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)

$\vec{F}=q \vec{v} \times \vec{B}$
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] $