Q. Which of the following pairs has/have the same dimensions?

Physical World, Units and Measurements Report Error

A

$h / e$ and magnetic flux

B

$h / e$ and electric flux

C

Electric flux and $q / \varepsilon_{0}$

D

Electric flux and $\mu_{0} I$

Solution:

Dimensions of magnetic flux $=$ magnetic field $\times$ area
$=\left[\frac{F}{i L}\right] \times[\text { Area }]=\frac{M L T^{-2}}{A L} L^{2}=\left[M L^{2} T^{-2} A^{-1}\right]$
Dimensions of $\frac{h}{a}=\left[\frac{\text { Planck's constant }}{\text { Charge }}\right]$
$=\left[\frac{M L^{2} T^{-1}}{A T}\right]=\left[M L^{2} T^{-2} A^{-1}\right]$
From Gauss theorem, electric flux $=\frac{q}{\varepsilon_{0}}$

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