Electrical Engineering - Electromagnetic Field Theory
Exam Duration: 45 Mins Total Questions : 30
If is \(\omega \) the angular velocity and \(\beta \) is the phase constant, group velocity is given by
- (a)
\(\frac { d\omega }{ d\beta } \)
- (b)
\(\frac { \beta }{ \omega } \)
- (c)
\(\frac { \omega }{ \beta } \)
- (d)
\(\frac { d\beta }{ d\omega } \)
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 100 nC/m lie along the entire extent of the three coordinates axes. The \(\overrightarrow { E } \) at P(-3,2,-1) is
- (a)
\(-1.92{ \hat { u } }_{ x }+2{ \hat { u } }_{ y }-1.08{ \hat { u } }_{ z }kV/m\)
- (b)
\(-0.96{ \hat { u } }_{ x }+{ \hat { u } }_{ y }-0.54{ \hat { u } }_{ z }kV/m\)
- (c)
\(-1.92{ \hat { u } }_{ x }+2{ \hat { u } }_{ y }-1.08{ \hat { u } }_{ z }kV/m\)
- (d)
\(-1.92{ \hat { u } }_{ x }+2{ \hat { u } }_{ y }-1.08{ \hat { u } }_{ z }kV/m\)
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)
\(\triangledown \times \overrightarrow { B } =\rho \)
If \(\oint { \overrightarrow { A } } .d\overrightarrow { l } =0\) then, \(\overrightarrow { A } \) is called
- (a)
conservation field
- (b)
harmonic field
- (c)
vortex field
- (d)
irrotational field
The Y - axis and Z - axis is carrying filamentary currents 12 mA along \({ \hat { u } }_{ y }\) and 24 mA along \({ -\hat { u } }_{ z }\). The magnetic field at (-3,4,5) is
- (a)
0.331\({ \hat { u } }_{ x }\) + 0.458\({ \hat { u } }_{ y }\) + 0.168\({ \hat { u } }_{z }\) mA/m
- (b)
0.0662\({ \hat { u } }_{ x }\) + 0.916\({ \hat { u } }_{ y }\) + 0.336\({ \hat { u } }_{z }\) mA/m
- (c)
0.165\({ \hat { u } }_{ x }\) + 0.229\({ \hat { u } }_{ y }\) + 0.84\({ \hat { u } }_{z }\) mA/m
- (d)
zero
If \(\left( r,\theta ,\phi \right) \) represents a spherical coordianate system then, the range of coordinates variables \(r,\theta ,\phi \) is
- (a)
\(0\le r\le \infty ,\quad 0\le \theta \le \pi ,\quad 0\le \phi \le 2\pi \)
- (b)
\(0\le r\le \infty ,\quad 0\le \theta \le \pi ,\quad -\pi \le \phi \le \pi \)
- (c)
\(0\le r\le \infty ,\quad -\pi \le \theta\le \pi ,\quad 0\le \phi \le 2\pi \)
- (d)
\(0\le r\le \infty ,\quad 0\le \theta \le 2\pi ,\quad 0\le \phi \le \pi \)
Which of the following equations is not Maxwell's equation for static electromagnetic field in a linear homogeneous medium? (3rd equation)
- (a)
\(\nabla \times \vec { D } =0\)
- (b)
\({ \nabla }^{ 2 }\vec { A } ={ \mu }_{ 0 }\vec { I } \)
- (c)
\(\nabla .\vec { B } =0\)
- (d)
\(\oint \vec { B } .d\vec { I } ={ \mu }_{ 0 }I\)
The vector component of \(\overrightarrow { F } =6\hat { u } _{ x }+4\hat { u } _{ y }+2\hat { u } _{ z }\) that is parallel to \(\overrightarrow { G } =2\hat { u } _{ x }+2\hat { u } _{ y }-1\hat { u } _{ z }\) is
- (a)
\(2\hat { u } _{ x }+4\hat { u } _{ z }\)
- (b)
\(2\hat { u } _{ x }-2\hat { u } _{ y }\)
- (c)
\(\hat { u } _{ x }+\hat { u } _{ y }+\hat { u } _{ z }\)
- (d)
\(\hat { u } _{ x }+3\hat { u } _{ y }+\hat { 2u } _{ z }\)
A rectangular coil of 200 turns has dimensuons 0.3\(\times \)0.15m with a current of 5 A, placed in an uniform field of 0.2 T. Then magnetic moment \(\vec { m } \) is
- (a)
4.5 A-m2
- (b)
45 A-m2
- (c)
0.45 A-m2
- (d)
0.225 A-m2
The work done in carrying a charge through an equipotential surface is
- (a)
zero
- (b)
depends on the charge Q
- (c)
infinity
- (d)
depends on the distance
A monopole consists of
- (a)
a single charge
- (b)
two positive and two negative charges
- (c)
two positive and one negative charges
- (d)
two negative charges and one positive charge
What is the major factor for determining whether a medium is free space, lossless dielectric, lossy dielectric or good conductor?
- (a)
Reflection coefficient
- (b)
Attenuation constant
- (c)
Loss tangent
- (d)
Constitutive parameters \(\left( \sigma ,\quad \varepsilon ,\quad \mu \right) \)
Two identical conducting spheres have charges of 1 nC and -1.5 nC. If they are brought into contact and then separated by 5cm, what will be the force between them?
- (a)
562 nN
- (b)
75 nN
- (c)
316 nN
- (d)
225 nN
In a material magnetic flux density is 0.02 Wb/m2 and the magnetic susceptibility is 0.003. The magnitude of the magnetization is
- (a)
47.6 A/m
- (b)
23.4 A/m
- (c)
16.3 A/m
- (d)
8.4 A/m
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
For a given material , magnetic susceptibility xm=5 and within which B=0.2 \(y\hat { u } _{ z }\)tesla
The magnetic field \(\vec { H } \) is
- (a)
\(0.986\quad y\hat { u } _{ z }\quad kA/m\)
- (b)
\(0.986\quad y\hat { u } _{ z }\quad kA/m\)
- (c)
\(0.986\quad y\hat { u } _{ z }\quad kA/m\)
- (d)
\(0.986\quad y\hat { u } _{ z }\quad kA/m\)
If v, w, q stand for voltage, energy and charge, then v can be expressed as
- (a)
\(v=\frac { dq }{ dw } \)
- (b)
\(v=\frac { dw }{ dq } \)
- (c)
\(dv=\frac { dw }{ dq } \)
- (d)
\(dv=\frac { dq }{ dw } \)
In a uniform electric field, field lines and equipotentials
- (a)
are parallel to one another
- (b)
insect at 45°
- (c)
insect at 30°
- (d)
are orthogonal
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
If the magnetic field intensity inside a cube of side 2 m is \(3\hat { a_{ x } } -4\hat { a_{ y } } \) A/cm and the relative permeability of the medium is 4, then the magnetic energy is
- (a)
1 mJ
- (b)
5 J
- (c)
10 J
- (d)
500 \(\mu J\)
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)
0.015 J
- (b)
0.15 J
- (c)
0.5 J
- (d)
1.15 J
An electron with velocity \(\overset { \rightarrow }{ u } \) is placed in an electric field \(\overset { \rightarrow }{ E } \) and magnetic field \(\overset { \rightarrow }{ B } \) , the force experienced by the electron e is given by
- (a)
\(-e\overset { \rightarrow }{ E } \)
- (b)
\(-e\overset { \rightarrow }{ u } \times \overset { \rightarrow }{ B } \)
- (c)
\(-e\left( \overset { \rightarrow }{ u } \times \overset { \rightarrow }{ E } +\overset { \rightarrow }{ B } \right) \)
- (d)
\(-e\left( \overset { \rightarrow }{ E } +\overset { \rightarrow }{ u } \times \overset { \rightarrow }{ B } \right) \)
\(\nabla \times \left( \nabla .\overset { \rightarrow }{ A } \right) \) is
- (a)
always a scalar
- (b)
always a vector
- (c)
meaningless
- (d)
Can be either a vector or a scalar
\(\oint { \overset { \rightarrow }{ A } .d\overset { \rightarrow }{ l } =0 } \) then, \(\overset { \rightarrow }{ A } \) is called
- (a)
conservative field
- (b)
harmonic field
- (c)
vortex field
- (d)
irrotational field
Spherical surfaces at r=2 and 4 carrying uniform charge densities of 20 nC/m2 and -4 nC/m2. The \(\overset { \rightarrow }{ D_{ r } } \) at 2
- (a)
\(-\frac { 16 }{ r^{ 2 } } nC/m^{ 2 }\)
- (b)
\(\frac { 16 }{ r^{ 2 } } nC/m^{ 2 }\)
- (c)
\(\frac { 80 }{ r^{ 2 } } nC/m^{ 2 }\)
- (d)
\(-\frac { 80 }{ r^{ 2 } } nC/m^{ 2 }\)
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)
\(-0.75\hat { u_{ y } } A/m\)
Consider the triangular loop shown in figure:
The magnetic moment of the above electric circuit is
- (a)
\(-12\left[ \hat { a_{ x } } +\hat { a_{ y } } +\hat { a_{ z } } \right] \)
- (b)
\(10\left[ \hat { a_{ x } } +\hat { a_{ y } } +\hat { a_{ z } } \right] \)
- (c)
\(-10\left[ \hat { a_{ x } } +\hat { a_{ y } } +\hat { a_{ z } } \right] \)
- (d)
\(12\left[ \hat { a_{ x } } +\hat { a_{ y } } +\hat { a_{ z } } \right] \)
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