The unit of √2I / ϵ₀c is: (I = intensity of an electromagnetic wave, c: speed of light)
❓ Question The unit of 2 I ε 0 c is to be found, where I I = intensity of an electromagnetic wave, ε 0 \varepsilon_0 = permittivity of free space, and c c = speed of light. 🖼️ Question Image ✍️ Short Solution Step 1: Expressing E 0 E_0 I = 1 2 ε 0 c E 0 2 ⇒ E 0 = 2 I ε 0 c So, 2 I ε 0 c = E 0 ε 0 c . Step 2: Dimensional Analysis We know the SI units : E 0 E_0 : electric field intensity → V/m = N/C = kg m s − 3 A − 1 ε 0 \varepsilon_0 : permittivity → C 2 N − 1 m − 2 = A 2 s 4 kg − 1 m − 3 c c : speed of light → m/s \text{m/s} Now substitute: Unit of E 0 ε 0 c = ( kg m s − 3 A − 1 ) ( A 2 s 4 kg − 1 m − 3 ) ( m s − 1 ) \text{Unit of } \frac{E_0}{\varepsilon_0 c} = \frac{(\text{kg·m·s}^{-3}\text{·A}^{-1})} {(\text{A}^2\text{·s}^4\text{·kg}^{-1}\text{·m}^{-3})(\text{m·s}^{-1})} Simplify powers of base units step-by-step: kg: 1 − ( − 1 ) = 2 1 - (-1) = 2 m: 1 − ( − 3 + 1 ) = 1 + 2 = 3 1 - (-3 + 1) = 1 + 2 =...