Electromagnetic Field Theory
Exam Duration: 45 Mins Total Questions : 30
Which one of the following vector fields is a uniform vector field?
- (a)
\(5z\hat { a } \)
- (b)
\(3x^{ 2 }z\hat { a } _{ z }\)
- (c)
\(\hat { a } _{ x }+2\hat { a } _{ y }\)
- (d)
\(2x\hat { a } _{ x }-3\hat { a } _{ z }\)
A \(2\mu C\) point charge is located at A(4,3,5) in free space. The electric field at P(8,12,2) is
- (a)
\(131.1\hat { u_{ \rho } } +1.597\hat { u_{ \phi } } -49.4\hat { u_{ z } } \)
- (b)
\(159.7\hat { u_{ \rho } } +27.4\hat { u_{ \phi } } -49.4\hat { u_{ z } } \)
- (c)
\(131.1\hat { u_{ \rho } } +27.4\hat { u_{ \phi } } -49.4\hat { u_{ z } } \)
- (d)
\(159.7\hat { u_{ \rho } } +137.1\hat { u_{ \phi } } -49.4\hat { u_{ z } } \)
A uniform volume charge density of \(0.2\ \mu C/m^{ 2 }\) is present throughout the special spherical shell extending from r=3 cm to r=5 cm. If \(\rho =0\) elsewhere, the total charge present throughout the shell will be
- (a)
41.05 pC
- (b)
257.92 pC
- (c)
82.1 pC
- (d)
129.0 pC
A material has angle of loss tangent equal to \(\frac { \pi }{ 4 } \) rad then the material is
- (a)
conductor
- (b)
insulator
- (c)
semiconductor
- (d)
Cannot be determined
A monopole consists of
- (a)
a single charge
- (b)
two positive and two negative charges
- (c)
two positive and one negative charges
- (d)
two positive and one positive charges
Uniform line charge of 20nC/m and -20 nC/m are located in the x = 0 plane at y = 3 and y = -3 m, respectively. The \(\overrightarrow { E } \) at P(6,0,6) will be
- (a)
\(-24{ \hat { u } }_{ y }\) V/m
- (b)
\(48{ \hat { u } }_{ y }\) V/m
- (c)
\(-48{ \hat { u } }_{ y }\) V/m
- (d)
\(24{ \hat { u } }_{ y }\) V/m
Maxwell's divergence equation for the magnetic field is given by
- (a)
\(\triangledown \times \overrightarrow { B } =0\)
- (b)
\(\triangledown .\overrightarrow { B } =0\)
- (c)
\(\triangledown .\overrightarrow { B } =\rho \)
- (d)
\(\triangledown \times \overrightarrow { B } =\rho \)
Region 1, z < 0 and region 2, z > 0 are both perfect dielectrics. A uniform plana wave travelling in the \(\hat { u } _{ z }\) direction has a frequecy of 3 x 1010 rad/s. Its wavelength in the two region are \({ \lambda }_{ 1 }=5cm\) and \({ \lambda }_{ 2 }=3cm\). The Standing Wave Ratio (SWR) is
- (a)
1.67
- (b)
0.6
- (c)
2
- (d)
1.16
A plane wave is normally incident from air onto a semi-infinite slab of perfect dielectric (\({ \varepsilon }_{ r }=3.45\)). The fraction of transmitted power is
- (a)
0.91
- (b)
0.3
- (c)
0.7
- (d)
0.49
We say that scalar field V is harmonic only if its ......... is zero.
- (a)
curl
- (b)
gradient
- (c)
divergence
- (d)
Laplacian
An electron with velocity \(\vec { v } =(3{ \hat { u } }_{ x }+12{ \hat { u } }_{ y }-4{ \hat { u } }_{ z })\times { 10 }^{ 5 }\) m/s experiences no net forces at a point in a magnetic field \(\vec { B } ={ \hat { u } }_{ x }+2{ \hat { u } }_{ z }+3{ \hat { u } }_{ z }\) mWb/m2. The electric field \(\vec { E } \) at that point is
- (a)
-4.4\({ \hat { u } }_{ x }\) + 1.3\({ \hat { u } }_{ y }\) + 0.6\({ \hat { u } }_{z }\) kV/m
- (b)
4.4\({ \hat { u } }_{ x }\) - 1.3\({ \hat { u } }_{ y }\) - 0.6\({ \hat { u } }_{z }\) kV/m
- (c)
-4.4\({ \hat { u } }_{ x }\) + 1.3\({ \hat { u } }_{ y }\) + 0.6\({ \hat { u } }_{z }\) kV/m
- (d)
4.4\({ \hat { u } }_{ x }\) - 1.3\({ \hat { u } }_{ y }\) - 0.6\({ \hat { u } }_{z }\) kV/m
The force on side AB is
- (a)
23.4\({ \hat { u } }_{ z }\quad \mu \)N
- (b)
16.4\({ \hat { u } }_{ z }\quad \mu \)N
- (c)
19.8 \({ \hat { u } }_{ z }\quad \mu \)N
- (d)
26.3 \({ \hat { u } }_{ z }\quad \mu \)N
In a material, the magnetic field intensity is \(\vec { H } \) = 1500 A/m when \(\vec { B } \) = 5 Wb/m2 . When \(\vec { H } \) is recuced to 800 A/m, \(\vec { B } \) = 3 Wb/m2. The change in the magnetization \(\vec { M } \) is
- (a)
1600 kA/m
- (b)
1550 kA/m
- (c)
1590 kA/m
- (d)
1625 kA/m
The scalar triple product \(\overrightarrow { A } .\left( \overrightarrow { A } \times \overrightarrow { B } \right) \) has the value
- (a)
\(\overrightarrow { A } .\overrightarrow { B } \)
- (b)
Zero
- (c)
\(\overrightarrow { A } \times \overrightarrow { B } \)
- (d)
None of these
The magnetic field \(\vec { H } \) is
- (a)
986.8y \({ \hat { u } }_{ z }\) kA/m
- (b)
151.6y \({ \hat { u } }_{ z }\) kA/m
- (c)
102.7 \({ \hat { u } }_{ z }\) kA/m
- (d)
77.6y \({ \hat { u } }_{ z }\) kA/m
In Fleming's left hand rule, the thumb points in the direction of ........... and the first finger in the direction of
- (a)
induced emf, current
- (b)
force, magnetic field
- (c)
force, current
- (d)
magnetic field, current
A uniform field \(\vec { H } =-600{ \hat { u } }_{ y }\) A/m exist in free space. The total energy stored in spherical region 1 cm in radius centered at the origin in free space is
- (a)
0.226 J/m3
- (b)
1.452 J/m3
- (c)
1.68 J/m3
- (d)
0.84 J/m3
The force extered on the filament by the current strip is
- (a)
12.2\({ \hat { u } }_{ y }\quad \mu \)N/m
- (b)
6.6\({ \hat { u } }_{ y }\quad \mu \)N/m
- (c)
-12.2\({ \hat { u } }_{ y }\quad \mu \)N/m
- (d)
-6.6\({ \hat { u } }_{ y }\quad \mu \)N/m
If the points given are A(3,5,-2), B(4,-1,3) and C(-2,3,1), the length of projection of \(\overrightarrow { R } _{ AB }\quad on\quad \overrightarrow { R } _{ AC }\)will be
- (a)
0.357 m
- (b)
3.57 m
- (c)
35.7 m
- (d)
3.57 m
The magnetization \(\vec { M } \) is
- (a)
\(2.986\quad y\hat { u } _{ z }\quad kA/m\)
- (b)
\(1.5\quad y\hat { u } _{ z }\quad kA/m\)
- (c)
\(132.6\quad y\hat { u } _{ z }\quad kA/m\)
- (d)
\(132.6\quad y\hat { u } _{ z }\quad kA/m\)
The integral of the vector potential \(\overset { \rightarrow }{ A } \) around the boundary of a surface S, represents
- (a)
flux through in the surface
- (b)
flux density in the surfaces
- (c)
magneticdensity
- (d)
current density
The parallel wires separated by a distance d are carrying a current / in the same direction. The magnetic field along a line running parallel to these wires and midway between them
- (a)
depends upon /
- (b)
is zero
- (c)
depends upon d
- (d)
depends upon the permeability of medium between the wires
In the figure given, the region \(0\le z\le 2\) filled with an infinite slab of magnetic material (\({ \mu }_{ r }=2.5\)). The surface of the slab at z=0 and z=2 respectively, carry surface current \(30{ \hat { u } }_{ x }\quad A/m\quad and\quad -40\hat { u } _{ x }\) as shown in figure.
In the region the 0<z<2, \(\vec { H } \) is
- (a)
\(-35\hat { u } _{ y }A/m\)
- (b)
\(35\hat { u } _{ y }A/m\)
- (c)
\(-5\hat { u } _{ y }A/m\)
- (d)
\(5\hat { u } _{ y }A/m\)
If \(\overset { \rightarrow }{ E } \) is the electric field intensity, \(\nabla \). \(\left( \nabla \times \overset { \rightarrow }{ E } \right) \) is equal to
- (a)
\(\overset { \rightarrow }{ E } \)
- (b)
\(\left| \overset { \rightarrow }{ E } \right| \quad \)
- (c)
null vector
- (d)
zero
The magnitude field due to a conductor carrying current / at a distance R from the current is directly proportional to
- (a)
R-1
- (b)
R2
- (c)
R
- (d)
R-2
If wave is incident from medium 1 having \(\mu _{ 1 }=4\) to medium 2 having \(\mu _{ 2 }=9\) then, reflection coefficient is (\(\eta _{ 0 }\) is the intrnsic impedance of free space.)
- (a)
\(\frac { 1 }{ 9 } \)
- (b)
\(\frac { 1 }{ 4 } \)
- (c)
\(\frac { 1 }{ 5 } \)
- (d)
None of these
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)
3.2 \(\mu H\)
- (b)
3.2 mH
- (c)
32.0 mH
- (d)
3.2 H
If C is closed curve enclosing a surface S, then the magnetic field intensity \(\overset { \rightarrow }{ H } \), the current density \(\overset { \rightarrow }{ J } \) and the electric flux density \(\overset { \rightarrow }{ D } \) are related by
- (a)
\(\int { \int _{ S }^{ }{ \overset { \rightarrow }{ H } . } d\overset { \rightarrow }{ S } } =\oint _{ C }^{ }{ \left( \frac { \partial \overset { \rightarrow }{ D } }{ \partial t } \right) } .d\overset { \rightarrow }{ I } \)
- (b)
\(\oint _{ C }^{ }{ \overset { \rightarrow }{ H } . } d\overset { \rightarrow }{ I } =\oint { \oint _{ s }^{ }{ \left( \frac { \partial \overset { \rightarrow }{ D } }{ \partial t } \right) } } .d\overset { \rightarrow }{ S } \)
- (c)
\(\oint { \oint _{ S }^{ }{ \overset { \rightarrow }{ H } . } } d\overset { \rightarrow }{ S } =\oint _{ C }^{ }{ \left( \frac { \partial \overset { \rightarrow }{ D } }{ \partial t } \right) } .d\overset { \rightarrow }{ I } \)
- (d)
\(\oint _{ C }^{ }{ \overset { \rightarrow }{ H } } .d\overset { \rightarrow }{ I } =\int { \int _{ S }^{ }{ \left( \overset { \rightarrow }{ J } +\frac { \partial \overset { \rightarrow }{ D } }{ \partial t } \right) } } .d\quad \overset { \rightarrow }{ S } \)
A loop is rotating about the Y-axis in a magnetic field \(\overset { \rightarrow }{ E } =B_{ 0 }\quad cos\quad (wt+\phi \hat { a_{ x } } \) tesla. The voltage in the loop is
- (a)
zero
- (b)
due to transformer action only
- (c)
due to rotation only
- (d)
due to both rotation and transformer action
A current sheet \(\overset { \rightarrow }{ K } =4\hat { u_{ x } } \) A/m flows in the region -2<y<2 in the plane at z=0. The magnetic field at point (0,0,3) is
- (a)
\(0.75\hat { u_{ z } } -0.68\hat { u_{ z } } A/m\)
- (b)
\(-0.68\hat { u_{ z } } A/m\)
- (c)
\(0.68\hat { u_{ y } } -0.75\hat { u_{ z } } A/m\)
- (d)
\(-0.75\hat { u_{ y } } A/m\)