A) \[\left[ M{{L}^{2}}{{T}^{-2}}{{Q}^{-1}} \right]\]
B) \[\left[ M{{L}^{2}}{{T}^{-1}} \right]\]
C) \[\left[ M{{L}^{-2}}{{Q}^{-1}} \right]\]
D) \[[ML{{T}^{-2}}\,{{Q}^{-2}}]\]
Correct Answer: A
Solution :
From Faradays law of electromagnetic induction, \[e=-\frac{\Delta \text{ }\!\!|\!\!\text{ }}{\Delta t}\] where \[\Delta \text{ }\!\!|\!\!\text{ }\]is magnetic flux and At is time. \[\therefore \] Dimensions of \[e=-\frac{\text{dimenstions}\,\text{of}\,\text{magnetic}\,\text{flux}}{\text{dimensions}\,\text{of}\,\text{time}}\] \[=-\frac{[M{{L}^{2}}{{T}^{-2}}{{A}^{-1}}]}{[T]}=[M{{L}^{2}}{{T}^{-2}}{{Q}^{-1}}]\] Where \[\theta \]is charge. Alternative: If during the flow of q coulomb of charge in an electric circuit, the energy supplied by cell is W joule, then the emf E of the cell is \[E=\frac{W}{q}J/C\] Dimensions of \[E=\frac{\text{dimensions}\,\text{of}\,\text{W}}{\text{dimensions}\,\text{of}\,\text{q}}=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[Q]}\] \[=[M{{L}^{2}}{{T}^{-2}}{{Q}^{-1}}]\]
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