Question

Multiple Correct Answers Type
Which of the following pairs have the same dimensions?

• A. $h/e$ and magnetic flux
• B. $h/e$ and electric flux
• C. Electric flux and $a/{ϵ}_0$
• D. Electric flux and ${\mu }_{0}I$

Answer 1

Answer: (A), (C)

The correct options are
A $h/e$ and magnetic flux
C Electric flux and $a/{ϵ}_0$

$\left[h\right]=[Joute\times second]=\left[{ML}^2{T}^{-1}\right]$

[Magnetic flux] $=$ [Magnetic field $\times$ Area]

$\Rightarrow \left[\varphi \right]=\left[{MTA}^{-1}\right]\left[L^2\right]$

$\Rightarrow \left[\varphi \right]=\left[{ML}^2{TA}^{-1}\right]$

And

$\left[\frac{h}{e}\right]=\left[\frac{{ML}^2{T}^{-1}}{AT}\right]=\left[{ML}^2{T}^{-2}{A}^{-1}\right]$

[Electric flux] $=\left[E\right]\left[A\right]=\left[\frac{E}{q}\right]\left[A\right]$

$\Rightarrow$ [Electric flux] $=\left[\frac{F}{IT}\right]\left[A\right]=\frac{\left[ML{T}^{-2}\right]\left[L^2\right]}{AT}$

$=\left[{ML}^3{T}^{-3}{A}^{-1}\right]$