Question

In the formula X = 3YZ², X and Z have dimensions of capacitance and magnetic induction respectively , what are the dimensions of Y in mks system

Answer 1

Given formula X= 3YZ² where X has dimension of capacitance and Z has dimension of magnetic induction.
As Q = CV
$$\begin{gathered} or,IT=\left[C\right]M{L}^2{I}^{-1}{T}^{-2},or\left[C\right]=M^{-1}{L}^{-2}{I}^2{T}^4 \\ NowF=qvB \\ or,ML{T}^{-2}=IT\times L{T}^{-1}\left[B\right] \\ or,\left[B\right]=M{I}^{-1}{T}^{-2} \end{gathered}$$
​Therefore dimension of Y is XZ^-2 =$=M^{-1}{L}^{-2}{I}^2{T}^4{\left[M{I}^{-1}{T}^{-2}\right]}^{-2}=M^{-3}{I}^4{L}^{-2}{T}^8$