Q 11-01-198JEE MainJEE Main 2020 (5 Sep, Shift 2)Easy
The quantities $x = \dfrac{1}{\sqrt{\mu_0\varepsilon_0}}$, $y = \dfrac{E}{B}$ and $z = \dfrac{l}{CR}$ 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 the free space permittivity and permeability respectively. Then:
Answer: (A) $x$, $y$ and $z$ have the same dimension
$\dfrac{1}{\sqrt{\mu_0\varepsilon_0}} = c$, the speed of light, so $x$ is a speed.
For an electromagnetic wave $E = cB$, so $y = E/B$ is also a speed.
$CR$ is a time constant (dimension of time), so $z = l/(CR)$ is length per time, again a speed.
All three have the dimension $[LT^{-1}]$.
Solution by Sreeraj P, M.Sc Physics