Question

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

• A. area
• B. length
• C. speed
• D. acceleration

Answer 1

Answer: (A)

$\left[\frac{nh}{2\pi qB}\right]$
where $n$ and $2\pi$ dimensionless quantity
So, $[h]=[mvr]$
$[qB]=\left[\frac{qvB}{v}\right]=\left[\frac{F}{v}\right]$
$\therefore \left[\frac{mvr}{F/v}\right]=\frac{[mvr][v]}{[F]}$
$=\frac{\left[m{v}^{2}r\right]}{\left[\frac{m{v}^2}{r}\right]}=\left[r^2\right]=$ Area