Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) State and explain Coulomb's law in vector form.
4 M
1 (b) Two point charges 20 nC and -20 nC are situated at (1, 0, 0)m and (0, 1, 0)m in free space. Determine electric field intensity at (0, 0, 1)m.
5 M
1 (c) A charge is uniformly distributed over a spherical over a spherical surface of radius 'a'. Determine electric field intensity everywhere in space. Use Gauss law.
6 M
1 (d) State and prove divergence theorem.
5 M

2 (a) Determine the potential difference between two points due to a point charges 'q' at the origin.
4 M
2 (b) Derive point form of continuity equation.
5 M
2 (c) A metallic sphere of sphere of radius 10 cm has a surface charge density of 10 nC/m2. Calculate electric energy stored in the system.
6 M
2 (d) The plane Z=0 marks the boundary between free space and a dielectric medium with dielectric constant of 40. The \( \widehat{E}) field next to the interface in free space is $\widehat{E}=13\widehat{x}+ 40\widehat{Y}+ 50 \widehat{Z} \ V/m.$ Determine \( \widehat{E}) on the other side of the interface.
5 M

3 (a) State and prove uniqueness theorem.
10 M
3 (b) The two metal having an area 'A' and a separation 'd' form a parallel plate capacitor. The upper plate is held at a potential VQ and lower plate is grounded. Determine:
i) Potential distribution
ii) The electric field intensity
iii) Capacitance of parallel plate capacitor.
10 M

4 (a) State and explain Ampere's circuital law.
4 M
4 (b) Explain scalar and vector magnetic potential.
8 M
4 (c) The magnetic field intensity is given [ widehat{H}=0.1 y^3 widehat{X}+ 0.4 x widehat{Z} A//m. ] Determine current flow through the path P1(5,4,1 ) - P2(5,6,1) - P3(0,6,1) - P4(0,4,1) and current density J.
8 M

5 (a) Derive Lorentz's force equation.
5 M
5 (b) Obtain the expression for reluctance in a series magnetic circuit.
5 M
5 (c) Derive the magnetic boundary conditions at the interface between two different magnetic materials.
6 M
5 (d) A ferrite materials is operating in linear mode with B=0.05 T. Assume μr=50. Calculate magnetic susceptibility, magnetization and magnetic field intensity.
4 M

6 (a) List Maxwell's equations in differential and integral forms.
8 M
6 (b) Write a note on retarded potential.
6 M
6 (c) A circular conduction loop of radius 40 cm lies in xy plane and has resistance of 200Ω. If the magnetic flux density in the region is given as, $\widehat{B}=0.2 \cos 500t \widehat{X} + 0.75 \sin 400 \widehat{Y} + 1.2 \cos 314 t \widehat{Z}T.$ Determine effective value in induced current in the loop.
6 M

7 (a) Obtain solution of the wave equation for a uniform plane wave (UPW) in free space.
6 M
7 (b) Discuss uniform plane wave propagation in a good conducting media.
6 M
7 (c) State and prove Poynting theorem.
8 M

8 (a) Derive the expression for transmission coefficient and reflection for a uniform plane wave with normal incidence at a plane dielectric boundary.
8 M
8 (b) Write a note on standing wave ratio (SWR).
7 M
8 (c) A 50 MHz uniform plane wave having electric field amplitude 10 V/m. The medium is lossless having ?r-?11=9 and μr=1. The wave propagates in the xy plane at a 30° angle to the x axis and is linearly polarized along z-axis. Write the phasor expression for the electric field.
5 M

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