Question

If $n$ denotes a positive integer, $h$ the Plancks constant, $q$ the charge and $B$ the magnetic field, then the quantity $\left(\begin{array}{c}\frac{nh}{2\pi qB}\end{array}\right)$ has the dimension of

• A. Area
• B. Length
• C. Speed
• D. Acceleration

Answer 1

Answer: (A)

Area

Since $qvB=F$

$⟹qB=\frac{F}{v}$

which has dimensions $\left[M{T}^{-1}\right]$

$h$ has dimensions $\left[M{L}^2{T}^{-1}\right]$

Hence the dimension of $\left(\frac{nh}{2\pi qB}\right)$ is $\left[L^2\right]$, which is that of area.