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UNIT I – INTRODUCTION
1. Define Scalar and Vector quantities. Give examples.
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2. A = ax + 2ay + 3az. Find the magnitude and direction.
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3. Cartesian P(1,2,3) to Cylindrical coordinates.
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4. A = 4ax + 2ay + az in Cylindrical coordinate system.
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5. A = 3x ax + 5z az + y ay. Find Curl(A).
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6. B = 4xy² + 2y³ ay + xyz az. Find Divergence(B).
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7. Two conditions of Null identities.
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8. Physical significance of Curl.
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9. State Stoke’s theorem.
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10. State Divergence theorem.
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PART B & C
11. Differentiate coordinate systems.
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12. Distance between A(X=2,Y=3,Z=-1), B(r=4,-50°,2) to region and each other.
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13. State and Prove Divergence theorem.
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14. D = 5r²/4 ar. Evaluate Divergence theorem for r = 4m, φ = π/4.
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15. Prove Stoke’s and Helmholtz theorems.
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UNIT II – ELECTROSTATICS.
16. State Coulomb’s law.
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17. Define permittivity.
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18. Define electric field intensity.
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19. Define Electric flux density.
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20. State Gauss’s law.
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21. Define Electric dipole, Dipole moment, Polarization.
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22. 10µC at (1,2,3), -3µC at (3,0,2). Find force.
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23. F = 2ax + ay + az N on 10C. Find E and its magnitude/direction.
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24. 10pC at rest. Find potential at 10 cm.
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25. Q = 10nC. Find E at P(1,0,1), and electric field density.
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26. Differentiate Dielectrics and Conductors.
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27. Define relaxation time and capacitance.
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PART B & C
28. Coulomb’s law, E-field due to charge distribution.
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29. Find E at P(3,-4,2) due to Q1 & Q2.
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30. 3 charges: 50nC at (0,0), 40nC at (3,0), -60nC at (0,4). E at (3,4).
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31. State and prove Gauss’s law and applications.
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32. State and prove electrostatic boundary conditions.
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33. Derive Laplace’s and Poisson’s equations.
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34. Derive equation of continuity.
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35. Explain capacitance and energy stored.
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36. Parallel plate capacitor problem – Capacitance, Charge, Energy.
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37. Explain current density and its types.
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UNIT III – MAGNETOSTATICS.
38. Define permeability.
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39. Define magnetic field intensity.
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40. Define magnetic flux density.
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41. State Biot-Savart law.
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42. State Ampere’s Circuital law.
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43. Applications of Biot-Savart & Ampere’s laws.
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44. Lorentz force equation.
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45. Classify magnetic materials.
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46. Toroid – Find inductance.
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47. Coaxial cable – L of 10m long cable.
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48. Force on current element, Force between elements, Torque.
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PART B & C
49. Explain Biot-Savart law and its applications.
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50. State, prove Ampere’s law and applications.
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51. Find H due to Idl = 3π(ax+2ay+3az) µA at (3,4,5).
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52. Derive magnetostatic boundary conditions.
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53. Find H at center of square loop, side = 2m, I = 1A.
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54. Q = -1.2C, V = (5ax+2ay+3az), E and B given – Find Force.
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55. Interface at x=0. µr1 = 2, µr2 = 5, H1 given – Find B2, B1, H2.
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56. χ = 3, B = 10y ax mWb/m². Find µr, µ, Jb, J, M, H.
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UNIT IV – TIME VARYING FIELDS.
57. Faraday’s Law
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58. Lenz’s Law
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59. Displacement current
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60. Conduction current
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61. Boundary conditions at time varying fields
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62. Integral form of Maxwell’s equations
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63. Differential form of Maxwell’s equations
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64. Give Maxwell’s equations in point and integral form
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PART B & C
65. Derive Maxwell’s equations from fundamental laws
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66. Derive Maxwell’s equations in integral and point forms
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67. Boundary condition for E and H between media
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68. Interface at x = 0, ε1 = 2, ε2 = 5. E1 = 3ax + 4ay – 6az.
Find D1, D2, E2
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69. Interface at y = 0, μr1 = 2, μr2 = 5. H1 = 5ax + 3ay + 6az.
Find B1, B2, H2
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UNIT V - ELECTROMAGNETIC WAVES.
70. Define wave and uniform plane wave
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71. Derive wave equation
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72. Define wave impedance
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73. Define polarization and types
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74. Define reflection coefficient
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75. Define transmission coefficient
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76. Define intrinsic impedance
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77. Define propagation constant
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78. Skin depth
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79. Attenuation and phase constant
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80. Reflection of plane waves
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PART B & C
1. Use Maxwell’s equations to obtain the wave equation for a conducting medium.
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2. State Poynting theorem. Derive electromagnetic power flow and Poynting vector
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3. A uniform plane wave in a medium having σ = 10-3 s/m. ε = 80 ε0 and µ = µ0 is having a frequency at 10 kHz. (a) Verify whether the medium is good conductor (b) Calculate the following Attenuation constant, Phase constant, Propagation constant, Intrinsic impedance, Wavelength, Velocity of propagation.
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4. A plane wave travelling in a medium of Ɛr = 1, µr = 1 has an electric field intensity of 100 x √ π V/m. Determine the energy density in the magnetic field and also the total energy density.
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5. Find the depth of penetration d of an EM wave in copper of f = 60 Hz and f = 100 MHz. For copper sigma = 5.8 x 107 mho/m Ɛr = 1, µr = 1.
6. Earth has a conductivity of sigma = 10-2 mho/m, Ɛr = 10, µr = 2. What are the conducting characteristics of the earth a) f = 50 Hz b) f = 1 KHz c) 1 MHz d) 100 MHz e) 10 GHz.
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7. Using Maxwell's equations, derive the expression for an electromagnetic plane wave in a lossless medium.
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8. Deduce the Oblique incidence of a plane wave on a boundary planes.
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9. Derive the expression for normal incidence at a plane conducting boundary and normal incidence at a plane dielectric boundary conditions.
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