Question

Consider three quantities : $x=\frac{E}{B},y=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$ and $z=\frac{l}{CR}$. Here $l$ is the length of a wire, $C$ is the capacitance, $E$is electric field, $B$ is magnetic field and $R$ is resistance. All other symbols have usual meanings. Then

• A. $x$ and $y$ have the same dimensions.
• B. $x$ and $y$ have the same dimensions.
• C. $y$ and $z$ have the same dimensions.
• D. None of the above three pairs have the same dimensions.

Answer 1

Answer: (A), (B), (C)

$y$ and $z$ have the same dimensions.

Unit of $x=\frac{\text{Unit of E}}{\text{Unit of B}}=\text{Unit of velocity}$

Because $E=vB$,

$y=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}=c\to \text{Velocity of light}$

Unit of $z=\frac{\text{Unit of}l}{\text{Unit of}RC}=\frac{\text{Length}}{\text{Time}}=\text{Velocity}$