question_answer

In the formula \[X=3\,Y{{Z}^{2}}\], X and Y have dimensions of capacitance and magnetic induction respectively. The dimensions of Y should be........ Fill in the blanks.

Answer:

                From \[X=\text{ 3}Y{{Z}^{2}}\] \[Y=\text{ }\frac{\text{X}}{\text{3}{{Z}^{2}}}=\frac{capaci\tan ce}{{{\left( mag.\,induction \right)}^{2}}}=\frac{{{M}^{-1}}{{L}^{-2}}{{T}^{2}}{{Q}^{2}}}{\left[ M{{T}^{-1}}{{Q}^{-1}} \right]}=\left[ {{M}^{-3}}{{L}^{-2}}{{T}^{4}}{{Q}^{4}} \right]\]