Question

Which of the following units denotes the dimensions $\frac {ML^{2}} {Q^{2}},$ where $Q$ denotes the electric charge ?

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

Answer 1

Answer: (B)

Henry (H)

Answer 2

Magnetic energy=$\frac{1}{2} Li^{2} =\frac{LQ^{2}}{2t^{2}}$ \left\\{L\to inductance, i\to current\right\\} Energy has the dimensions $\left[ML^{2} T^{2}\right]\cdot$ Equate the dimensions, we have $\left[ML^{2} T^{2}\right]=\left(henry\right) \times\frac{\left[Q^{2}\right]}{\left[T^{2}\right]}$ $\Rightarrow\, \quad\left[henry\right]=\frac{\left[ML^{2}\right]}{\left[Q^{2}\right]}$