z$$
direction in vacuum. A particle of
mass m with a small charge q i...

GATE ECE 2016 Set 2

Consider the time-varying vector $$I = \,\hat x\,\,15\,\cos \,(\omega \,t) + \,\hat y\,5\,sin(\omega \,t)$$ in Cartesian coordinates, where $$\omega $...

GATE ECE 2016 Set 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 ρs
,respectively. The value o...

GATE ECE 2015 Set 2

In a source free region in vacuum, if the electrostatic potential
$$\varphi\;=\;2x^2\;+y^2+cz^2$$ , the value of
constant c must be ________________.

GATE ECE 2013

The divergence of the vector field $$\overrightarrow A\;=\;x{\widehat a}_x\;+\;y{\widehat a}_y\;+\;z{\widehat a}_z$$ is

GATE ECE 2011

Consider a closed surface S surrounding volume V. If $$\overrightarrow{\mathrm r}$$
is the position vector of a
point inside S, with $$\widehat n$$ t...

GATE ECE 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 i...

GATE ECE 2007

If C is a closed curve enclosing a surface S, then the magnetic field intensity $$\overrightarrow H $$, the current density $$\overrightarrow J $$
and...

GATE ECE 2006

$$\int\int\left(\nabla\times\mathrm P\right)\;\cdot\mathrm{ds}$$ , where is a vector, is equal to

GATE ECE 2006

$$\nabla \times \nabla \times P$$, where P is a vector, is equal to

GATE ECE 2003

The unit of $$\nabla\times\mathrm H$$ is

GATE ECE 1999

An electric field on a plane is described by its potential V = $$20\left(r^{-1}\;+\;r^{-2}\right)$$ where r
is the distance from the source. The field...

GATE ECE 1999

Identify which one of the following will NOT satisfy the wave equation.

GATE ECE 1998

A loop is rotating about the y-axis in a magnetic field $$$\overrightarrow B\;=\;B_0\cos\left(\mathrm{ωt}\;+\;\mathrm\phi\;\right)\;{\overrightarrow a...

GATE ECE 1998

The Maxwell's equation $$\nabla\times\overrightarrow H\;=\;\overrightarrow J\;+\;\frac{\partial\overrightarrow D}{\partial t}$$ is based on

GATE ECE 1998

The time averaged Poynting vector, in W/m2, for a wave with $$\vec E = 24{e^{j\left( {\omega t + \beta z} \right)}}{\mkern 1mu} {\overrightarrow a _y}...

GATE ECE 1996

A metal sphere with 1 m radius and a surface charge density of 10 Coulombs/m2 is enclosed in
a cube of 10 m side. The total outward electric displac...

GATE ECE 1995

The electric field strength at a distance point, P, due to a point charge, +q,
located at the origin, is 100 $$\mu $$V/m. If the point charge is now...

GATE ECE 1995

In the infinite plane, y = 6 m, there exists a uniform surface charge density of (1/6000$$\pi $$) $$\mu $$C/m2. The associated electric field strength...

GATE ECE 1994

...

## Marks 2

GATE ECE 2022

In an electrostatic field, the electric displacement density vector, $$\overrightarrow D $$, is given by
$$\overrightarrow D (x,y,z) = ({x^3}\overrigh...

GATE ECE 2017 Set 2

An electron (q1) is moving in free space with velocity 105 m/s towards a stationary electron
(q2) far away. The closest distance that this moving elec...

GATE ECE 2016 Set 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 sepa...

GATE ECE 2015 Set 3

A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per
unit length of 172 pF/m. If the ratio of outer radius to inner is...

GATE ECE 2014 Set 4

If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\mathrm{xz}^2\right)\widehat{\m...

GATE ECE 2014 Set 4

The electric field (assumed to be one-dimensional) between two points A and B is shown. Let
$$\psi_A$$ and $$\psi_B$$ be the electrostatic potentials ...

GATE ECE 2014 Set 3

Given the vector $$$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\;+\;\left(\sin\;\mathrm x\righ...

GATE ECE 2012

An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$
The magnetic field at a distance r f...

GATE ECE 2012

An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$.
A hole of radius b (b < a) is no...

GATE ECE 2010

If $$\overrightarrow{\mathrm A}\;=\;\mathrm{xy}\;{\widehat{\mathrm a}}_\mathrm x\;+\;\mathrm x^2\;{\widehat{\mathrm a}}_\mathrm y$$ then $$\oint\overr...

GATE ECE 2008

The value of the integral of the function $$\mathrm g\left(\mathrm x,\mathrm y\right)=4\mathrm x^3\;+\;10\mathrm y^4$$ along the straight
line segment...

GATE ECE 2003

If the electric field intensity is given by $$\mathrm E=\left(\mathrm x{\widehat{\mathrm u}}_\mathrm x\;+\mathrm y{\widehat{\mathrm u}}_\mathrm y+\mat...

GATE ECE 2001

A material has conductivity of 10-2 mho/m and a relative permittivity of 4. The
frequency at which the conduction current in the medium is equal to th...

GATE ECE 1993

Given,$$\overrightarrow V=x\cos^2y\;\;\widehat{\mathrm i}\;+\;\mathrm x^2\mathrm e^\mathrm z\;\widehat{\mathrm j}\;+\;\mathrm{zsin}^2\mathrm y\;\wideh...

GATE ECE 1990

The incoming solar radiation at a place on the surface of the earth is 1.2 KW/m2.The amplitude of the electric field corresponding to this incident po...

GATE ECE 1990

Which of the following field equations indicate that the free magnetic charges do not exits?

GATE ECE 1989

The electric field strength at a far-off point P due to a point charge + q, located at the origin O is 100 millivolts/metre. The point charge is now e...

GATE ECE 1988

Vector potential is a vector

GATE ECE 1988

On either side of a charge-free interface between two media,

GATE ECE 1987

An electrostatic field is said to be conservative when

GATE ECE 1987

Two long parallel wires in free space are separated by a distance R and carry currents of equal magnitude but opposite in direction. At any general po...