The dimensional formula of \(\dfrac{1}{2}\epsilon_0 E^2\) (\(\epsilon_0\) = permittivity of vacuum and \(E\) = electric field) is \(M^a L^b T^c\). The value of \(2a - b + c = \) _______.

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: \(1\)