i) Which diagram represents linear polarized light at 45 degrees?
ii) Which diagram represents left circular light? Explain.
iii) Which diagram represents un-polarized light?
b) Consider the following expression for a harmonic wave travelling in the positive x direction
(full equation in the attached file)
Identify each of the parameters in the attached expression, and show that this wave is a solution of the differential wave equation, attached.
c) Consider the following two harmonic waves:
i) Show each of these waves in a phasor diagram.
ii) In the same diagram, show the wave that results from the addition of these two harmonic waves.
iii) Determine the mathematical expression for the resultant wave. What sort of wave is the resultant? Use the expression you derived to justify your answer.
We solve problems involving polarization, superposition of harmonic waves, and the wave equation.
Electromagnetism & optics
a. A fixed volume charge distribution of constant charge density p_0 is contained within a rectangular box centered at the origin of a Cartesian coordinate system (x, y, z). The box has dimensions w X w X d, where d << w ( i.e. you can model the sheet as infinite in the x and y directions).
i) Find the total charge inside the box
ii) Find the electric field E(z) on the z-axis above, below and inside the box under the assumption that z << w.
iii) On the z-axis, find the difference in the electric potential between the bottom and center of the box i.e., find V(z = 0) - V(z = -d/2), and between the bottom and the top of the box i.e., find V(z = d/2) -V(z = -d/2).
b. A large plane parallel slab of a linear homogeneous dielectric material also of thickness f with a relative permittivity, E_p is placed on the top surface of the charged box of question 2(a).
i) Find the electric field inside the diaelectric
ii) Fine the polarization vector P on the z-axis
iii) Find the bound volume and surface polarization charge densities along the z- axis
c. Consider a charge distribution enclosed in a box with the same geometry as the box in question 2(a) and 2(b), but rather than having a constant charge density, the charge density varies inside the box with z as p(z) = k(z + d/2), where k is a constant.
i) Fine the total charge inside the box.
ii) Find the electric field E(z) on the z-axis inside the box.
iii) On the z-axis, find the difference in the electric potential between the bottom and center of the box, i.e., find V(z = 0) - V(z = -d/2), and between the bottom and the top of the box, i.e., find V(z = d/2) - V(z = -d/2).