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)

area

The quantity is given as $[\frac{nh}{2\pi qB}]$ ..........(1)

where the symbols have their usual meaning.

$mvr=\frac{nh}{2\pi }$ ............(a)

Also using:

$Bqr=mv$

$⟹qB=\frac{mv}{r}$ .........(b)

Using (a) and (b) in (1), we get: $[\frac{nh}{2\pi qB}]$ $=[\frac{mvr}{\frac{mv}{r}}]=\left[r^2\right]$

As $r$ has the dimension of length, thus the given quantity has the dimension of area.