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Answer 1 · 2017-09-21T17:13:03

$M T^{- 2} A^{- 1}$ $MT^(-2)A^(-1)$

Magnetic induction is defined from the Lorentz force law.

In scalar form,

$F = q v B$ $F = qvB$
$\Rightarrow [B] = \frac{[F]}{[q] [v]}$ $implies [B] = [[F]]/([q][v])$

Now,

$[F] = M L T^{- 2}$ $[F] = MLT^(-2)$
$[q] = A T$ $[q] = AT$
$[v] = L T^{- 1}$ $[v] = LT^(-1)$

Substituting these,

$[B] = \frac{M L T^{- 2}}{A T L T^{- 1}}$ $[B] = (MLT^(-2))/(ATLT^(-1))$
$\Rightarrow [B] = M T^{- 2} A^{- 1}$ $implies [B] = MT^(-2)A^(-1)$