The dimensional formula of 1/2ε₀ E² ( ε₀ = permittivity of vacuum and E = electric field) is MaLbTc. The value of 2a - b + c = ________. (a) 0 (b) 1 (c) -1 (d) 2

Answer: (b). 1/2ε₀E² is energy density: [ML⁻¹T⁻²]. a = 1, b = -1, c = -2. 2a - b + c = 2 + 1 - 2 = 1. So the answer is (b) 1.

The dimensional formula of 1/2ε₀ E² ( ε₀ = permittivity of vacuum and… | JEE Main 2026 (2 Apr, Shift 1)

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Applications of Dimensional Analysis

The dimensional formula of $\frac{1}{2}\epsilon_0 E^2$ ( $\epsilon_0$ = permittivity of vacuum and $E$ = electric field) is $M^aL^bT^c$ . The value of $2a - b + c =$ ________.

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Answer: (b)

$\frac{1}{2}\epsilon_0E^2$ is energy density: $[ML^{-1}T^{-2}]$ .
$a = 1$ , $b = -1$ , $c = -2$ .
$2a - b + c = 2 + 1 - 2 = 1$ .
So the answer is (b) 1.

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