The dimensional formula of (1)/(2) _0 E^2 ( _0 = permittivity of...

The quantity $\dfrac{1}{2}\epsilon_0 E^2$ represents the energy density of an electric field.

Energy density is defined as energy per unit volume.

Dimensional formula of energy is $[M L^2 T^{-2}]$.

Dimensional formula of volume is $[L^3]$.

Dimensional formula of energy density $= \dfrac{[M L^2 T^{-2}]}{[L^3]} = [M L^{-1} T^{-2}]$.

Comparing this with $M^a L^b T^c$, we get:
$a = 1$
$b = -1$
$c = -2$

The value of $2a - b + c = 2(1) - (-1) + (-2) = 2 + 1 - 2 = 1$.

Answer: $1$