Question

Dimensional formula of magnetic field of induction (B) is:

Given Force on a charged particle is given by: $F=qvBsin\theta$ where $\theta$ is angle between velocity and magnetic field.

• A. $M{L}^2{T}^2{I}^{-1}$
• B. $ML{T}^2{I}^{-1}$
• C. $M{T}^{-2}{I}^{-1}$
• D. $M{T}^2{I}^1$

Answer 1

Answer: (C)

$M{T}^{-2}{I}^{-1}$

It is given:

$F=qvBsin\theta$

Hence, $B=\frac{F}{qvsin\theta }$

Dimensional formula of magnetic field is:

$\left[B\right]=\left[F/qv\right]$ as $sin\theta$ is dimensionless

$\left[B\right]=\left[ML{T}^{-2}\right]\left[I^{-1}{T}^{-1}\right]\left[L^{-1}T\right]$

$\left[B\right]=\left[M{T}^{-2}{I}^{-1}\right]$