Question

What is the dimensional formula of the energy density of an electromagnetic wave?

• A. $ [ML^{-1}T^{-2}] $
• B. $ [ML^{-2}T^{-2}] $
• C. $ [ML^{-1}T^{-3}] $
• D. $ [ML^{-2}T^{-3}] $

Hint:

To find the dimensional formula of energy density, simply divide the dimensional formula of energy by that of volume.

Answer 1

The Correct Option is A

Step 1: Understand what energy density means
Energy density is defined as energy per unit volume: \[ \text{Energy Density} = \frac{\text{Energy}}{\text{Volume}} \] \vspace{0.3cm} Step 2: Recall dimensional formulas of related quantities
Energy has the dimensional formula: \[ [E] = [ML^2T^{-2}] \] Volume has the dimensional formula: \[ [V] = [L^3] \] \vspace{0.3cm} Step 3: Find the dimensional formula of energy density
Using: \[ \text{Energy Density} = \frac{\text{Energy}}{\text{Volume}} = \frac{[ML^2T^{-2}]}{[L^3]} = [ML^{-1}T^{-2}] \] \vspace{0.3cm} Step 4: Match with correct option
This matches option: \[ {[ML^{-1}T^{-2}]} \]