EX-504-B Electromagnetic Theory - Dec 2024 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aState and prove Divergence theorem.
   How to answer

   • Statement of Divergence theorem relating volume integral of divergence to surface integral
   • Definition of vector field and closed surface
   • Steps of proof using Cartesian volume element
   • Conversion to integral form and conclusion
2. 7 Marks
   bExplain Cartesian and cylindrical co-ordinate system with example.
   How to answer

   • Definition of Cartesian coordinate system with unit vectors
   • Definition of cylindrical coordinate system with variables
   • Transformation relations with example point
   • Diagram of both systems
3. 7 Marks
   aExplain the potential and electric field intensity due to dipole.
   How to answer

   • Definition of electric dipole and dipole moment
   • Expression for potential $V$ due to dipole
   • Derivation of electric field intensity $E = -\nabla V$
   • Components in spherical coordinates
4. 7 Marks
   bWrite and explain equation of continuity.
   How to answer

   • Statement of principle of conservation of charge
   • Derivation from current through closed surface
   • Differential form $\nabla \cdot J = -\partial \rho_v/\partial t$
   • Physical interpretation
5. 7 Marks
   aDescribe 'Biot-Savart's' law.
   How to answer

   • Statement of Biot-Savart law for current element $Idl$
   • Formula $dH = Idl \times a_R / 4\pi R^2$
   • Meaning of terms and direction
   • Application to filament
6. 7 Marks
   bExplain and drive magnetic field intensity due to straight current carrying filament.
   How to answer

   • Geometry of infinite straight current filament
   • Application of Biot-Savart law
   • Integration over length to get $H = I/2\pi \rho \, a_\phi$
   • Special cases for finite and semi-infinite line
7. 7 Marks
   aDefine displacement current with it's application.
   How to answer

   • Definition $J_d = \partial D/\partial t$
   • Need in Ampere's law for time-varying fields
   • Physical meaning and applications
   • Example in capacitor
8. 7 Marks
   bExplain Maxwell's equations in differential and integral form.
   How to answer

   • List of four Maxwell's equations
   • Differential form with curl and divergence
   • Integral form using Stokes and Divergence theorems
   • Physical significance of each equation
9. 7 Marks
   aDescribe the properties of electro-magnetic waves.
   How to answer

   • Transverse nature and $E \perp H \perp$ propagation
   • Velocity $c = 1/\sqrt{\mu_0\varepsilon_0}$
   • Impedance of free space and energy
   • No charge or current needed for propagation
10. 7 Marks
    bExplain the uniform plane wave in dielectric and conductors.
    How to answer

    • Wave equation from Maxwell's equations
    • Propagation constant and attenuation in dielectric
    • Skin depth and loss in good conductor
    • Comparison of dielectric vs conductor behaviour
11. 7 Marks
    aExplain Ampere's circuital law and its applications.
    How to answer

    • Statement $\oint H \cdot dl = I_{enc}$
    • Differential form $\nabla \times H = J$
    • Derivation steps and assumptions
    • Applications to coaxial cable, solenoid, toroid
12. 7 Marks
    bDescribe the relationship between magnetic flux, flux density and magnetic field intensity.
    How to answer

    • Definitions: $\Phi = \int B \cdot ds$, $B = \mu H$
    • Relation $B = \mu_0(H+M)$
    • Units of flux, flux density and field intensity
    • Permeability and magnetization link
13. 7 Marks
    aDescribe Faraday's law with suitable diagram.
    How to answer

    • Statement of Faraday's law $emf = -d\Phi/dt$
    • Lenz's law and sign
    • Neat diagram of coil and changing flux
    • Differential and integral forms
14. 7 Marks
    bExplain vector magnetic potential and its properties.
    How to answer

    • Definition $B = \nabla \times A$
    • Integral expression for $A$ due to current
    • Gauge condition and properties
    • Relation to magnetic flux
15. 14 Marks
    Write short note :

    1. a)Polarization
    2. b)Laplace's and Poisson's equations
    3. c)Surface impedance
    4. d)Perfect conductor
    How to answer

    • Definition of polarization, Laplace/Poisson equations
    • Surface impedance concept and formula
    • Perfect conductor properties and boundary conditions
    • Relevant equations and examples