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...

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...

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...

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...

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...

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...

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...

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}+...

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 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...

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...

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...

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...

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...

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

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 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...

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 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...

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 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...

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...

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\;+\...

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

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

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...

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

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...

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...

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...

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...

An electromagnetic field is radiated from

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...

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...

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

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 $$...

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

In a uniform electric field, field lines and equipotentials

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

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

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

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...

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...

Static magnetic fields induce currents in closed conducting loops.

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

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