end553.html

SESSION 2003-2004: Semester I

PHY 553: ELECTRODYNAMICS

End-Semester Examination: Answers to Part I

Q.1. No credit for writing equations and symbols, even if they are relevant

i) Green's function (no credit for any other answer)

        ii) radiation zone

       iii) + i \epsilon prescription (or: Feynman's + i \epsilon prescription ) (no credit unless the + is specified)

        iv) Poynting's theorem

         v) duality transformation

        vi) Hertz potential (or: Hertz vector)

       vii) Fresnel's rhomb (quarter-wave plate is also okay, but not half-wave plate)

      viii) Fresnel relations (or: Fresnel equations, or: Fresnel coefficients)

        ix) skin depth (no credit for any other answer)

         x) anomalous dispersion (just dispersion is not enough)

        xi) Kramers-Krȍnig relations (the names must be there)

       xii) stellar aberration (just aberration is also okay)

      xiii) light cone (no credit for any other answer)

       xiv) Krȍnecker delta (no credit for just delta, or delta function, or writing the symbol)

        xv) orthochronous (no credit for proper orthochronous or improper orthochrnous)

       xvi) Bianchi identity (no credit for any other answer or equations)

      xvii) Larmor formula (any variation which has the word Larmor is okay)

     xviii) pulsars (this word must be there: neutron star will get no credit)

       xix) Nȍther's theorem (the word Nȍther must be there)

        xx) gauge invariance

Q.2. No credit if a correct staments is replaced by another correct statement. No credit for just writing incorrect.

i) The electric and magnetic fields are always perpendicular to each other for harmonic fields.

        ii) Microwaves have frequencies ranging from a few to a few thousand GigsHertz.
(Okay if radio frequencies are correctly given; no credit if Giga is just replaced by Mega)

       iii) Maxwell's stress tensor measures the electromagnetic force on a boundary containing fields inside.
(Okay so long as it is realised that sources ned not be inside).

        iv) correct

         v) div A + (1/c) dø/dt = 0 (no credit for any other answer, except same equation in SI units)

        vi) correct

       vii) There is no such thing as multipole radiation because charge is conserved.

      viii) The laws of reflection and refrction at a dielectric interface follow from the continuity of phase across teh surface.
(No credit if the word phase is missing)

        ix) The Brewster angle for glass of R.I. = 1.5 is about 56.3 degrees
(arctan 1.5 is also acceptable)

         x) The Lorentz-Lorenz formula relates the atomic polarisability to the refractive index of the medium.
(Dielectric constant instead of refractive index is also okay)

        xi) In a metal the skin-depth is given by \delta = c \epsilon / 4\pi \sigma
(Any correct formula containing \sigma is acceptable)

       xii) correct

      xiii) The longitudinal mass m_L = m_0 / (1 - \beta^2)^(3/2)
OR
The transverse mass m_T = m_0 / (1 - \beta^2)^(1/2)

       xiv) We can always transform away the space component of a timelike vector.
OR
We can always transform away the time component of a spacelike vector.

        xv) The 4x4 Lorentz matrix has 6 independent components.

       xvi) The retarded time for a moving particle corresponds to its world line intersecting the backward light cone.
(Absolute past light cone is also okay; full credit is given if this fact was realised)

      xvii) The Lienard-Weichert potentials lead to B = \hat{r} x E
OR
The Lienard-Weichert potentials lead to B = beta x E for slowly-moving charges

     xviii) correct

       xix) The Euler-Lagrange equations for a classical field ø are obtained by extremising the action w.r.t. fixed-end-point
            variations.
(Full credit for any equivalent statement)

        xx) The photon mass term m² A_µA^µ is forbidden by gauge invariance.
(Full credit for charge conservation in place of gauge invariance).