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,Q

_{1}and Q_{2}are located at (1,2,0)_{m}and (2,0,0)_{m}respectively.Find the relation between the charges Q_{1}and Q_{2}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

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