Question

In the formula, $a=3bc^{2}$ , $a$ and $c$ have dimensions of electric capacitance and magnetic field intensity respectively. The dimensions of $b$ in $S.I.$ system are

• A. $\left[\right.M^{- 3}L^{- 2}T^{4}Q^{4}\left]\right.$
• B. $\left[\right.M^{- 3}T^{4}Q^{4}\left]\right.$
• C. $\left[\right.M^{- 3}T^{3}Q\left]\right.$
• D. $\left[\right.M^{- 3}L^{2}T^{4}Q^{- 4}\left]\right.$

Answer 1

Answer: (A)

Given, $a=3bc^{2}$
$⇒ \, \, \, b=\frac{a}{3 c^{2}}$
Writing dimensions for $a$ and $c$ , we have
$\left[b\right]=\frac{\left[Q / V\right]}{\left[B\right]^{2}}=\frac{\left[Q\right] \left[\right. M L^{2} T^{- 2} Q^{- 1} \left]\right.^{- 1}}{\left[M T^{- 1} Q^{- 1}\right]^{2}}$
$=\left[\right.M^{- 3}L^{- 2}T^{4}Q^{4}\left]\right.$