Q. In the formula, $a = 3bc^{2},a$ and $c$ have dimensions of electric capacitance and magnetic induction respectively. What are dimensions of $b$ in MKS system?
A) $\lbrack M^{- 3}L^{- 2}T^{4}Q^{4}\rbrack$
B) $\lbrack M^{- 3}T^{4}Q^{4}\rbrack$
C) $\lbrack M^{- 3}T^{3}Q\rbrack$
D) $\lbrack M^{- 3}L^{2}T^{4}Q^{- 4}\rbrack$
Explanation
Given, $a = 3bc^{2}$ $\Longrightarrow \ b = \frac{a}{3c^{2}}$ Writing dimensions for $a$ and $c$, we have $\lbrack b\rbrack = \frac{\lbrack Q/V\rbrack}{\lbrack B\rbrack^{2}} = \frac{\lbrack Q\rbrack\lbrack ML^{2}T^{- 2}Q^{- 1}\rbrack}{\left\lbrack MT^{- 1}Q^{- 1} \right\rbrack^{2}}$ $= \lbrack M^{- 3}L^{- 2}T^{4}Q^{4}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.