Question

The magnetic force on a point charge is $\vec{F}=q(\vec{v}\times \vec{B})$ Here, $q=$ electric charge $\vec{v}=$ velocity of point charge $\vec{B}=$ magnetic field The dimensions of $\vec{B}$ is:

• A. $[ML{{T}^{-1}}A]$
• B. $[{{M}^{2}}L{{T}^{-2}}{{A}^{-1}}]$
• C. $[M{{T}^{-2}}{{A}^{-1}}]$
• D. none of these

Answer 1

Answer: (C)

$[M{{T}^{-2}}{{A}^{-1}}]$

Answer 2

$\vec{F}=q \vec{v} \times \vec{B}$ or $F=q v B \sin \theta$ $\therefore [B] =\left[\frac{F}{q v}\right]=\frac{M L T^{-2}}{[A T]\left[L T^{-1}\right]}$ $=\left[M T^{-2} A^{-1}\right]$