GATE Electrical Engineering

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. $\rho=-3 \rho_0$ f...

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...

The given equation represents a magnetic field strength $\bar{H}(r, \theta, \phi)$ in the spherical coordinate system, in free space. Here, $\hat{r}$ and $\hat{\theta}$ represent t...

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...

A long conducting cylinder having a radius b is placed along the z-axis. The current density is $$\overrightarrow J = {J_a}{r^3}\widehat z$$ for the region r

If the magnetic field intensity ($$\overrightarrow H $$) in a conducting region is given by the expression, $$\overrightarrow H = {x^2}\widehat i + {x^2}{y^2}\widehat j + {x^2}{y^2...

One Coulomb of point charge moving with a uniform velocity $10 \hat{x} \mathrm{~m} / \mathrm{s}$ enters the region $x \geq 0$ having a magnetic flux density $\vec{B}=(10 y \hat{x}+...

Which one of the following vector functions represents a magnetic field $\vec{B}$ ? ( $\hat{x}, \hat{y}$, and $\hat{z}$ are unit vectors along $x$-axis, $y$-axis and $z$-axis respe...

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...

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 charge...

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 c...

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 \tim...

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...

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.

A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines in...

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

In cylindrical coordinate system, the potential produced by a uniform ring charge is given $$\phi=f\left(r,\;z\right)$$, where f is a continuous function of r and z. Let $$\overrig...

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 divergenc...

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...

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

The following four vector fields are given in cartesian coordinate system. The vector field which does not satisfy the property of magnetic flux density is

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...

The flux density at a point in space is given by $$\overrightarrow B=\;4x{\widehat a}_x\;+\;2ky{\widehat a}_y\;+\;8{\widehat a}_z\;\;Wb/m^2$$. The value of constant k must be equal...

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...

Divergence of the three-dimentional radial vector field $$\overrightarrow F$$ is

$$$F\left(x,y\right)=\left(x^2\;+\;xy\right)\;{\widehat a}_x\;+\;\left(y^2\;+\;xy\right)\;{\widehat a}_y$$$. Its line integral over the straight line from (x, y)=(0,2) to (2,0) eva...

A coil of 300 turns is wound on a non-magnetic core having a mean circumference of 300 mm and a cross-sectional area of 300 mm 2 . The inductance the coil corresponding to a magnet...

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 $$4$$ $...

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 fl...

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\;+\...

An inductor designed with $$400$$ turns coil wound on an iron core of $$16\,\,c{m^2}$$ cross sectional area and with a cut of an air gap length of $$1$$ $$mm$$. The coil is connect...

An inductor designed with $$400$$ turns coil wound on an iron core of $$16\,\,c{m^2}$$ cross sectional area and with a cut of an air gap length of $$1$$ $$mm$$. The coil is connect...

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 intensit...

The concept of an electrically short, medium, and long line is primarily based on the

Consider the following statements with reference to the equation $$\nabla.\overrightarrow J=-\frac{\partial\rho}{\partial t}$$ 1. This is a point from the continuity equation 2. Di...

Which of the following statements holds for the divergence of electric and magnetic flux densities?

The inductance of a long solenoid of length $$1000$$ $$mm$$ wound uniformly with $$3000$$ turns on a cylindrical paper tube of $$60$$ $$mm$$ diameter is

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 per...

Two conductors are carrying forward and return current of $$ + {\rm I}$$ and $$ - {\rm I}$$ as shown in Fig. The magnetic field intensity $$\overrightarrow H $$ at point $$P$$ is

Given a vector field $$\overrightarrow F ,$$ the divergence theorem states that

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 $$\left( { - 1,\,1,\,1} \right)$$ (coordi...

The conductors of a $$10$$ $$km$$ long, single phase, two wire line are separated by a distance of $$1.5$$ $$m.$$ The diameter of each conductor is $$1$$ $$cm.$$ If the conductors...

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 th...

An electron with velocity $$'u'$$ is placed in an electric field, $$E$$ and magnetic field, $$B.$$ The force experienced by the electron is given by

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...

An electromagnetic field is radiated from

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...

Two parallel wires separated by a distance $$'d'$$ are carrying a current $$'{\rm I}'$$ in the same direction. The magnetic field along a line running parallel to these wires at mi...

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 thes...

The laws of electromagnetic induction (Faraday's and Lenz's law) are summarized in the following equation

An electron moves in the $$X$$-$$Y$$ plane with a speed of $${10^6}\,\,m/s.$$ Its velocity vector makes an angle of $${60^ \circ }$$ with $$X$$ axis. A magnetic field of magnitude...

A infinitely long straight wire carries $$1000$$ $$A$$ of current and in the vicinity, there is a circular conducting loop of $$100$$ $$mm$$ diameter with the center of the loop $$...

In a uniform electric field, field lines and equipotentials

The capacitance of an isolated sphere of radius 10 cm in air is equal to _____ pF.

The velocity of propagation of electromagnetic wave 'n' an underground cable with relative permittivity of 3 will be ________m/sec

If v, w, q stand for voltage, energy and charge, then v can be expressed

The energy stored in the magnetic field of solenoid $$30$$ $$cm$$ long and $$3$$ $$cm$$ diameter wound with $$1000$$ turns of wire carrying a current of $$10$$ $$A$$ is

A monochromatic plane electromagnetic wave travels in vacuum in the position $$x$$ direction ($$x, y, z$$ system of coordinates). The electric and magnetic fields can be expressed...

In electrostatic field $$\nabla\times\overrightarrow E\equiv0$$

Static magnetic fields induce currents in closed conducting loops.

Match the following List-$${\rm I}$$ with List-$${\rm II}$$ List $$-$$ $${\rm I}$$ $$(a)$$ Line charge $$(b)$$ Magnetic Flux Density $$(c)$$ Displacement current $$(d)$$ Power flow...

The line integral of the vector potential A around the boundary of a surface S represents

Which of the following equations represents the Gauss's law in a homogeneous isotropic medium?

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