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Q.
If $n$ denotes a positive integer, $h$ the Planck’s constant, $q$ the charge and $B$ the magnetic field, then the quantity $\left(\frac{nh}{2\,\pi qB}\right)$ has the dimension of
WBJEEWBJEE 2014Physical World, Units and Measurements
Solution:
$\left[\frac{n h}{2 \pi q B}\right]$
where $n$ and $2 \pi$ dimensionless quantity
So, $[h]=[m v r]$
$[q B]=\left[\frac{q v B}{v}\right]=\left[\frac{F}{v}\right]$
$\therefore \left[\frac{m v r}{F / v}\right]=\frac{[m v r][v]}{[F]}$
$=\frac{\left[m v^{2} r\right]}{\left[\frac{m v^{2}}{r}\right]}=\left[r^{2}\right]=$ Area