An experimental setup is designed to investigate the polarization of electromagnetic waves. A VHF transmitter emits horizontally polarized radio waves. A receiver consisting of a straight dipole antenna is positioned to detect the signal, and its output is connected to a power meter that displays the relative intensity of the detected signal.
Initially, the receiving dipole antenna is oriented horizontally (aligned parallel to the electric field of the transmitter), so that the detected intensity is at its maximum value, I0I_0I0. The dipole antenna is then slowly rotated in a plane perpendicular to the direction of wave propagation through a full 360∘ 360^\circ\,360∘ rotation.
Sketch a graph to show how the relative intensity I/I0 I/I_0\,I/I0 of the detected signal varies with the angle of rotation θ\thetaθ, as the antenna is rotated from 0∘ 0^\circ\,0∘ to 360∘360^\circ360∘. Start your graph from the initial parallel position (θ=0∘\theta = 0^\circθ=0∘). Clearly label the key angles on the horizontal axis and the values on the vertical axis.
Maxwell's electromagnetic theory relates the speed of light c c\,c in a vacuum to the permeability of free space μ0 \mu_0\,μ0 and the permittivity of free space ε0 \varepsilon_0\,ε0 via the equation:
c=1μ0ε0 c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} c=μ0ε01Using the accepted speed of light c=3.00×108 m s−1c = 3.00 \times 10^8 \text{ m s}^{-1}c=3.00×108 m s−1 and the permeability of free space μ0=4π×10−7 H m−1\mu_0 = 4\pi \times 10^{-7} \text{ H m}^{-1}μ0=4π×10−7 H m−1, calculate the value of the permittivity of free space ε0 \varepsilon_0\,ε0 predicted by this relationship. Show your working. Explain how the historical determination of the value of c c\,c using Maxwell's equation provided crucial evidence that light is an electromagnetic wave.
