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Question: Answered & Verified by Expert
If $n$ denotes a positive integer, $h$ the Planck constant, $q$ the charge and $B$ the magnetic field, then the quantity $\left[\frac{n h}{2 \pi q B}\right]$ has the
PhysicsUnits and DimensionsWBJEEWBJEE 2014
Options:
  • A area
  • B length
  • C speed
  • D acceleration
Solution:
2546 Upvotes Verified Answer
The correct answer is: area
$\left[\frac{n h}{2 \pi q B}\right]$
where $n$ and $2 \pi$ dimensionless quantity
So, $[h]=[m v r]$
$\begin{aligned}
\mid q B] &=\left[\frac{q v B}{v}\right]=\left[\frac{F}{v}\right] \\
\therefore \quad\left[\frac{m v r}{F / v}\right] &=\frac{[m v r][v]}{[F]} \\
&=\left[\frac{\left[m v^{2} r\right]}{r}\right]=\left[r^{2}\right\}=\text { Area }
\end{aligned}$

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