Question

Sol. [Key Concept: Recognize $\frac{1}{2}\varepsilon_{0}E^{2}$ as energy density $\lbrack{ML}^{- 1}T^{- 2}\rbrack$; match the powers for $2a - b + c$.]

$\frac{1}{2} \in_{0}E^{2} =$ Energy density

$$\therefore\left\lbrack \frac{1}{2}\epsilon_{0}E^{2} \right\rbrack = \frac{{ML}^{2}{\text{ }T}^{- 2}}{{\text{ }L}^{3}} = {ML}^{- 1}{\text{ }T}^{- 2} $$

$$\therefore a = 1,\text{ }b = - 1,c = - 2 $$

$$\therefore 2a - b + c = 2 + 1 - 2 = 1 $$