Question

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

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

Answer 1

Answer: (A)

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