Question Bank for Electromagnetic Field Theory.

  1. Discuss the significance of Electric field Intensity. Electric flux density, Electric Susceptibility, Permittivity & Dielectric strength in the context of any medium considered.
  2. Discuss the significance of
    • (i) the Curl of a vector,
    • (ii) the Divergence of a vector, and the Divergence theorem.
    • (iii) Gradient of scalar function, with their significance to Electromagnetic Field Theory.
  3. If E= x²y ax + (2x² + y) ay– (y-z) az, find
    • (i) ∇.E
    • (ii) ∇(∇.E)
    • (iii) ∇ x E
  4. What is a constant coordinate surface ? Discuss its different cases for the cylindrical coordinate systems.
  5. Discuss the analogy between Electrostatics and Magnetostatics in terms of various parameters. And also discuss Capacitor and Inductor as energy storage components.
  6. Discuss the difference between conduction current and displacement current. Further discuss the modification in Maxwell’s equation due to consideration of displacement current.
  7. A coil is made of 150 turns of copper wire wound on a cylindrical core. If the mean radius of the turns is 6.5 mm and the diameter of the wire is 0.4 mm, calculate the resistance of the coil.
  8. Discuss Gauss law of Electrostatics in terms of difference from Coulomb’s law.
  9. Two point charges when located in free space exert a force of 4.5 µN on each other. When the space between them is filled with a dielectric material, the force changes to 2 µN. Find the dielectric constant of the material.
  10. Discuss Gauss law of Magnetostatics in terms of difference from Ampere’s law.
  11. Write down and briefly explain all the Maxwell’s Equations in Integral form.
  12. Write down and briefly explain all the Maxwell’s Equations in Differential form.
  13. Discuss magnetization, susceptibility & permeability. Discuss different materials in the context of magnetic field.
  14. Write short notes on following:
    • (i) Divergence theorem,
    • (ii) Stokes Theorem,
    • (iii) Phasors and Complex Numbers,
    • (iv) Poisson’s Equation
  15. State divergence theorem and write the related mathematical equation.
  16. Define constant coordinate surfaces. What is done to obtain a surface in a three-coordinate system ?
  17. Show that the field given by (2xy + z²) Î + (x²-2yz) ĵ + (3z²-y2)𝐤̂ is conservative at point (-2, 0,1).
  18. State Coulomb’s Law of electrostatics and write mathematical expression in vector form.
  19. Point charges 10 nC and -3 nC are located at points (2, 3, 4) and (-3, 1, 5), respectively Determine the electric field intensity at point (1, 1, 1) Consider the distance in meter.
  20. Determine the gradient of the field F = 4x + 2xy3 + 4xz at point (2. 4, 3).
  21. Find the curl of the field 𝐹⃗ = 2x²Î + xy ĵ + 6xyz 𝐤̂.
  22. Point charges 5 nC and -2 nC are located at points (2, 4, 0) and (0, -3, 5), respectively.
    Find the potential at the origin. Consider the distance in meter.
  23. Using Gauss’s Law, derive the Maxwell’s first equation.
  24. Using suitable diagrams, write the relevant mathematical equations to show the transformation among the following coordinates
    (a) Spherical coordinates to/from Cartesian coordinates

    (b) Cylindrical coordinates to/from Cartesian coordinates
  25. Prove that the energy stored in a group of n point charges is equal to ,
    • where Q and V denote charge and potential, respectively

      Also, derive the mathematical expression for electrostatic energy density.
  26. Using Stokes Theorem, show that electric field is an irrotational field.
  27. Define constant coordinate surfaces. Draw relevant diagram in any one of the coordinate systems.
  28. State Coulomb’s Law and write mathematical expression in vector form.
  29. Point charges 5 nC and -2 C are located at points (2, 0, 4) and (-3, 0, 5), respectively. Determine the force between them.
  30. Determine the gradient of the scalar field F = 5x+6xy² + 2xz.
  31. Find the curl of the vector field 𝐹⃗ = 4xÎ + 2xy ĵ + 6xz 𝐤̂.
  32. Using Gauss’s Law, derive the expression of electric field due to infinite line charge of uniform density p.
  33. With the help of suitable diagrams and mathematical expressions, write about line integral, surface integral, and volume integral.
  34. Three point charges 4 µC, 5 µC, and 3 µC are located at (2, -1, 3), (0, 4, -2), & (0,0,0), respectively. Find the potential due to these charges at the point (-1, 5, 2).
  35. If E = Sin (2x+y) ax + e(-4y)x ay – (z2 – x) az, find
    • (i) ∇.E
    • (ii) ∇(∇.E)
    • (iii) ∇ x E
  36. Discuss Laplacian operator and evaluate Laplacian of following scalar fields,
    • g = Cos (x + 4y) Sin (z2)
    • h = e(3x) Sin (z+2y)
  37. Discuss with example cylindrical coordinate system and spherical coordinate system with their usage. Taking example of Earth as a spherical object, discuss how coordinates of Spherical coordinate system can be related with Latitude and Longitude of Globe.