Question

The dimensional formula for permittivity of free space $\left(\left(\epsilon \right)_{0}\right)$ in the equation $F=\frac{1}{4 \pi \epsilon _{0}}\frac{q_{1} q_{2}}{r^{2}}$ , where symbols have their usual meaning, is

• A. $\left[M^{1} \, L^{3} \, A^{- 2} \, T^{- 4}\right]$
• B. $\left[M^{- 1} \, L^{- 3} \, T^{4} \, A^{2}\right]$
• C. $\left[M^{- 1} \, L^{- 3} \, A^{- 2} \, T^{- 4}\right]$
• D. $\left[M^{1} \, L^{3} \, T^{2} \, A^{- 4}\right]$

Answer 1

Answer: (B)

$\left[M^{- 1} \, L^{- 3} \, T^{4} \, A^{2}\right]$

Answer 2

As, $F = \frac{1}{4 \pi \epsilon _{0}} \frac{q_{1} q_{2}}{r^{2}}$ $\Rightarrow \epsilon _{0} = \frac{q_{1} q_{2}}{4 \pi F r^{2}}$ $=\frac{\left[T A\right]^{2}}{\left[L^{2}\right] \left[M L T^{- 2}\right]}$ $=\left[M^{- 1} L^{- 3} \, T^{4} A^{2}\right]$