Explanation

$F_{m} = Bqv$ or $\lbrack B\rbrack = \left\lbrack \frac{F_{m}}{qv} \right\rbrack = \left\lbrack \frac{F_{m}}{Itv} \right\rbrack$ $= \frac{\left\lbrack MLT^{- 2} \right\rbrack}{\lbrack A\rbrack\lbrack T\rbrack\lbrack LT^{- 1}\rbrack} = \lbrack ML^{0}T^{- 2}A^{- 1}\rbrack$ Alternate $F = BIl \Rightarrow \lbrack B\rbrack = \left\lbrack \frac{F}{Il} \right\rbrack = \lbrack ML^{0}T^{- 2}A^{- 1}\rbrack$