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    Ends em 2021

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    Hriday Mittal
    The document is a 50-mark end-semester exam for PH444 Electromagnetic Theory consisting of 5 questions. Question 1 involves calculating the force on a point charge near a conducting surface and deriving the Green's function for this geometry. Question 2 calculates the rms value of the magnetic field due to solar radiation. Question 3 finds the stress tensor elements for a plane electromagnetic wave. Question 4 examines the electric fields from moving point charges. Question 5 derives expressions for the velocity and retarded distance used to calculate the electric field on a stationary charge from an accelerating moving charge.

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    © All Rights Reserved
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    Ends em 2021

    Uploaded by

    Hriday Mittal
    17 views2 pages
    The document is a 50-mark end-semester exam for PH444 Electromagnetic Theory consisting of 5 questions. Question 1 involves calculating the force on a point charge near a conducting surface and deriving the Green's function for this geometry. Question 2 calculates the rms value of the magnetic field due to solar radiation. Question 3 finds the stress tensor elements for a plane electromagnetic wave. Question 4 examines the electric fields from moving point charges. Question 5 derives expressions for the velocity and retarded distance used to calculate the electric field on a stationary charge from an accelerating moving charge.

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    Ends Em 2021

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    The document is a 50-mark end-semester exam for PH444 Electromagnetic Theory consisting of 5 questions. Question 1 involves calculating the force on a point charge near a conducting surface and deriving the Green's function for this geometry. Question 2 calculates the rms value of the magnetic field due to solar radiation. Question 3 finds the stress tensor elements for a plane electromagnetic wave. Question 4 examines the electric fields from moving point charges. Question 5 derives expressions for the velocity and retarded distance used to calculate the electric field on a stationary charge from an accelerating moving charge.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    17 views2 pages

    Ends em 2021

    Uploaded by

    Hriday Mittal
    The document is a 50-mark end-semester exam for PH444 Electromagnetic Theory consisting of 5 questions. Question 1 involves calculating the force on a point charge near a conducting surface and deriving the Green's function for this geometry. Question 2 calculates the rms value of the magnetic field due to solar radiation. Question 3 finds the stress tensor elements for a plane electromagnetic wave. Question 4 examines the electric fields from moving point charges. Question 5 derives expressions for the velocity and retarded distance used to calculate the electric field on a stationary charge from an accelerating moving charge.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    PH444 (Jan 2021): End semester exam

    PH444 : Electromagnetic Theory (Jan 2021): End-semester


    50 marks (to be scaled later) : Time 4 hours (including uploading to Moodle etc) April 27, 2021

    Note :
    ˆ The exam is open-note and open-book. You can use your computer if needed. Internet browsing is
    ok, but no group discussions/chats etc!S
    ˆ You do not need to derive the fields of a charge in motion. Use the results derived in the lectures
    as standard, but show the steps of your calculation clearly starting from the general formula.

    1. Consider a conducting surface formed by joining the xy plane and a conducting hemispherical shell
    of radius a, centered at the origin as shown. A point charge q is placed at the location (0, 0, L)
    where L > a and the conducting surface is held at a potential V = 0.

    (a) What is the force experienced by the point charge? Your answer should be in closed form.
    (b) Utilise this and generalise your solution to get the Green’s function for this geometry. This
    means solving for
    
    2 3 ~0 G=0 r→∞
    ∇ G = −δ (~r − r )
    G=0 plane + hemisphere

    Note that r~0 ≡ (x0 , y 0 , z 0 ) is not necessarily on the z axis. Your answer should be in closed form.
    Use (x, y, z, x0 , y 0 , z 0 ) co-ordinates to write your answer.

    (5+5=10 marks)
    2. The amount of solar energy the upper atmosphere receives is approximately 1300 W.m−2 . Calculate
    the rms value of the magnetic field due to this radiation assuming the entire radiation is concentrated
    in one wavelength. Compare this (rms value) with the earth’s magnetic field at the surface (≈ 50µT ).
    (5 marks)
    3. A monochromatic plane EM wave has an electric field
    ~ r, t) = ŷE0 sin (kx − ωt)
    E(~

    Calculate all the elements of the stress tensor (Tij )in terms of Ey only.
    (5 marks)

    page 1 of 2
    PH444 (Jan 2021): End semester exam

    4. A point charge q is held stationary on the y axis, at y = L (L > 0). Another charge q moves
    q
    with uniform velocity v along x axis. Let E0 = denote the strength of the electric field with
    4π0 L2
    which we normalise other quantities.
    ~
    E
    
    Ex Ey Ez
    
    (a) What are all the components of the field = , , acting on the stationary charge
    E0 E0 E0 E0
    at the instant the moving charge crosses the origin?
    (b) Now suppose the moving charge was approaching the origin from the negative y axis with
    uniform velocity v as before. What are the components of the field it creates at the location
    of the stationary charge at the instant it is at the origin?
    (c) What are the components of the field acting on the moving charge at that instant due to the
    static charge in the first and second case?
    (d) A point charge is moving with a constant velocity v, such that the electric field in the forward
    direction and transverse direction at the same radial distance (from the instantaneous position
    of the charge) differ by 1%. With what fraction of the speed of light (v/c) must the particle
    be moving ?

    (5×4=20 marks)

    5. Suppose a charge q is stationary at y = L (L > 0) and a charge is moving along y towards the
    origin from the negative side. The charge has a constant acceleration a along the y axis, and when
    it arrives at the origin it has a velocity v. Obviously v is not constant.

    (a) Show that the velocity (say u) at the appropriate retarded time and the appropriate retarded
    distance (Rr ) for calculating the field at the location of stationary charge at that instant is
    v  r v 2 aL
    −1 + 1− +2 2
    c c c
    Rr =
    a/c2
    r
    u v 2 aL
    = 1− 1− +2 2
    c c c

    (b) Find an expression for the electric field on the stationary particle at the instant when the
    moving particle is at the origin, in terms of u and Rr .

    (5+5=10 marks)

    page 2 of 2

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