Dimensional Formula of Energy Density – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Dimensions

Dimensional Formula of Energy Density

The dimensional formula of \(\frac{1}{2}\epsilon_0 E^2\) is (All symbols have their usual meaning)
\([ML^{-1} T^{-2}]\)
\([M^0 L^0 T^0]\)
\([MLT^{-3}]\)
\([ML^{-3} T^{-2}]\)

Solution:

The term \(\frac{1}{2}\epsilon_0 E^2\) represents the electrostatic energy density (energy per unit volume). Therefore, its dimensional formula is \(\frac{[ML^2T^{-2}]}{[L^3]} = [ML^{-1}T^{-2}]\).

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