Question

Which of the following units denotes the dimensions $[M{L}^2/Q^2]$, where Q denotes the electric charge ?

• A. $Wb/m^2$
• B. Henry (H)
• C. $H/m^2$
• D. Weber (Wb)

Answer 1

Answer: (B)

Magnetic energy $=\frac{1}{2}L{i}^2=\frac{L{Q}^2}{2t^2}$
$[L\to$ inductance, $i\to$ current $]$
Energy has the dimensions $\left[M{L}^2{T}^{-2}\right]$
Equate the dimensions, we have
$\left[M{L}^2{T}^{-2}\right]=$ henry $\times \frac{\left[Q^2\right]}{\left[T^2\right]}$
$\Rightarrow$ henry $=\frac{\left[M{L}^2\right]}{\left[Q^2\right]}$