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Physics Question on Inductance

Which of the following units denotes the dimensions [ML2/Q2],[ML^2/Q^2], where QQ denotes the electric charge ?

A

Wb/m2Wb/m^2

B

henry (H)

C

H/m2H/m^2

D

weber (Wb)

Answer

henry (H)

Explanation

Solution

Magnetic energy =12Li2=LQ22t2=\frac{1}{2}Li^{2}=\frac{LQ^{2}}{2t^{2}} [L→L \rightarrow inductance, i→i \rightarrow current] Energy has the dimensions [ML2T−2].[ML^2T^{-2}]. Equate the dimensions, we have [ML3T−2]=(henry)×[Q2][T2]\left[ML^{3}T^{-2}\right]=\left(henry\right)\times \frac{\left[Q^{2}\right]}{\left[T^{2}\right]} ⇒[henry]=[ML2][Q2]\Rightarrow \left[henry\right]=\frac{\left[ML^{2}\right]}{\left[Q^{2}\right]}