Magnetostatics · Electromagnetic Fields · GATE EE

Marks 1
15
Marks 2
12
Marks 5
4
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Marks 1

1

A positive point charge with velocity $\vec{v}=5 \hat{x}$ enters a region having electric field $\vec{E}=4 \hat{y}$ and magnetic field $\vec{B}=-6 \hat{z}$. Which one of the following statements is correct for the force on the charge as it enters the region?

GATE EE 2026
2

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 < b where r is the distance in the radial direction. The magnetic field intensity ($$\overrightarrow H $$) for the region inside the conductor (i.e., for r < b) is

GATE EE 2022
3

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 respectively)

GATE EE 2021
4
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
GATE EE 2017 Set 1
5
The figures show diagrammatic representations of vector fields $$\overrightarrow X,\;\overrightarrow Y,\;and\;\overrightarrow Z$$ respectively. Which one of the following choices is true? GATE EE 2017 Set 2 Electromagnetic Fields - Magnetostatics Question 29 English
GATE EE 2017 Set 2
6
A steady current I is flowing in the −x direction through each of two infinitely long wires at $$y=\pm\frac L2$$ as shown in the figure. The permeability of the medium is $$\mu_0$$. The $$\overrightarrow B$$ field at (0,L,0) is GATE EE 2015 Set 1 Electromagnetic Fields - Magnetostatics Question 27 English
GATE EE 2015 Set 1
7
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 to
GATE EE 2013
8
Which of the following statements holds for the divergence of electric and magnetic flux densities?
GATE EE 2006
9
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
GATE EE 2004
10
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

GATE EE 2003
11
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
GATE EE 2000
12
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 midway between them
GATE EE 1999
13
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
GATE EE 1996
14
Static magnetic fields induce currents in closed conducting loops.
GATE EE 1994
15
The line integral of the vector potential A around the boundary of a surface S represents
GATE EE 1993

Marks 2

1

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 the unit vectors along $r$ and $\theta$, respectively. The value of $P$ in the equation should be _________________ (rounded off to the nearest integer).

$$\bar{H}(r, \theta, \phi) = \frac{1}{r^3} ( \hat{r} P \cos \theta + \hat{\theta} P \sin \theta)$$

GATE EE 2024
2

In the figure, the electric field E and the magnetic field B point to x and z directions, respectively, and have constant magnitudes. A positive charge 'q' is released from rest at the origin. Which of the following statement(s) is/are true.

GATE EE 2023 Electromagnetic Fields - Magnetostatics Question 6 English

GATE EE 2023
3

An infinite surface of linear current density $$K = 5{\widehat a_x}$$ A/m exists on the x-y plane, as shown in the figure. The magnitude of the magnetic field intensity (H) at a point (1, 1, 1) due to the surface current in Ampere/meter is ____________ (Round off to 2 decimal places).

GATE EE 2023 Electromagnetic Fields - Magnetostatics Question 5 English

GATE EE 2023
4

If the magnetic field intensity ($$\overrightarrow H $$) in a conducting region is given by the expression, $$\overrightarrow H = {x^2}\widehat i + {x^2}{y^2}\widehat j + {x^2}{y^2}{z^2}\widehat k$$ A/m. The magnitude of the current density, in A/m2, at x = 1 m, y = 2 m and z = 1 m is

GATE EE 2022
5

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 $\vec{B}=(10 y \hat{x}+10 x \hat{y}+10 \hat{z}) \mathrm{T}$. The magnitude of force on the charge at $x=0^{+}$is

$\_\_\_\_$ N. ( $\hat{x}, \hat{y}$ and $\hat{z}$ are unit vectors along x -axis, y -axis and z -axis respectively)

GATE EE 2021
6
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 = 1A), and placed in vacuum as shown in the figure is __________. GATE EE 2017 Set 1 Electromagnetic Fields - Magnetostatics Question 25 English
GATE EE 2017 Set 1
7
The magnitude of magnetic flux density ($$\overrightarrow B$$) at a point having normal distance d meters from an infinitely extended wire carrying current of I A is $$\frac{\mu_0I}{2\mathrm{πd}}$$ (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction. μ0 is permeability of free space. Assume $$\widehat i,\;\widehat j,\;\widehat k$$ to be unit vectors along x, y and z axes respectively. GATE EE 2014 Set 2 Electromagnetic Fields - Magnetostatics Question 24 English Assuming right handed coordinate system, magnetic field intensity, $$\overrightarrow H$$ at coordinate (2,1,0) will be
GATE EE 2014 Set 2
8
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
GATE EE 2014 Set 1
9
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 mm2. The inductance the coil corresponding to a magnetizing current of 3 A will be ( Given that $$\mu_0=4\mathrm\pi\times10^{-7}\;\mathrm H/\mathrm m$$)
GATE EE 2008
10
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 connected to a $$230$$ $$V,$$ $$50$$ $$Hz$$ ac supply. Neglect coil resistance, core loss, iron reluctance and leakage inductance. $$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,H/m} \right)$$

The current in the inductor is

GATE EE 2007
11
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 connected to a $$230$$ $$V,$$ $$50$$ $$Hz$$ ac supply. Neglect coil resistance, core loss, iron reluctance and leakage inductance. $$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,H/m} \right)$$

The average force on the core to reduce the air gap will be

GATE EE 2007
12
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 are of copper, the inductance of the circuit is
GATE EE 2001

Marks 5

1
The magnetic vector potential in a region is defined by $$\overrightarrow A = {e^{ - y}}\sin \left( x \right){\widehat a_z}.$$ An infinitely long conductor, having a cross section area, $$a=5$$ $$m{m^2}$$ and carrying a $$dc$$ current, $${\rm I} = 5\,A$$ in the $$Y$$ direction, passes through this region as shown in Fig. Determine the expression for $$(a)$$ $$\overrightarrow B $$ and $$(b)$$ force density $$\overrightarrow f $$ exerted on the conductor GATE EE 2002 Electromagnetic Fields - Magnetostatics Question 9 English
GATE EE 2002
2
A current $${\rm I}$$ in the short conducting element shown in Fig. produces a flux density $${B_1}$$ at point $$1.$$ Determine the magnitude and the direction of the flux density vector at point $$2$$ GATE EE 2000 Electromagnetic Fields - Magnetostatics Question 11 English
GATE EE 2000
3
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 $${10^{ - 2}}T$$ exists along the $$Y$$ axis. Compute the magnetic force exerted on the electron and its direction.
GATE EE 1998
4
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 $$1$$ $$m$$ away from the straight conductor. Both the wire and the loop are coplanar. Determine the magnitude and direction of current in the loop that produces a zero flux density at its center.
GATE EE 1997
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