Electrical Engineering - Electromagnetic Field Theory
Exam Duration: 45 Mins Total Questions : 30
We say that scalar field V is harmonic only if its .......... is zero.
- (a)
curl
- (b)
divergence
- (c)
gradient
- (d)
Laplacian
If \(\overset { \rightarrow }{ A } \) is vector orthogonal to \(\overset { \rightarrow }{ B } \) then \(\overset { \rightarrow }{ A } \times \left( \overset { \rightarrow }{ B } \times \overset { \rightarrow }{ C } \right) \) is equal to
- (a)
\(-\left( \overset { \rightarrow }{ B } .\overset { \rightarrow }{ C } \right) \quad \overset { \rightarrow }{ A } \)
- (b)
\(-\left( \overset { \rightarrow }{ A } .\overset { \rightarrow }{ C } \right) \quad \overset { \rightarrow }{ B } \)
- (c)
\(\left( \overset { \rightarrow }{ A } .\overset { \rightarrow }{ C } \right) \quad \overset { \rightarrow }{ B } \)
- (d)
\(\overset { \rightarrow }{ A } \left( \overset { \rightarrow }{ B } .\overset { \rightarrow }{ C } \right) \)
Four 5 nC positive charge are located in the z=0 plane at the corners of a square 8 mm on a side. A fifth 5 ncC positive charge is located at a point 8 mm distant from each of the other charge. The magnitude of the total force on this fifth charge is
- (a)
\(2\times 10^{ -4 }N\)
- (b)
\(4\times 10^{ -4 }N\)
- (c)
0.014 N
- (d)
0.01 N
The region in which \(4<r<5,\quad 0<\theta <25°\) and \(0.9\pi <\phi <1.1\pi \) contains the volume charge density of \(\rho _{ v }=10(r-4)(r-5)\quad sin\theta sin\frac { \theta }{ 2 } \) . Outside the region, \(\quad \rho _{ v }=0\) . The charge within the region
- (a)
0.57 C
- (b)
0.68 C
- (c)
0.46 C
- (d)
0.23 C
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
The region in which 4<r<5, 0<\(\theta \) <25o and 0.9 \(\pi \) < \(\phi \) <1. 1\(\pi \) contains the volume charge density of \({ \rho }_{ v }\) = 10 (r - 4) (r - 5) sin\(\theta \) sin \(\frac { \phi }{ 2 } \). Outside the region, \({ \rho }_{ v }\) = 0. The charge within the region
- (a)
0.57 C
- (b)
0.68 C
- (c)
0.46 C
- (d)
0.23 C
The positive y-axis carries a filamentary current of 2 A in the -4\({ \hat { u } }_{ y }\) direction. The magnetic field \(\overrightarrow { H } \) at point P(2,3,0) is
- (a)
\(72.9{ \hat { u } }_{ z }\) mA/m
- (b)
\(-72.9{ \hat { u } }_{ z }\) mA/m
- (c)
\(145.8{ \hat { u } }_{ z }\) mA/m
- (d)
\(-145.8{ \hat { u } }_{ z }\) mA/m
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
\(\left( \triangledown \times \triangledown .\overrightarrow { A } \right) \) is
- (a)
always a scalar
- (b)
always a vector
- (c)
meaningless
- (d)
Can be either a vector or a scalar
In cylindrical coordinates Laplacian of a scalar V can be expressed as
- (a)
\({ \triangledown }^{ 2 }V=\frac { 1 }{ { \rho }^{ 2 } } \frac { \partial }{ \partial \rho } \left( \rho \frac { \partial V }{ \partial \rho } \right) +\frac { 1 }{ { \rho }^{ 2 } } \left( \frac { { \partial }^{ 2 }V }{ { \partial }\phi ^{ 2 } } \right) +\frac { 1 }{ \rho } \frac { { \partial }^{ 2 }V }{ { \partial }z^{ 2 } } \)
- (b)
\({ \triangledown }^{ 2 }V=\frac { 1 }{ { \rho } } \frac { \partial }{ \partial \rho } \left( \frac { \partial V }{ \partial \rho } \right) +\frac { 1 }{ { \rho } } \frac { { \partial }^{ 2 }V }{ { \partial }\phi ^{ 2 } } +\frac { { \partial }^{ 2 }V }{ { \partial }z^{ 2 } } \)
- (c)
\({ \triangledown }^{ 2 }V=\frac { 1 }{ { \rho } } \frac { \partial }{ \partial \rho } \left( \rho \frac { \partial V }{ \partial \rho } \right) +\frac { 1 }{ { { \rho }^{ 2 } } } \left( \frac { { \partial }^{ 2 }V }{ { \partial }\phi ^{ 2 } } \right) +\frac { { \partial }^{ 2 }V }{ { \partial }z^{ 2 } } \)
- (d)
\({ \triangledown }^{ 2 }V=\frac { 1 }{ { \rho }^{ 2 } } \frac { \partial }{ \partial \rho } \left( \rho \frac { \partial V }{ \partial \rho } \right) +\frac { 1 }{ { { \rho } } } \left( \frac { { \partial }^{ 2 }V }{ { \partial }\phi ^{ 2 } } \right) +\frac { { \partial }^{ 2 }V }{ { \partial }z^{ 2 } } \)
The force on side BC is
- (a)
-18\({ \hat { u } }_{ x }\) nN
- (b)
18\({ \hat { u } }_{ x }\) nN
- (c)
36\({ \hat { u } }_{ x }\) nN
- (d)
-36\({ \hat { u } }_{ x }\) nN
Consider \(\overrightarrow { A } =3\hat { a } _{ x }+4\hat { a } _{ y }\) and \(\overrightarrow { B } =7\hat { a } _{ y }-2\hat { a } _{ z }\). The smaller angle between the two vectors \(\overrightarrow { A } \) and \(\overrightarrow { B } \) will be
- (a)
39.72\(^{o}\)
- (b)
27.93\(^{o}\)
- (c)
41.9\(^{o}\)
- (d)
19.4\(^{o}\)
Two vector field are \(\overrightarrow { F } =-2\hat { u } _{ x }+4x\left( y-1 \right) \hat { u } _{ y }\) and \(\overrightarrow { G } ={ 1x }^{ 2 }y\hat { u } _{ x }-2\hat { u } _{ y }+2\hat { u } _{ z }\). At point A (4, 6, -8) a unit vector in the direction of \(\overrightarrow { F } .\overrightarrow { G } \) is
- (a)
\(0.8\hat { u } _{ x }+0.8\hat { u } _{ y }-0.05\hat { u } _{ z }\)
- (b)
\(0.1\hat { u } _{ x }-1\hat { u } _{ y }+0.05\hat { u } _{ z }\)
- (c)
\(0.97\hat { u } _{ x }+0.2\hat { u } _{ y }-0.009\hat { u } _{ z }\)
- (d)
\(-0.18\hat { u } _{ x }-0.98\hat { u } _{ y }+1\hat { u } _{ z }\)
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 \(\left( \sigma ,\quad \varepsilon ,\quad \mu \right) \)
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
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)
\(dv=\frac { dq }{ dw } \)
The laws of electromagnetic induction (Faraday's and Lenz's law are summarized in the following equation
- (a)
e=iR
- (b)
\(e=L\frac { di }{ dt } \)
- (c)
\(e=-\frac { d\Psi }{ dt } \)
- (d)
None of these
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
\(In\quad the\quad cylindrical\quad region\\ \vec { H } _{ \phi }=\frac { 2 }{ \rho } +\frac { \rho }{ 2 } for\quad \rho \le 0.6\\ \vec { H } _{ \phi }=\frac { 3 }{ \rho } for\quad \rho >0.6\)
The current density \(\bar { J } \quad for\quad \rho <0.6\quad mm\) is
- (a)
\(2\hat { u } _{ z }A/m\)
- (b)
\(-3\hat { u } _{ z }A/m\)
- (c)
\(3\hat { u } _{ z }A/m\\ \\ \)
- (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
For a given material magnetic ssceptibility xm=5 and within which \(\vec { B } =0.2y\hat { u } _{ z }\) tesla
The magnetization \(\vec { M } \) is
- (a)
\(2.986y\hat { u } _{ z }kA/m\)
- (b)
\(2.986y\hat { u } _{ z }kA/m\)
- (c)
\(132.6y\hat { u } _{ z }kA/m\)
- (d)
\(1.55y\hat { u } _{ z }kA/m\)
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
The unit vector directed from point A (5, -1, 0) towards point B(3, 0, 2) is
- (a)
\(-\frac { 2 }{ 3 } \hat { u_{ x } } +\frac { 1 }{ 3 } \hat { u_{ y } } +\frac { 2 }{ 3 } \hat { u_{ z } } \)
- (b)
\(\frac { 2 }{ 3 } \hat { u_{ x } } -\frac { 1 }{ 3 } \hat { u_{ y } } +\frac { 1 }{ 3 } \hat { u_{ z } } \)
- (c)
\(-\frac { 2 }{ 3 } \hat { u_{ x } } +\frac { 1 }{ 3 } \hat { u_{ y } } +\frac { 1 }{ 3 } \hat { u_{ z } } \)
- (d)
\(\frac { 2 }{ 3 } \hat { u_{ x } } -\frac { 1 }{ 3 } \hat { u_{ y } } -\frac { 1 }{ 3 } \hat { u_{ z } } \)
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
The flux through each turn of a 100 turn coil is (t3-2t) mWb where, t is in second. The induced emf at t=2s is
- (a)
\(\overset { \rightarrow }{ H } =\int { \frac { \left| d \right| \times r }{ 4\pi r^{ 2 } } } \)
- (b)
\(\overset { \rightarrow }{ H } =\frac { 1 }{ \mu } \left( \nabla \times \overset { \rightarrow }{ A } \right) \)
- (c)
\(\nabla .\overset { \rightarrow }{ H } =0\)
- (d)
\(\nabla \times \overset { \rightarrow }{ H } =\hat { j } \)
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)
\(12\left[ \hat { a_{ x } } +\hat { a_{ y } } +\hat { a_{ z } } \right] \)
The polarization of wave with electric field vector \(\overset { \rightarrow }{ E } =24e^{ j(\omega t+\beta z) }\hat { a_{ y } } \quad V/m\) in free space is
- (a)
\(\frac { 4.8\pi }{ \pi } \hat { a_{ z } } \)
- (b)
\(-\frac { 4.8\pi }{ \pi } \hat { a_{ z } } \)
- (c)
\(-\frac { 2.4\pi }{ \pi } \hat { a_{ z } } \)
- (d)
\(\frac { 2.4\pi }{ \pi } \hat { a_{ z } } \)