STUPIDSID
1(a)
State vector form of Coulomb's law of force between two point charges and indicate the units of the quantities in the equation.
6 M
1(b)
State and prove Gauss law for point charge.
6 M
1(c)
Two point charges,Q1 and Q2 are located at (1,2,0)m and (2,0,0)m respectively.Find the relation between the charges Q1 and Q2 such that the total force on a unit positive charge at (-1,1,0) have i) no x-component.
8 M
2(a)
Define potential difference and absolute potential.
4 M
2(b)
Establish the relation \[E=\bigtriangleup \vee.\]
6 M
2(c)
Electrical potential at an arbitrary point free - space is given as :
\[V-(x+1)^{2}+(y+2)^{2}+(z-3)^{2}. At \ P (2,1,0)\ find\\ i) v\ ii) E^{\rightarrow }\ iii) E^{\rightarrow }\ iv) D^{\rightarrow }\ v) D^{\rightarrow }\ vi) P_{v}.\]
\[V-(x+1)^{2}+(y+2)^{2}+(z-3)^{2}. At \ P (2,1,0)\ find\\ i) v\ ii) E^{\rightarrow }\ iii) E^{\rightarrow }\ iv) D^{\rightarrow }\ v) D^{\rightarrow }\ vi) P_{v}.\]
10 M
3(a)
Derive the expression for Poisson's equation.
4 M
3(b)
Write the expression for Laplace's equation in cylindrical and spherical coordinates.
4 M
3(c)
State and prove uniqueness theorem.
6 M
3(d)
Given the potential field\[V=x^{2}yz-ky^{3}z\] volts :
i) Find k if potential field satisfies Laplace's equation
ii) find\[E^{\rightarrow }\]at (1,2,3).
i) Find k if potential field satisfies Laplace's equation
ii) find\[E^{\rightarrow }\]at (1,2,3).
6 M
4(a)
Starting form Biot-Savort's law, derive the expression for the magnetic field intensity at a point due to finite length current carrying conductor.
8 M
4(b)
Verify stoke's theorem for the field \[\underset{H}{\rightarrow}\]_\[2rcos\Theta a\ r^{\vee }+ra\Theta ^{\wedge }\] for the path shown r=0 to 1; 0 to \[90^{0}\]
8 M
4(c)
Explain scalar and vector magnetic potenial.
4 M
5(a)
Derive expression for magnetic force on :
i) Moving point charge
Differential current element.
i) Moving point charge
Differential current element.
10 M
5(b)
A current element\[I_{1}dI_{2}-10^{-4}\ \widehat{a_z}\] (AM) is located at\[P_{1}\](-2,0,0).Both are in free space :
Find force exerted on \[I_{2}d1_{2}-10^{-6}[{\widehat{ax}}-2\widehat{ay}+3\widehat{az}](Am)\] is located at \[P_{2}\](-2,0,0). Both are in free space:
i) Find force exerted on \[I_{2}dl_{2}by I_{2}dI_{1}\]
ii) Find force exerted on\[I_{1}dl_{1}by I_{2}dI_{2}.\]
Find force exerted on \[I_{2}d1_{2}-10^{-6}[{\widehat{ax}}-2\widehat{ay}+3\widehat{az}](Am)\] is located at \[P_{2}\](-2,0,0). Both are in free space:
i) Find force exerted on \[I_{2}dl_{2}by I_{2}dI_{1}\]
ii) Find force exerted on\[I_{1}dl_{1}by I_{2}dI_{2}.\]
10 M
6(a)
List Maxwell's equations in point form and lntergral form.
8 M
6(b)
A homogeneous material has ?=2×1\[\epsilon =2×10^{6} F/M and\ \mu =1.25×10^{5}\] and\[\sigma =0.\].Electric field intensity \[\overrightarrow{E}\]=400 cos\[(10^{9}t-kz)a\widehat{x}\ V/m\]. If all the field vary sinsoidally,find\[\overrightarrow{D},\overrightarrow{B},\overrightarrow{H} and k using Maxwell's equations.
12 M
7(b)
State and explain Poynting theorem.
10 M
7(c)
Starting form Maxwell's equations derive wave equation in E and H for a uniform plane wave travelling in free space.
10 M
8(a)
Write short notes on :
i) SWR and reflection coefficient
ii) Skin depth.
i) SWR and reflection coefficient
ii) Skin depth.
10 M
8(b)
A Ghz plane wave in free space has electric field intensity 15 V/m. Find:
i) Velocity of propagation
ii) Wavelength
iii) Characteristic impedance of the medium
iv) Amplitude of magnetic field intensity
v) Propagation constant\[\beta \].
i) Velocity of propagation
ii) Wavelength
iii) Characteristic impedance of the medium
iv) Amplitude of magnetic field intensity
v) Propagation constant\[\beta \].
10 M
More question papers from Field Theory