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Q.
Which of the following units denotes the dimensions $ [ ML^2 / Q^2 ]$, where Q denotes the electric charge ?
BHUBHU 2007Physical World, Units and Measurements
Solution:
Magnetic energy $=\frac{1}{2} L i^{2}=\frac{L Q^{2}}{2 t^{2}}$
$[L \rightarrow$ inductance, $i \rightarrow$ current $]$
Energy has the dimensions $\left[ ML ^{2} T ^{-2}\right]$
Equate the dimensions, we have
$ \left[ ML ^{2} T ^{-2}\right]=$ henry $\times \frac{\left[ Q ^{2}\right]}{\left[ T ^{2}\right]} $
$\Rightarrow $ henry $=\frac{\left[ ML ^{2}\right]}{\left[ Q ^{2}\right]}$