# GATE Questions & Answers of Electromagnetic Fields Electrical Engineering

#### Electromagnetic Fields 22 Question(s)

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 $\in_0=8.85\times10^{-12}$ F/m. The $Z$ component of the E field at (0, 0, 0.1) is closest to

A transformer with toroidal core of permeability $\mu$ is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius $r\ll\;R$ , and neglecting any leakage flux, the best estimate for the mean radius R is

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).

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 inside the cylinder will

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 release but are constrained to move along the same straight line. Which of these will collide first?

The magnitude of magnetic flux density (B) in micro Teslas (µT), at the center of a loop of wire wound as a regular hexagon of side length 1 m carrying a current (I=1 A), and placed in vacuum as shown in the figure is ___________. (Give the answer up to two decimal places.)

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

The figures show diagramatic representations of vector fields $\overrightarrow{X,}\overrightarrow{Y,}$ and $\overrightarrow Z,$ respectively. Which one of the following choices is true?

A thin soap bubble of radius $R=1$ cm, and thickness $a=3.3\;\mu m(a\ll R)$, 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 $4\mathrm{πR}^2$ 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.)

In cylindrical coordinate system, the potential produced by a uniform ring charge is given by $\phi =f\left(r,z\right)$, where $f$ is a continuous function of r and z. Let $\stackrel{\to }{E}$ be the resulting electric field. Then the magnitude of $\nabla ×\stackrel{\to }{E}$

A soft-iron toroid is concentric with a long straight conductor carrying a direct current I. If the relative permeability μr of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent points located just inside and just outside the toroid, is _______.

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

A parallel plate capacitor filled with two dielectrics is shown in the figure below. If the electric field in the region A is 4 kV/cm, the electric field in the region B, in kV/cm, is

Two electrodes, whose cross-sectional view is shown in the figure below, are at the same potential. The maximum electric field will be at the point

A rotating conductor of 1 m length is placed in a radially outward (about the z-axis) magnetic flux density (B) of 1 Tesla as shown in figure below. Conductor is parallel to and at 1 m distance from the z-axis. The speed of the conductor in r.p.m. required to induce a voltage of 1 V across it, should be __________.

Consider a one-turn rectangular loop of wire place in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4Ω, and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is given by where radian/second. The power absorbed ( in Watt) by the loop from the magnetic field is __________.

A steady current I is flowing in the –x direction through each of two infinitely long wires at $y=±\frac{L}{2}$ as shown in the figure. The permeability of the medium is ${\mu }_{0}$. The $\stackrel{\to }{B}$ -field at (0,L,0) is

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 _______.

Match the following

Two semi-infinite dielectric regions are separated by a plane boundary at $y=0$ . The dielectric constant of region $1\left(y<0\right)$ and region $2\left(y>0\right)$ are 2 and 5, respectively. Region 1 has uniform electric field $\stackrel{\to }{E}=3{\stackrel{^}{a}}_{x}+4{\stackrel{^}{a}}_{y}+2{\stackrel{^}{a}}_{z,}$where ${\stackrel{^}{a}}_{x}$, ${\stackrel{^}{a}}_{y}$ and are unit vector along the $x, y$ and $z$ axes, respectively. The electric field in region 2 is

A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown in the figure. The value of μ0 is $4\mathrm{\pi }×{10}^{-7}$ in SI unit. If a uniform magnetic field intensity $\stackrel{\to }{H}={10}^{7}\stackrel{^}{z}$ A/m is applied, then the peak value of the induced voltage,${V}_{turn}$ (in volts), is __________.
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 $\frac{{Q}^{2}}{4{\mathrm{\pi \epsilon }}_{0}}\frac{K}{{d}^{2}}$ where K is given by