Question

In terms of potential difference V; electric current I, permittivity ${\epsilon }_0$, permeability ${\mu }_0$ and speed of light c, the dimensionally correct equation(s) is(are).

• A. ${\mu }_0{I}^2={\epsilon }_0{V}^2$
• B. ${\epsilon }_{0}I={\mu }_{0}V$
• C. $I={\epsilon }_{0}cV$
• D. ${\mu }_{0}cl={\epsilon }_{0}V$

Answer 1

Answer: (A), (C)

${\mu }_0{I}^2={\epsilon }_0{V}^2$
$I={\epsilon }_{0}cV$

Dimensional formula of potential difference $=M{L}^2{T}^{-3}{A}^{-1}$

Current $=A$

$C=L{T}^{-1}{N}_0=ML{T}^{-2}{A}^{-2}{\epsilon }_0=M^{-1}{L}^{-3}{T}^4{A}^2$

By evaluation equation we get

$N_0{I}^2={\epsilon }_0{V}^2\to \left(1\right)I={\epsilon }_{0}cV$