ELECTROMAGNETIC THEORY (EC-504 (A)) - Important Questions

Define divergence and curl of a vector field and explain their physical significance.

Explain Gauss's law and derive the electric field due to an infinite line charge

State Coulomb's law in vector form, define electric field intensity and electric flux density, and derive the relation between D and E.

Give mathematical expressions for gradient, divergence and curl in spherical coordinates.

State and prove Gauss's law and derive the electric field due to a uniformly charged infinite plane sheet

Define electric flux and electric flux density. Derive the boundary conditions at the interface between two dielectric media.

Using the method of images, find the electric field due to a point charge near an infinite grounded conducting plane.

State, derive and explain the continuity equation for current in integral and differential (point) form, including the steady-current case.

State and explain the divergence theorem, including physical significance of del operator.

Determine the nature (solenoidal, irrotational, etc.) of a given vector field in cylindrical coordinates by computing divergence and curl.

Verify that the vector field $\bar{A} = yz\bar{a}_x + xz\bar{a}_y + xy\bar{a}_z$ is both irrotational and solenoidal.

State Coulomb's law.

Derive the force (per unit length) between two parallel infinitely long current-carrying wires, including its significance in defining the ampere.

Verify Stokes theorem numerically for a given vector field over a given surface/contour.

Define magnetic flux density, magnetic field intensity and magnetization vector and derive the relation between them, $\mathbf{B} = \mu_0(\mathbf{H}+\mathbf{M})$

Derive the expression for magnetic field intensity due to a long straight current-carrying conductor.

State and explain Stokes theorem and calculate displacement current for a capacitor with time-varying electric field.

State and explain Stokes theorem and give its expression/importance.

Define magnetic field and state its properties.

Explain displacement current and derive Maxwell's correction to Ampere's circuital law for time-varying fields.

State and explain Faraday's law of electromagnetic induction and derive its integral and differential forms.

Show how Maxwell's equations unify electricity and magnetism and discuss their importance in modern physics.

Given magnetic field intensity $\vec{H}$ in free space, determine the displacement current density.

State and explain Faraday's law of electromagnetic induction and derive the equation of continuity.

Derive Maxwell's equations in differential form and explain their significance.

Define the Poynting vector and state, derive and prove the Poynting theorem, explaining its physical significance for electromagnetic energy flow.

Derive/state the electromagnetic wave equation for a uniform plane wave in free space in time domain and explain the procedure for its solution.

Derive expressions for plane electromagnetic waves in a dielectric medium, including attenuation constant and boundary conditions for electric and magnetic fields.

Calculate the average electric and magnetic field intensities at a distance from a uniformly radiating lamp of given power.

Derive expressions for attenuation constant, phase constant and skin depth in a conducting medium.

Write a short note on skin depth and its physical significance.

For a plane wave in free space with given frequency and electric field amplitude, calculate phase velocity, wavelength, propagation constant and characteristic impedance.

Calculate the depth of penetration (skin depth) for copper at a given frequency.

Propagation of uniform plane waves in a perfect (lossless) dielectric: propagation constant and electric and magnetic field expressions.

Derive the wave equation and propagation parameters (attenuation constant, phase constant) for wave propagation in a lossy dielectric medium.

Derive the reflection coefficient for a plane wave at normal incidence and explain reflection of a plane wave at oblique incidence.

What is Brewster's angle? Derive the condition for polarization by reflection at oblique incidence.

Write short notes on (any two):