The quantities $x = \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$,$y = \frac{E}{B}$,and $z = \frac{l}{CR}$ are defined,where $C$ is capacitance,$R$ is resistance,$l$ is length,$E$ is electric field,$B$ is magnetic field,and $\varepsilon_{0}, \mu_{0}$ are free space permittivity and permeability respectively. Then:

  • A
    Only $x$ and $y$ have the same dimension
  • B
    $x, y$ and $z$ have the same dimension
  • C
    Only $x$ and $z$ have the same dimension
  • D
    Only $y$ and $z$ have the same dimension

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Suppose that the electric field part of an electromagnetic wave in vacuum is $E = \{(3.1 \; N/C) \cos [(1.8 \; rad/m) y + (5.4 \times 10^{6} \; rad/s) t] \} \hat{i}$.
$(a)$ What is the direction of propagation?
$(b)$ What is the wavelength $\lambda$?
$(c)$ What is the frequency $\nu$?
$(d)$ What is the amplitude of the magnetic field part of the wave?
$(e)$ Write an expression for the magnetic field part of the wave.

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